caption stringlengths 0 5.16k | code stringlengths 99 1.67M | image imagewidth (px) 336 336 | uri stringlengths 21 93 | origin stringclasses 9 values | date timestamp[us] |
|---|---|---|---|---|---|
A typical pair production of two resonances A_1 and A_2 having masses m_A_1 and m_A_2 decaying semi-invisibly in a collider. p_i is a sum of momenta of the visible particles from the resonance A_i. q_i is a momentum of the invisible particle from the resonance A_i. A system having semi-invisibly decaying N resonances can be considered in a similar fashion. | \documentclass[11pt, a4paper]{article}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}
%incoming proton
\draw (-0.5,0.5) -- (-2,0.5);
\draw (-0.5,0.55) -- (-2,0.55);
\draw (-0.5,0.45) -- (-2,0.45);
\node[draw=none] at (-2.2,0.5) {$p$};
\draw (-0.5,-0.5) -- (-2,-0.5);
\draw (-0.5,-0.55) -- (-2,-0.55);
\draw (-0.5,-0.45) -- (-2,-0.45);
\node[draw=none] at (-2.2,-0.5) {$p$};
%ISR
\draw[->,>=latex] (-0.5,0.5) -- (0.5,1.5);
\draw[->,>=latex] (-0.5,-0.5) -- (0.5,-1.5);
%intermediate resonances
\draw (-1,0.5) -- (2,0.5);
\draw (-1,-0.5) -- (2,-0.5);
\node[draw=none] at (1.2,0.7) {$A_1$};
\node[draw=none] at (1.2,-0.7) {$A_2$};
%invisible final states
\draw[->,>=latex,dashed] (2,0.5) -- (4.7,0.5);
\draw[->,>=latex,dashed] (2,-0.5) -- (4.7,-0.5);
\node[draw=none] at (4.3,0.7) {$q_1$};
\node[draw=none] at (4.3,-0.7) {$q_2$};
%visible final states
\draw[->,>=latex] (2,0.5) -- (2.5,1.5);
\draw[->,>=latex] (2,-0.5) -- (2.5,-1.5);
\draw[->,>=latex] (2,0.5) -- (3.2,1.5);
\draw[->,>=latex] (2,-0.5) -- (3.2,-1.5);
%curly braces
\draw[decorate,decoration={brace,amplitude=3pt}]
(2.3, 1.6) --
(3.3, 1.6) ;
\draw[decorate,decoration={brace,amplitude=3pt,mirror}]
(2.3, -1.6) --
(3.3, -1.6) ;
\node[draw=none] at (2.8,1.9) {$p_1$};
\node[draw=none] at (2.8,-1.9) {$p_2$};
\node[draw=none] at (2.8,1.4) {$\cdots$};
\node[draw=none] at (2.8,-1.45) {$\cdots$};
%decay dots
\filldraw [color=black, fill=gray] (2,0.5) circle (0.1);
\filldraw [color=black, fill=gray] (2,-0.5) circle (0.1);
%upstream box
\node[draw=none] at (0.0,-2.5) {Upstream};
\draw[decorate,decoration={brace,amplitude=3pt,mirror}]
(-1, -2.1) --
(0.8,-2.1) ;
%first collision ellipse
\filldraw [color=black, fill=white] (-0.5,0) ellipse (0.3 and 1);
\draw[pattern=north west lines, pattern color=gray] (-0.5,0) ellipse (0.3 and 1);
%visible box
\node[draw=none] at (2.6,-2.5) {Visible};
\draw[decorate,decoration={brace,amplitude=3pt,mirror}]
(1.7, -2.1) --
(3.5,-2.1) ;
%invisible box
\node[draw=none] at (4.2,-2.5) {Invisible};
\draw[decorate,decoration={brace,amplitude=3pt,mirror}]
(3.7, -2.1) --
(4.7,-2.1) ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.01981 | arxiv | 2016-08-24T02:02:21 | |
Flow diagram of the bi-LSTM character sequence labeling model, unrolled for time, for the word pair jn -- ihn `him'. | \documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning}
\usepackage{pgfplots}
\pgfplotsset{compat=1.5}
\newcommand{\bos}{\_}
\newcommand{\eps}{$\epsilon$}
\begin{document}
\begin{tikzpicture}[scale=0.77,transform shape,>=stealth',auto]
\tikzset{state/.style={draw,rectangle,minimum height=1.7em,minimum width=3.5em,
inner xsep=1em,inner ysep=0.5em,text depth=0.15em},
emptystate/.style={inner sep=0.4em},
outer/.style={outer sep=0},
label/.style={align=center,font=\itshape\small}}
\node[emptystate] (I1) at (0, 0) {{\bos}};
\node[emptystate] (I2) at (2, 0) {{j}};
\node[emptystate] (I3) at (4, 0) {{n}};
\node[state] (M1) at (0, 1.2) {~};
\node[state] (M2) at (2, 1.2) {~};
\node[state] (M3) at (4, 1.2) {~};
\node[emptystate] (E0) at (-2, 2.7) {~};
\node[state] (E1) at (0, 2.7) {~};
\node[state] (E2) at (2, 2.7) {~};
\node[state] (E3) at (4, 2.7) {~};
\node[emptystate] (E4) at (6, 2.7) {~};
\node[emptystate] (F0) at (-2, 3.9) {~};
\node[state] (F1) at (0, 3.9) {~};
\node[state] (F2) at (2, 3.9) {~};
\node[state] (F3) at (4, 3.9) {~};
\node[emptystate] (F4) at (6, 3.9) {~};
\node[emptystate] (G0) at (-2, 5.1) {~};
\node[state] (G1) at (0, 5.1) {~};
\node[state] (G2) at (2, 5.1) {~};
\node[state] (G3) at (4, 5.1) {~};
\node[emptystate] (G4) at (6, 5.1) {~};
\node[state] (P1) at (0, 6.6) {~};
\node[state] (P2) at (2, 6.6) {~};
\node[state] (P3) at (4, 6.6) {~};
\node[emptystate] (O1) at (0, 7.8) {\eps};
\node[emptystate] (O2) at (2, 7.8) {ih};
\node[emptystate] (O3) at (4, 7.8) {n};
\node[emptystate] (L1) at (-4.0, 1.2) {\emph{embedding layer}};
\node[emptystate] (L2) at (-4.0, 4.1) {\emph{stack of}};
\node[emptystate] (L3) at (-4.0, 3.5) {\emph{bi-LSTM layers}};
\node[emptystate] (L4) at (-4.0, 6.6) {\emph{prediction layer}};
\draw [->] (I1) to (M1);
\draw [->] (I2) to (M2);
\draw [->] (I3) to (M3);
\draw [->] (M1) to (E1);
\draw [->] (M2) to (E2);
\draw [->] (M3) to (E3);
\coordinate[above=0.15 of E4.west] (E4_tw);
\coordinate[above=0.15 of E3.east] (E3_te);
\coordinate[above=0.15 of E3.west] (E3_tw);
\coordinate[above=0.15 of E2.east] (E2_te);
\coordinate[above=0.15 of E2.west] (E2_tw);
\coordinate[above=0.15 of E1.east] (E1_te);
\coordinate[below=0.15 of E3.west] (E3_bw);
\coordinate[below=0.15 of E2.east] (E2_be);
\coordinate[below=0.15 of E2.west] (E2_bw);
\coordinate[below=0.15 of E1.east] (E1_be);
\coordinate[below=0.15 of E1.west] (E1_bw);
\coordinate[below=0.15 of E0.east] (E0_be);
\coordinate[above=0.15 of F4.west] (F4_tw);
\coordinate[above=0.15 of F3.east] (F3_te);
\coordinate[above=0.15 of F3.west] (F3_tw);
\coordinate[above=0.15 of F2.east] (F2_te);
\coordinate[above=0.15 of F2.west] (F2_tw);
\coordinate[above=0.15 of F1.east] (F1_te);
\coordinate[below=0.15 of F3.west] (F3_bw);
\coordinate[below=0.15 of F2.east] (F2_be);
\coordinate[below=0.15 of F2.west] (F2_bw);
\coordinate[below=0.15 of F1.east] (F1_be);
\coordinate[below=0.15 of F1.west] (F1_bw);
\coordinate[below=0.15 of F0.east] (F0_be);
\coordinate[above=0.15 of G4.west] (G4_tw);
\coordinate[above=0.15 of G3.east] (G3_te);
\coordinate[above=0.15 of G3.west] (G3_tw);
\coordinate[above=0.15 of G2.east] (G2_te);
\coordinate[above=0.15 of G2.west] (G2_tw);
\coordinate[above=0.15 of G1.east] (G1_te);
\coordinate[below=0.15 of G3.west] (G3_bw);
\coordinate[below=0.15 of G2.east] (G2_be);
\coordinate[below=0.15 of G2.west] (G2_bw);
\coordinate[below=0.15 of G1.east] (G1_be);
\coordinate[below=0.15 of G1.west] (G1_bw);
\coordinate[below=0.15 of G0.east] (G0_be);
\draw [densely dotted,->] (E4_tw) to (E3_te);
\draw [densely dotted,->] (E3_tw) to (E2_te);
\draw [densely dotted,->] (E2_tw) to (E1_te);
\draw [densely dotted,->] (E0_be) to (E1_bw);
\draw [densely dotted,->] (E1_be) to (E2_bw);
\draw [densely dotted,->] (E2_be) to (E3_bw);
\draw [->] (E1) to (F1);
\draw [->] (E2) to (F2);
\draw [->] (E3) to (F3);
\draw [densely dotted,->] (F4_tw) to (F3_te);
\draw [densely dotted,->] (F3_tw) to (F2_te);
\draw [densely dotted,->] (F2_tw) to (F1_te);
\draw [densely dotted,->] (F0_be) to (F1_bw);
\draw [densely dotted,->] (F1_be) to (F2_bw);
\draw [densely dotted,->] (F2_be) to (F3_bw);
\draw [->] (F1) to (G1);
\draw [->] (F2) to (G2);
\draw [->] (F3) to (G3);
\draw [densely dotted,->] (G4_tw) to (G3_te);
\draw [densely dotted,->] (G3_tw) to (G2_te);
\draw [densely dotted,->] (G2_tw) to (G1_te);
\draw [densely dotted,->] (G0_be) to (G1_bw);
\draw [densely dotted,->] (G1_be) to (G2_bw);
\draw [densely dotted,->] (G2_be) to (G3_bw);
\draw [->] (G1) to (P1);
\draw [->] (G2) to (P2);
\draw [->] (G3) to (P3);
\draw [->] (P1) to (O1);
\draw [->] (P2) to (O2);
\draw [->] (P3) to (O3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.07844 | arxiv | 2016-10-26T02:05:18 | |
RDF graph. | \documentclass[letterpaper,10pt]{paper}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\begin{scope}[auto, every node/.style={draw,circle,minimum size=2em,inner sep=1},node distance=2cm]
\def\margin {8}
\node[draw,circle](a) at (0,0) {\texttt{:a}};
\node[draw,circle](j) at (1.5,-2) {\texttt{:j}};
\node[draw,circle](b) at (3,0) {\texttt{:b}};
\node[draw,circle](c) at (6,0) {\texttt{:c}};
\node[draw,circle](k) at (6,-2) {\texttt{:k}};
\node[draw,circle](d) at (9,0) {\texttt{:d}};
\end{scope}
\begin{scope}[->,>=latex,semithick,shorten >=1pt, auto]
\draw(a) to node {{\small\texttt{:parent}}} (b);
\draw(b) to node {{\small\texttt{:parent}}} (c);
\draw(c) to node {{\small\texttt{:parent}}} (d);
\draw(a) to node[swap] {{\small\texttt{:country}}} (j);
\draw(b) to node {{\small\texttt{:country}}} (j);
\draw(c) to node {{\small\texttt{:country}}} (k);
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1606.01441 | arxiv | 2016-07-13T02:03:54 | |
An example for our localization terminology. Here we have 3 levels of localization with L_0 = 2, L_1 = 3 and L_2 = 5. The marked subproblem (in green) can be addressed by a tuple (1,1,3) where each index respectively denotes its position in the hierarchical structure. | \documentclass[format=acmsmall, review=false, screen=true]{acmart}
\usepackage{tikz}
\usetikzlibrary{shapes.misc, positioning}
\usetikzlibrary{fit}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[every node/.style={thick,rectangle,inner sep=0pt}]
\def\dx{1}
\def\a{0}
\def\recx{0.15}
\def\recy{0.75}
\node (a1) at (0 * \dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap1) at (0.25 * \dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap1) at (0.5 * \dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap1) at (0.75 * \dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (a2) at (1*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (a3) at (2*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap3) at (2.25*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap3) at (2.5*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap3) at (2.75*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (a4) at (3*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (a5) at (4*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap5) at (4.25*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap5) at (4.5*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap5) at (4.75*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (a6) at (5*\dx,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (a7) at (6*\dx + \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap7) at (6.25*\dx + \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap7) at (6.5*\dx + \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap7) at (6.75*\dx + \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (a8) at (7*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (a9) at (8*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap9) at (8.25*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap9) at (8.5*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (app9) at (8.75*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north, fill=green] {};
\node (a10) at (9*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\draw[->] (app9) -- (8.75*\dx + \a, -1.65);
\node (text) at (8.75*\dx + \a + 0.1, -1.75) {\scriptsize$(1,1,3)$};
\node (a11) at (10*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap11) at (10.25*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap11) at (10.5*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (ap11) at (10.75*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (a12) at (11*\dx+ \a,0) [draw, minimum width=\recx cm, minimum height=\recy cm, anchor=north] {};
\node (b1) [draw, minimum width=10*\recx cm, minimum height=2*\recy cm, anchor=north, label=$L_2$, fit = (a1)(a2), rounded corners=0.1cm] {};
\node (b2) [draw, minimum width=10*\recx cm, minimum height=2*\recy cm, anchor=north, label=$L_2$, fit = (a3)(a4), rounded corners=0.1cm] {};
\node (b3) [draw, minimum width=10*\recx cm, minimum height=2*\recy cm, anchor=north, label=$L_2$, fit = (a5)(a6), rounded corners=0.1cm] {};
\node (b4) [draw, minimum width=10*\recx cm, minimum height=2*\recy cm, anchor=north, label=$L_2$, fit = (a7)(a8), rounded corners=0.1cm] {};
\node (b5) [draw, minimum width=10*\recx cm, minimum height=2*\recy cm, anchor=north, label=$L_2$, fit = (a9)(a10), rounded corners=0.1cm] {};
\node (b6) [draw, minimum width=10*\recx cm, minimum height=2*\recy cm, anchor=north, label=$L_2$, fit = (a11)(a12), rounded corners=0.1cm] {};
\node (c1) [draw, minimum width=38*\recx cm, minimum height=3* \recy cm, anchor=north, label=$L_1$, fit = (b1)(b2)(b3), rounded corners=0.1cm] {};
\node (c2) [draw, minimum width=38*\recx cm, minimum height=3* \recy cm, anchor=north, label=$L_1$, fit = (b4)(b5)(b6), rounded corners=0.1cm] {};
\node (d1) [draw, minimum width=80*\recx cm, minimum height=4 * \recy cm, anchor=north, label=$L_0$, fit = (c1)(c2), rounded corners=0.1cm] {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.01189 | arxiv | 2017-01-06T02:01:45 | |
RDF graph. | \documentclass[letterpaper,10pt]{paper}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\begin{scope}[auto, every node/.style={draw,circle,minimum size=2em,inner sep=1},node distance=2cm]
\def\margin {8}
\node[draw,circle](a) at (0,0) {\texttt{:a}};
\node[draw,circle](b) at (3,0) {\texttt{:b}};
\node[draw,circle](c) at (6,0) {\texttt{:c}};
\node[draw,circle](d) at (9,0) {\texttt{:d}};
\node[draw,circle](e) at (0,-1) {\texttt{:e}};
\node[draw,circle](f) at (3,-1) {\texttt{:f}};
\node[draw,circle](g) at (6,-1) {\texttt{:g}};
\node[draw,circle](h) at (0,-2) {\texttt{:h}};
\node[draw,circle](i) at (3,-2) {\texttt{:i}};
\end{scope}
\begin{scope}[->,>=latex,semithick,shorten >=1pt, auto]
\draw(a) to node {{\small\texttt{:p}}} (b);
\draw(b) to node {{\small\texttt{:q}}} (c);
\draw(c) to node {{\small\texttt{:r}}} (d);
\draw(e) to node {{\small\texttt{:p}}} (f);
\draw(f) to node {{\small\texttt{:q}}} (g);
\draw(h) to node {{\small\texttt{:p}}} (i);
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1606.01441 | arxiv | 2016-07-13T02:03:54 | |
Universal Construction C(G) | \documentclass[11pt]{article}
\usepackage{amsmath, amsthm, amsfonts, amssymb}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{calc,positioning,fit,backgrounds}
\begin{document}
\begin{tikzpicture}[>=latex]
\tikzstyle{gate}=[rectangle, thick, fill=white, minimum size=0.5cm, draw, align=center]
\tikzstyle{dots}=[rectangle, fill=white, minimum size=0.5cm, align=center]
\newcommand{\gatewidth}{.8cm}
\newcommand{\wiresep}{.3cm}
\matrix[row sep=.3cm,column sep=.5cm] {
\coordinate(start1); \node[minimum width=\wiresep]{}; & & \node(TOP)[inner sep=0pt]{$\times$}; & & \node[minimum width=\wiresep]{}; \coordinate(end1); \\ [.3cm]
\coordinate(start2); & \node(GT)[minimum width=\gatewidth]{}; & \node(BOT)[inner sep=0pt]{$\times$}; & \node(GIT)[minimum width=\gatewidth]{}; & \coordinate(end2); \\
\coordinate(start3); & & & \node(GINV)[minimum width=1cm]{};& \coordinate(end3); \\
\node[dots]{$\vdots$}; & & \node[dots]{$\vdots$};& & \node[dots]{$\vdots$};\\
\coordinate(start4); & \node(GB)[minimum width=\gatewidth]{}; & &\node(GIB)[minimum width=\gatewidth]{}; & \coordinate(end4); \\
};
\node[gate, fit={(GT.west) (GB.east)}] {$G$};
\node[gate, fit={(GIT.west) (GIB.east)}] {$G^{-1}$};
% EDGES
\begin{pgfonlayer}{background}
\path[draw]
(start1) edge (end1)
(start2) edge (end2)
(start3) edge (end3)
(start4) edge (end4)
(TOP.center) edge (BOT.center);
\end{pgfonlayer}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.03999 | arxiv | 2016-11-23T02:02:27 | |
Each row of H belongs to a different bucket. Results from different subproblems in different levels are added together to form a lower level bucket count. This process is continued until reaching the first level where H is completed. | \documentclass[format=acmsmall, review=false, screen=true]{acmart}
\usepackage{tikz}
\usetikzlibrary{shapes.misc, positioning}
\usetikzlibrary{fit}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[every node/.style={thick,rectangle,inner sep=0pt}]
\def\recB{3.5}
\def\recX{3.5}
\def\recXX{3.5}
\def\recXXX{3.5}
\def\aXX{0.5}
\def\recY{0.5}
\def\midX{0.75}
\def \a {0.6}
\node (d1) at (0 * \recB, 1.5) [draw=black,rectangle,minimum width = \recB cm, minimum height = \recY cm] {\small$0$th row of $\mathbf{H}$};
\node (md1) [right=-1pt of d1, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (d2) [right=-1pt of md1,draw=black,rectangle,minimum width = \recB cm, minimum height = \recY cm] {\small$i$th row of $\mathbf{H}$};
\node (md2) [right=-1pt of d2, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (d3) [right=-1pt of md2,draw=black,rectangle,minimum width = \recB cm, minimum height = \recY cm] {\small($m-1$)th row of $\mathbf{H}$};
\node at (d1.north) [anchor=south] {$B_0$};
\node at (d2.north) [anchor=south] {$B_i$};
\node at (d3.north) [anchor=south] {$B_{m-1}$};
\node (a1) at (0 * \recX + \aXX, 0) [draw=black,rectangle,minimum width = \recX cm, minimum height = \recY cm] {$h_{i, (0, \ast, \dots, \ast)}$};
\node (m1) [right=-1pt of a1, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (a2) [right=-1pt of m1,draw=black,rectangle,minimum width = \recX cm, minimum height = \recY cm] {$h_{i, (\ell_0, \ast, \dots, \ast)}$};
\node (m2) [right=-1pt of a2, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (a3) [right=-1pt of m2,draw=black,rectangle,minimum width = \recX cm, minimum height = \recY cm] {$h_{i, (L_{0} - 1, \ast, \dots, \ast)}$};
\node (sum1) [below=8pt of a2] {\large$\sum$};
\node at (a1.north) [anchor=south] {$H_{i,0}$};
\node at (a2.north) [anchor=south] {$H_{i,\ell_0}$};
\node at (a3.north) [anchor=south] {$H_{i, L_0-1}$};
\node (b1) at (0 * \recXX + 2*\aXX, -1.5) [draw=black,rectangle,minimum width = \recXX cm, minimum height = \recY cm] {$h_{i, (\ell_0, 0, \ast, \dots, \ast)}$};
\node (mb1) [right=-1pt of b1, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (b2) [right=-1pt of mb1,draw=black,rectangle,minimum width = \recXX cm, minimum height = \recY cm] {$h_{i, (\ell_0, \ell_1, \ast, \dots, \ast)}$};
\node (mb2) [right=-1pt of b2, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (b3) [right=-1pt of mb2,draw=black,rectangle,minimum width = \recXX cm, minimum height = \recY cm] {$h_{i, (\ell_0, L_{1} - 1, \ast, \dots, \ast)}$};
\node (sum2) [below=8pt of b2] {\large$\sum$};
\draw [thick, black, dashed] (a2.south west) -- (b1.north west);
\draw [thick, black, dashed] (a2.south east) -- (b3.north east);
\node (c1) at (0 * \recXXX + 3*\aXX, -3) [draw=black,rectangle,minimum width = \recXXX cm, minimum height = \recY cm] {$h_{i, (\ell_0, \ell_1, 0, \ast, \dots, \ast)}$};
\node (mc1) [right=-1pt of c1, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (c2) [right=-1pt of mc1,draw=black,rectangle,minimum width = \recXXX cm, minimum height = \recY cm] {$h_{i, (\ell_0, \ell_1, \ell_2,\ast, \dots, \ast)}$};
\node (mc2) [right=-1pt of c2, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (c3) [right=-1pt of mc2,draw=black,rectangle,minimum width = \recXXX cm, minimum height = \recY cm] {$h_{i, (\ell_0, \ell_1, L_{2} - 1, \ast, \dots, \ast)}$};
\draw [thick, black, dashed] (b2.south west) -- (c1.north west);
\draw [thick, black, dashed] (b2.south east) -- (c3.north east);
\draw [thick, black, dashed] (d2.south west) -- (a1.north west);
\draw [thick, black, dashed] (d2.south east) -- (a3.north east);
\node (dots1) [below=4pt of c2] {\large$\ddots$};
\node (e1) at (0 * \recXXX + 4*\aXX, -4.5) [draw=black,rectangle,minimum width = \recXXX cm, minimum height = \recY cm] {$h_{i, (\ell_0, \ell_1, \dots, 0)}$};
\node (me1) [right=-1pt of e1, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (e2) [right=-1pt of me1,draw=black,rectangle,minimum width = \recXXX cm, minimum height = \recY cm] {$h_{i, (\ell_0, \ell_1, \dots, \ell_{\lambda-1})}$};
\node (me2) [right=-1pt of e2, draw=black,rectangle,minimum width = \midX cm, minimum height = \recY cm] {$\dots$};
\node (e3) [right=-1pt of me2,draw=black,rectangle,minimum width = \recXXX cm, minimum height = \recY cm] {$h_{i, (\ell_0, \ell_1, \dots, L_{\lambda-1})}$};
\node (sum3) [below=12pt of e2,draw,circle, inner sep=3pt]{\large $6$};
\def\inputKeys{{"*","i","*","*","i","i","*","*","i","*","*","i","*","*","i","*"}}
\def\localOffset{{"*","0","*","*","1","2","*","*","3","*","*","4","*","*","5","*"}}
\node (A) at (0 * \recXXX + 4*\aXX, -6.5) [minimum height = \recY cm] {\text{buckets }};
\node (l) [below=0pt of A, minimum height = \recY cm] {\small\text{local offset }};
\foreach \x in {0,...,15}{
\node (A) [right=-1pt of A, draw=black,rectangle,minimum width = \a cm, minimum height = \recY cm] {$\pgfmathparse{\inputKeys[\x]}\pgfmathresult$};
\node (l) [below=6pt of A] {$\pgfmathparse{\localOffset[\x]}\pgfmathresult$};
\ifthenelse{\x=1 \OR \x=4 \OR \x=5 \OR \x=8 \OR \x=11 \OR \x=14}{\draw(A.north)--(sum3);}{}
}
\draw [thick,black] (sum3.north) -- (e2.south);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.01189 | arxiv | 2017-01-06T02:01:45 | |
Decomposition of the lattice in the definitions of local approximate quantum error correction. B shields A from C by a distance at least , and R represents the purifying space of the code. | \documentclass[pra,aps,floatfix,superscriptaddress,11pt,tightenlines,longbibliography,onecolumn,notitlepage]{revtex4-1}
\usepackage{amsmath, amsfonts, amssymb, amsthm, braket, bbm, xcolor}
\usepackage{tikz}
\usepackage[pdftex,colorlinks=true,linkcolor=darkblue,citecolor=darkred,urlcolor=blue]{hyperref}
\begin{document}
\begin{tikzpicture}
% rectangles
\draw[shift={(.5,-.5)}] (-3.2,-2) rectangle (3.2,2);
\draw[fill=white] (-3.2,-2) rectangle (3.2,2);
% circles
\draw (0,0) circle (1);
\draw (0,0) circle (1.5);
% labels
\node at (0,0) {$A$};
\node at (.88,.88) {$B$};
\node at (2.6,1.4) {$C$};
\node[below right] at (3.2,-2) {$R$};
% arrow
\draw[<->] (1,0) -- (1.5,0);
\node[below, align=center] at (1.25,0) {$\ell$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.06169 | arxiv | 2016-10-20T02:08:59 | |
Construction of the largest correctable square by successively adding rings of size at most d. | \documentclass[pra,aps,floatfix,superscriptaddress,11pt,tightenlines,longbibliography,onecolumn,notitlepage]{revtex4-1}
\usepackage{amsmath, amsfonts, amssymb, amsthm, braket, bbm, xcolor}
\usepackage{tikz}
\usepackage[pdftex,colorlinks=true,linkcolor=darkblue,citecolor=darkred,urlcolor=blue]{hyperref}
\begin{document}
\begin{tikzpicture}
\def\rr{.38} % r step size
% main rectangles
\draw[shift={(.5,-.5)}] (-3.2,-2) rectangle (3.2,2);
\draw[fill=white] (-3.2,-2) rectangle (3.2,2);
% nested rectangles
\foreach \r in {1,...,4} {
\draw (-.1-\r*\rr,-.1-\r*\rr) rectangle (.1+\r*\rr,.1+\r*\rr);
}
% node labels
\node at (0,0) {$A_0$};
\node[anchor=south west] at (.2+\rr/2,.05+\rr/2) {${}_{B_1}$};
\node[anchor=south west] at (.2+3*\rr/2,.05+2*\rr/2) {${}_{B_2}$};
\node[anchor=south west] at (.2+5*\rr/2,.05+3*\rr/2) {${}_{B_3}$};
\node[anchor=south east] at (3.2,-2) {$C$};
% reference
\node[below right] at (3.2,-2) {$R$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.06169 | arxiv | 2016-10-20T02:08:59 | |
Decomposition of the lattice used for Theorem~thm:logical-operator-tradeoff. | \documentclass[pra,aps,floatfix,superscriptaddress,11pt,tightenlines,longbibliography,onecolumn,notitlepage]{revtex4-1}
\usepackage{amsmath, amsfonts, amssymb, amsthm, braket, bbm, xcolor}
\usepackage{tikz}
\usepackage[pdftex,colorlinks=true,linkcolor=darkblue,citecolor=darkred,urlcolor=blue]{hyperref}
\begin{document}
\begin{tikzpicture}
% choose fill colors
[a/.style ={fill=white},
b/.style ={fill=black!90!white},
c/.style ={fill=black!20!white}]
\def\xx{6.4/5} % x step size
\def\yy{4/3} % y step size
% rectangles
\draw[shift={(.5,-.5)}] (-.1*\xx,-.1*\yy) rectangle (6.4+.1*\xx,4+.1*\yy);
\draw[a] (-.1*\xx,-.1*\yy) rectangle (6.4+.1*\xx,4+.1*\yy);
% shaded grid
\foreach \x in {0,...,4} {
\foreach \y in {0,1,2}
\draw[shift={(\x*\xx,\y*\yy)},c] (.1*\xx,+.1*\yy) rectangle (.9*\xx,.9*\yy);
}
% labels
\node at (\xx/2,5*\yy/2) {$X$};
\node[below right] at (6.4+.1*\xx,-.1*\yy) {$R$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.06169 | arxiv | 2016-10-20T02:08:59 | |
Decomposition of the lattice in 2D used to define flexible logical operators. The diameter of the disk Z is . | \documentclass[pra,aps,floatfix,superscriptaddress,11pt,tightenlines,longbibliography,onecolumn,notitlepage]{revtex4-1}
\usepackage{amsmath, amsfonts, amssymb, amsthm, braket, bbm, xcolor}
\usepackage{tikz}
\usepackage[pdftex,colorlinks=true,linkcolor=darkblue,citecolor=darkred,urlcolor=blue]{hyperref}
\begin{document}
\begin{tikzpicture}
% choose fill colors
[a/.style ={fill=white},
b/.style ={fill=black!90!white},
c/.style ={fill=black!20!white}]
\def\xx{1.5} % x step size
\def\yy{1.5} % y step size
% rectangles
\draw[shift={(.5,-.5)}] (0,0) rectangle (2*\xx, 2*\yy);
\draw[b] (0,0) rectangle (2*\xx, 2*\yy);
% shaded grid
\draw[shift={(0*\xx,1*\yy)}, a] (0,0) rectangle (\xx,\yy);
\draw[shift={(1*\xx,0*\yy)}, a] (0,0) rectangle (\xx,\yy);
% c region
\draw[shift={(1*\xx,1*\yy)},c] (0,0) circle (.25*\xx);
\draw[c] (0,0) -- (.25*\xx,0) arc [start angle=0, end angle=90, radius=.25*\xx] -- (0,0);
\draw[c] (2*\xx,0) -- (1.75*\xx,0) arc [start angle=180, end angle=90, radius=.25*\xx] -- (2*\xx,0);
\draw[c] (0,2*\yy) -- (.25*\xx,2*\yy) arc [start angle=0, end angle=-90, radius=.25*\xx] -- (0,2*\yy);
\draw[c] (2*\xx,2*\yy) -- (1.75*\xx,2*\yy) arc [start angle=180, end angle=270, radius=.25*\xx] -- (2*\xx,2*\yy);
\draw[c] (.75*\xx,0) arc [start angle=180, end angle=0, radius=.25*\xx] -- (.75*\xx,0);
\draw[c] (0,1.25*\yy) arc [start angle=90, end angle=-90, radius=.25*\xx] -- (0,.75*\yy); \draw[c] (2*\xx,.75*\yy) arc [start angle=270, end angle=90, radius=.25*\xx] -- (2*\xx,1.25*\yy);
\draw[c] (1.25*\xx,2*\yy) arc [start angle=0, end angle=-180, radius=.25*\xx] -- (.75*\xx,2*\yy);
% labels
\node at (\xx/2, 1.5*\yy) {$X$};
\node[color=white] at (0.5*\xx, 0.5*\yy) {$Y$};
\node at (\xx,\yy) {$Z$};
\node[below right] at (2*\xx,0) {$R$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.06169 | arxiv | 2016-10-20T02:08:59 | |
Decomposition of the lattice in 2D leading to the tradeoff bound of Theorem thm:ABPT. | \documentclass[pra,aps,floatfix,superscriptaddress,11pt,tightenlines,longbibliography,onecolumn,notitlepage]{revtex4-1}
\usepackage{amsmath, amsfonts, amssymb, amsthm, braket, bbm, xcolor}
\usepackage{tikz}
\usepackage[pdftex,colorlinks=true,linkcolor=darkblue,citecolor=darkred,urlcolor=blue]{hyperref}
\begin{document}
\begin{tikzpicture}
% choose fill colors
[a/.style ={fill=white},
b/.style ={fill=black!90!white},
c/.style ={fill=black!20!white}]
\def\xx{6.4/5} % x step size
\def\yy{4/3} % y step size
% rectangles
\draw[shift={(.5,-.5)}] (0,0) rectangle (6.4,4);
\draw[b] (0,0) rectangle (6.4,4);
% shaded grid
\foreach \x in {0,2,4} {
\foreach \y in {0,2}
\draw[shift={(\x*\xx,\y*\yy)},a] (0,0) rectangle (\xx,\yy);
}
\draw[shift={(1*\xx,\yy)},a] (0,0) rectangle (\xx,\yy);
\draw[shift={(3*\xx,\yy)},a] (0,0) rectangle (\xx,\yy);
% c region
\foreach \x in {1,2,3,4} {
\foreach \y in {1,2}
\draw[shift={(\x*\xx,\y*\yy)},c] (0,0) circle (.25cm);
}
% labels
\node at (\xx/2,5*\yy/2) {$X$};
\node[color=white] at (\xx/2,3*\yy/2) {$Y$};
\node at (\xx,\yy) {$Z$};
\node[below right] at (6.4,0) {$R$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.06169 | arxiv | 2016-10-20T02:08:59 | |
Starting from _0 = 1_\{0\}, following the arrows, if U_1^0 < _2_1 and U_2^0 < _2_1, the wild population occupies at time t the set H_t = \{-1,0,1\} in the asymmetric case and the set H_t=\{-2,-1,0,1\} in the symmetric case. | \documentclass[reqno,12pt]{amsart}
\usepackage{amsmath,amssymb}
\usepackage{mathtools,multicol,enumitem,tikz,caption}
\begin{document}
\begin{tikzpicture}
\draw[help lines,line width=2pt,step=2,draw=black] (-4,0) to (6,0);
\draw[help lines,line width=1pt,step=2,draw=black] (-4,8) to (6,8);
\draw[help lines,line width=0.5pt,step=2,draw=black] (-3,0) to (-3,8);
\draw[help lines,line width=0.5pt,step=2,draw=black] (-1,0) to (-1,8);
\draw[help lines,line width=0.5pt,step=2,draw=black] (1,0) to (1,8);
\draw[help lines,line width=0.5pt,step=2,draw=black] (3,0) to (3,8);
\draw[help lines,line width=0.5pt,step=2,draw=black] (5,0) to (5,8);
\node[anchor=north] at (-3,0) {-2};
\node[anchor=north] at (-1,0) {-1};
\node[anchor=north] at (1,0) {0};
\node[anchor=north] at (3,0) {1};
\node[anchor=north] at (5,0) {2};
\draw[->,line width=1pt,black] (-1,1)--(1,1) node [midway,above] {};
\draw[->,line width=1pt,black] (3,3)--(5,3) node [midway,above] {};
\draw[->,line width=1pt,black] (-1,5)--(-3,5) node [midway,above] {};
\draw[->,line width=1pt,black] (3,5)--(1,5) node [midway,above] {};
\draw[->,line width=1pt,black] (1,4)--(-1,4) node [midway,above] {};
\draw[->,line width=1pt,black] (-1,7)--(1,7) node [midway,above] {};
\draw[->,line width=1pt,black] (1,6)--(3,6) node [midway,above] {};
\filldraw[fill=white,draw=black] (-1,6) circle [radius=2pt];
\node at (3,4) {$\mathbin{\tikz [x=1.4ex,y=1.4ex,line width=.2ex,black] \draw (0,0) -- (1,1) (0,1) -- (1,0);}$};
\filldraw[fill=white,draw=black] (5,7) circle [radius=2pt];
\node at (-3,1) {$\mathbin{\tikz [x=1.4ex,y=1.4ex,line width=.2ex,black] \draw (0,0) -- (1,1) (0,1) -- (1,0);}$};
\draw[fill,black] (1,2) circle [radius=2pt];
\draw[fill,black] (5,1) circle [radius=2pt];
\draw[fill,black] (-3,4) circle [radius=2pt];
\draw[help lines,line width=1pt,step=2,draw=black] (-3,4) to (-3,8);
\draw[help lines,line width=1pt,step=2,draw=black] (1,2) to (1,8);
\draw[help lines,line width=1pt,step=2,draw=black] (5,1) to (5,7);
\draw [->,line width=1pt] (-5,0) -- (-5,8.5);
\node at (-5.8,9) {$\mbox{time}$};
\draw[help lines,line width=1pt,step=2,draw=black] (-5.2,0) to (-4.8,0);
\draw[help lines,line width=1pt,step=2,draw=black] (-5.2,8) to (-4.8,8);
\node at (-5.4,8) {$t$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1501.00921 | arxiv | 2015-08-27T02:01:22 | |
Random environment on vertices | \documentclass[reqno,12pt]{amsart}
\usepackage{amsmath,amssymb}
\usepackage{mathtools,multicol,enumitem,tikz,caption}
\begin{document}
\begin{tikzpicture} [domain=0:10, scale=0.6, baseline=0, >=stealth]
\node (0) at (-4,0) [draw, circle={4pt}]{$k-2$};
\node (1) at (0,0) [draw, circle={4pt}]{$k-1$};
\node (2) at (4,0) [draw, circle={4pt}]{$ \ \ k \ \ $};
\node (3) at (8,0) [draw, circle={4pt}]{$k+1$};
\node (4) at (12,0) [draw, circle={4pt}]{$k+2$};
\draw[-,thick]
(0) edge [] node [below] {} (1)
(1) edge [] node [below] {} (2)
(2) edge [] node [below] {} (3)
(3) edge [] node [below] {} (4)
(0) edge [bend left=45] node [sloped, anchor=left,above=0.2cm] {} (1);
\draw[dotted] (13.5,0) -- (14,0);
\draw[dotted] (-6,0) -- (-5.5,0);
\draw[->,thick]
(3) edge [bend left=45] node [above] {$\lambda_v(k+1)$} (4)
(4) edge [bend left=45] node [below] {$\lambda_v(k+2)$} (3)
(2) edge [bend left=45] node [above] {$\lambda_v(k)$} (3)
(3) edge [bend left=45] node [below] {$\lambda_v(k+1)$} (2)
(1) edge [bend left=45] node [above] {$\lambda_v(k-1)$} (2)
(2) edge [bend left=45] node [below] {$\lambda_v(k)$} (1)
(0) edge [bend left=45] node [above] {$\lambda_v(k-2)$} (1)
(1) edge [bend left=45, below] node [below] {$\lambda_v(k-1)$} (0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1501.00921 | arxiv | 2015-08-27T02:01:22 | |
Random environment on oriented edges | \documentclass[reqno,12pt]{amsart}
\usepackage{amsmath,amssymb}
\usepackage{mathtools,multicol,enumitem,tikz,caption}
\begin{document}
\begin{tikzpicture} [domain=0:10, scale=0.6, baseline=0, >=stealth]
\node (0) at (-4,0) [draw, circle={4pt}]{$k-2$};
\node (1) at (0,0) [draw, circle={4pt}]{$k-1$};
\node (2) at (4,0) [draw, circle={4pt}]{$ \ \ k \ \ $};
\node (3) at (8,0) [draw, circle={4pt}]{$k+1$};
\node (4) at (12,0) [draw, circle={4pt}]{$k+2$};
\draw[-,thick]
(0) edge [] node [below] {} (1)
(1) edge [] node [below] {} (2)
(2) edge [] node [below] {} (3)
(3) edge [] node [below] {} (4)
(0) edge [bend left=45] node [sloped, anchor=left,above=0.2cm] {} (1);
\draw[dotted] (13.5,0) -- (14,0);
\draw[dotted] (-6,0) -- (-5.5,0);
\draw[->,thick]
(3) edge [bend left=45] node [above] {$\lambda_e(k+2)$} (4)
(4) edge [bend left=45] node [below] {$\rho_e(k+1)$} (3)
(2) edge [bend left=45] node [above] {$\lambda_e(k+1)$} (3)
(3) edge [bend left=45] node [below] {$\rho_e(k)$} (2)
(1) edge [bend left=45] node [above] {$\lambda_e(k)$} (2)
(2) edge [bend left=45] node [below] {$\rho_e(k-1)$} (1)
(0) edge [bend left=45] node [above] {$\lambda_e(k-1)$} (1)
(1) edge [bend left=45, below] node [below] {$\rho_e(k-2)$} (0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1501.00921 | arxiv | 2015-08-27T02:01:22 | |
Good partial embeddings form embeddings when restricted to the mapped vertices x,x' and guarantee sizes and regularity for the underlying restriction sets of unmapped vertices y,y',z. The thick lines are edges of G, the wavy lines of , and the hatched areas represent regular pairs in G. | \documentclass[a4paper,reqno,oneside,final]{amsbook}
\usepackage{amsmath,amsfonts,amssymb,amsthm,mathrsfs}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\tikzset{snake it/.style={decorate, decoration={snake,segment length=1.5mm,amplitude=0.5mm}}}
\usetikzlibrary{patterns}
\usepackage[colorlinks,bookmarks,linkcolor=black,citecolor=black]{hyperref}
\begin{document}
\begin{tikzpicture}
\tikzstyle{every node}=[draw,circle,fill=black,minimum size=4pt,
inner sep=0pt]
\node at (-3,-0.5) (x) [label=left:$x$] {} ;
\node at (-3,1.5) (xp) [label=left:$x'$] {} ;
\node at (1,0.75) (y) [label=above left:$y$] {} ;
\node at (1,-1.75) (yp) [label=below left:$y'$] {} ;
\node at (5,0.75) (z) [label=right:$z$] {} ;
\draw (xp)--(x)--(yp)--(y) ;
\draw (x)--(y)--(z) ;
\node at (-3,4) (psx) [label=left:$\psi(x)$] {} ;
\node at (-3,6) (psxp) [label=left:$\psi(x')$] {} ;
\tikzstyle{every node}=[draw=none,fill=none]
\draw[line width=1pt] (psx)--(psxp) ;
\draw (1,2.75) ellipse (1.5cm and 0.75cm) ;
\draw[line width=1pt] (1,2.75) ellipse (0.65cm and 0.3cm) ;
\path[draw] (psx) edge [snake it] node {} (1-1.418*0.75,2.75+1.418*0.375) ;
\path[draw] (psx) edge [line width=1pt,bend right] node {} (0.35,2.75) ;
\draw (1,5.25) ellipse (1.5cm and 0.75cm) ;
\draw[line width=1pt] (1,5.25) ellipse (0.65cm and 0.3cm) ;
\path[draw] (psx) edge [snake it] node {} (1-1.418*0.75,5.25-1.418*0.375) ;
\path[draw] (psx) edge [line width=1pt,bend left] node {} (0.35,5.25) ;
\draw (5,5.25) ellipse (1.5cm and 0.75cm) ;
\draw[line width=1pt] (5,5.25) ellipse (0.65cm and 0.3cm) ;
\filldraw[pattern=north east lines] (2.5,5.25)--(2.6,5.45)--(3.4,5.45)--(3.5,5.25)--(3.4,5.05)--(2.6,5.05)--(2.5,5.25) ;
\filldraw[pattern=north east lines] (1,3.5)--(1.2,3.6)--(1.2,4.4)--(1,4.5)--(0.8,4.4)--(0.8,3.6)--(1,3.5) ;
\node at (-4.5,0.5) {$H$} ;
\node at (-4.5,5) {$G\subset\Gamma$} ;
\node[fill=white] at (2,2.15) {$U(y')$} ;
\node[fill=white] at (2,5.85) {$U(y)$} ;
\node[fill=white] at (6,5.85) {$U(z)$} ;
\node at (1,2.75) {$C(y')$} ;
\node at (1,5.25) {$C(y)$} ;
\node at (5,5.25) {$C(z)$} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1612.00622 | arxiv | 2016-12-06T02:12:07 | |
A retraction from a self-map | \documentclass{amsart}
\usepackage{mathpartir,mathtools,amsmath,amssymb,phonetic,aliascnt,ifmtarg,enumitem,scalefnt}
\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[>=stealth]
\draw (0,0) circle (2);
\node[circle,fill,inner sep=1pt,label=below:$f(z)$] (fz) at (-1,-.5) {};
\node[circle,fill,inner sep=1pt,label=$r(z)$] (rz) at (0,2) {};
\node[circle,fill,inner sep=1pt,label=left:$z$] (z) at ($(fz)!0.3!(rz)$) {};
\draw[->] (fz) -- (rz);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1509.07584 | arxiv | 2017-04-26T02:05:12 | |
Timings of three Poisson segmentation algorithms on simulated data sets of varying size B. The grey shaded area represents the range of problem sizes selected in the McGill benchmark data sets. | \documentclass{article}
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\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] (335.75, 98.90) circle ( 2.13);
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\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.85] at (222.03,122.42) {cDPA $O(B^2)$};
\definecolor[named]{drawColor}{rgb}{0.97,0.46,0.43}
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.85] at (222.03, 99.86) {pDPA $O(B\log B)$};
\definecolor[named]{drawColor}{rgb}{0.38,0.61,1.00}
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.85] at (189.39, 77.83) {PeakSegJoint $O(B\log B)$};
\definecolor[named]{drawColor}{rgb}{0.50,0.50,0.50}
\path[draw=drawColor,line width= 0.6pt,line join=round,line cap=round] ( 51.05, 33.22) rectangle (349.30,132.50);
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (361.35,144.54);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.96] at ( 43.93, 49.27) {1e-03};
\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.96] at ( 43.93, 85.73) {1e-01};
\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.96] at ( 43.93,122.19) {1e+01};
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (361.35,144.54);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\path[draw=drawColor,line width= 0.6pt,line join=round] ( 46.78, 52.39) --
( 51.05, 52.39);
\path[draw=drawColor,line width= 0.6pt,line join=round] ( 46.78, 88.86) --
( 51.05, 88.86);
\path[draw=drawColor,line width= 0.6pt,line join=round] ( 46.78,125.32) --
( 51.05,125.32);
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (361.35,144.54);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\path[draw=drawColor,line width= 0.6pt,line join=round] (118.83, 28.95) --
(118.83, 33.22);
\path[draw=drawColor,line width= 0.6pt,line join=round] (227.29, 28.95) --
(227.29, 33.22);
\path[draw=drawColor,line width= 0.6pt,line join=round] (335.75, 28.95) --
(335.75, 33.22);
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (361.35,144.54);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.96] at (118.83, 19.86) {1e+02};
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.96] at (227.29, 19.86) {1e+04};
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.96] at (335.75, 19.86) {1e+06};
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (361.35,144.54);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.20] at (200.18, 9.03) {data size to segment $B$};
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (361.35,144.54);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\node[text=drawColor,rotate= 90.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.20] at ( 16.85, 82.86) {seconds};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1506.01286 | arxiv | 2015-06-04T02:11:44 | |
Type 1 incoherent FFL composed of p53, miR-34a and MDM2 | \documentclass[12pt]{article}
\usepackage[]{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[ ->,>=stealth']
\path (2,5) node (p53) {p53};
\path (2,3) node (miR-34a) {miR-34a};
\path (2,1) node (MDM2) {MDM2};
\draw[thick, ->] (p53) -- (miR-34a);
\draw[thick, -|] (miR-34a) -- (MDM2);
\draw[thick] (p53) -- (1,5) -- (1,1) -- (MDM2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1608.02756 | arxiv | 2016-08-11T02:05:08 | |
Graphic model of transferred factorisation machines. | \documentclass{llncs}
\usepackage{amsmath,amssymb,amscd,epsfig,amsfonts,rotating}
\usepackage{xcolor, colortbl}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{fit}
\newcommand{\bs}{\boldsymbol}
\newcommand{\tweb}{\text{c}}
\newcommand{\td}{\text{d}}
\newcommand{\tads}{\text{r}}
\begin{document}
\begin{tikzpicture}[->,>=stealth',scale=0.6]
\node at (-1.8,-1.9) [circle] {$\bs{\mu}_{\bs{V}^\tweb},\sigma_{\bs{V}^\tweb}^2 \bs{I}$};
\node at (-4.3,-1.9) [circle] {$\mu_{\bs{w}^\tweb},\sigma_{\bs{w}^\tweb}^2$};
\node at (-2,-2) [circle] (uvl) {};
\node at (-4,-2) [circle] (uwl) {};
\node at (-2,-4) [circle,draw] (Vl) {$\bs{v}^{\tweb}_i$};
\node at (-4,-4) [circle,draw] (wl) {$w^{\tweb}_i$};
\node at (-1.2,-6) [circle,draw] (xl) {$\bs{x}^{\tweb}$};
\node at (-4,-8) [circle,draw] (w0l) {$w_0^{\tweb}$};
\node at (-2,-8) [circle,draw] (yl) {$y^{\tweb}$};
\node at (4,-1.9) [circle] {$\sigma_{\bs{V}^{\td}}^2 \bs{I}$};
\node at (2,-1.9) [circle] {$\sigma_{\bs{w}^\td}^2$};
\node at (9.3,-1.9) [circle] {$\mu_{\bs{w}^{\tads,a}},\sigma_{\bs{w}^{\tads,a}}^2$};
\node at (6.3,-1.9) [circle] {$\bs{\mu}_{\bs{V}^{\tads,a}},\sigma_{\bs{V}^{\tads,a}}^2\bs{I}$};
\node at (4,-2) [circle] (uvr) {};
\node at (2,-2) [circle] (uwr) {};
\node at (8.8,-2) [circle] (uwa) {};
\node at (6,-2) [circle] (uVa) {};
\node at (4,-4) [circle,draw] (Vr) {$\bs{v}^{\tads}_i$};
\node at (2,-4) [circle,draw] (wr) {$w^{\tads}_i$};
\node at (8.8,-6) [circle,draw] (wa) {$w^{\tads,a}_l$};
\node at (6,-4) [circle,draw] (Va) {$\bs{v}^{\tads,a}_l$};
\node at (4,-6) [circle,draw] (xr) {$\bs{x}^{\tads}$};
\node at (6,-6) [circle,draw] (xa) {$\bs{x}^{\tads,a}$};
\node at (2,-8) [circle,draw] (w0r) {$w_0^{\tads}$};
\node at (4,-8) [circle,draw] (yr) {$y^{\tads}$};
\path[every node/.style={font=\sffamily\small}]
(uvl) edge (Vl)
(uwl) edge (wl)
(uvr) edge (Vr)
(uwr) edge (wr)
(uwa) edge (wa)
(uVa) edge (Va)
(Vl) edge [bend left=45] (Vr)
edge (yl)
(wl) edge [bend left=45] (wr)
edge (yl)
(xl) edge (yl)
(w0l)edge (yl)
(Vr) edge [bend right=25] (yr)
(wr) edge (yr)
(wa) edge (yr)
(Va) edge (yr)
(xr) edge (yr)
(xa) edge (yr)
(w0r)edge (yr)
;
\draw (-0.5,-5.1) rectangle (-3,-9);
\draw (-0.3,-3) rectangle (-5,-7);
\draw (3,-5.1) rectangle (7,-9);
\draw (0.3,-3) rectangle (4.9,-7);
\draw (10,-3) rectangle (5.1,-7);
\node at(-4,-6.7) [circle] {$I^{\tweb} + J^{\tweb}$};
\node at(-0.8,-8.7) [circle] {$|D^{\tweb}|~~$};
\node at(1.1,-6.7) [circle] {$I^{\tads} +J^{\tads}$};
\node at(9.6,-6.7) [circle] {$L^{\tads}$};
\node at(6.7,-8.7) [circle] {$|D^{\tads}|~~$};
\node at(5.7,-9.4) [circle] {CTR Task};
\node at(-1.8,-9.4) [circle] {CF Task};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1601.02377 | arxiv | 2016-01-12T02:12:11 | |
The graph G=g_3(G_1,G_2) | \documentclass[12pt]{article}
\usepackage{amsmath,pgf,tikz,tkz-graph}
\usetikzlibrary{arrows}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[scale=1]
\renewcommand*{\VertexSmallMinSize}{1.5pt}
\renewcommand*{\VertexInnerSep}{1.5pt}
\GraphInit[vstyle=Classic]
\Vertex[x=1, y=5,Lpos=90,Math,L=u_1]{A}
\Vertex[x=-1.85, y=0.01,Lpos=180,Math,L=u_3]{B}
\Vertex[x=3.87, y=0.01,Lpos=0,Math,L=v_3]{C}
\Vertex[x=-0.43, y=2.5,Lpos=0,Math,L=u_2]{D}
\Vertex[x=2.44, y=2.5,Lpos=180,Math,L=v_2]{E}
\tikzset{VertexStyle/.append style={fill=white}}
\Vertex[x=1, y=1.68,Lpos=-90,Math,L=z]{H}
\Edges(A,E)
\Edges(C,B)
\Edges(D,A)
\Edges(D,H,E)
\Edge(H)(A)
\tikzset{EdgeStyle/.style = {-,bend left=80,color=gray}}
\Edge(A)(C)
\tikzset{EdgeStyle/.style = {-,bend right=80,color=gray}}
\Edge(A)(B)
\draw [dash pattern=on 3pt off 3pt] (E)-- (C);
\draw [dash pattern=on 3pt off 3pt] (B)-- (D);
\draw (3.5,2.5) node{$G_2$};
\draw (-1.5,2.5) node{$G_1$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1508.07526 | arxiv | 2015-09-03T02:09:55 | |
The graph G=G_1 G_2 G_3 G_4 G_5 | \documentclass[12pt]{article}
\usepackage{amsmath,pgf,tikz,tkz-graph}
\usetikzlibrary{arrows}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[scale=0.6]
\renewcommand*{\VertexSmallMinSize}{1.pt}
\renewcommand*{\VertexInnerSep}{1.pt}
\GraphInit[vstyle=Classic]
\Vertex[x=8.02, y=4.18,Lpos=90,Math,L=u_1]{u_1}
\Vertex[x=5, y=2,Lpos=180,Math]{v_1}
\Vertex[x=6.51, y=3.09,Lpos=0,Math]{u_2}
\Vertex[x=6.14, y=-1.54,Lpos=-90,Math]{w_1}
\Vertex[x=9.86, y=-1.55,Lpos=-45,,Ldist=-3pt,Math]{x_1}
\Vertex[x=11.04, y=1.97,Math]{y_1}
\Vertex[x=5.57, y=0.23,Lpos=87.5,Ldist=-1pt,Math]{v_2}
\Vertex[x=8, y=-1.55,Lpos=45,Ldist=-3pt,Math]{w_2}
\Vertex[x=10.45, y=0.21,Lpos=95,Math]{x_2}
\Vertex[x=9.52, y=3.08,Lpos=-90,Math]{y_2}
\Vertex[x=8.01, y=1.01,Ldist=-1pt,Lpos=90,Math]{z}
\Edges(u_2,v_1)
\Edges(v_2,w_1)
\Edges(w_2,x_1)
\Edges(x_2,y_1)
\Edges(y_2,u_1)
\Edges(z,u_2)
\Edges(z,v_2)
\Edges(z,w_2)
\Edges(z,x_2)
\Edges(z,y_2)
\AddVertexColor{white}{z}
\draw [dash pattern=on 3pt off 3pt] (u_1)-- (u_2);
\draw [dash pattern=on 3pt off 3pt] (v_1)-- (v_2);
\draw [dash pattern=on 3pt off 3pt] (w_1)-- (w_2);
\draw [dash pattern=on 3pt off 3pt] (x_1)-- (x_2);
\draw [dash pattern=on 3pt off 3pt] (y_1)-- (y_2);
\draw (u_1) .. controls (11,5) .. (y_1);
\draw (u_1) .. controls (5,5) .. (v_1);
\draw (v_1) .. controls (3,-1) .. (w_1);
\draw (w_1) .. controls (8,-4) .. (x_1);
\draw (x_1) .. controls (13,-1) .. (y_1);
\draw (6,4) node{$G_1$};
\draw (4.44,-0.36) node{$G_2$};
\draw (8,-3) node{$G_3$};
\draw (11.84,-0.32) node{$G_4$};
\draw (10,4) node{$G_5$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1508.07526 | arxiv | 2015-09-03T02:09:55 | |
An undirected graph representing interpersonal ties (edges) between users (nodes). | \documentclass[runningheads,a4paper]{llncs}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{chains,positioning,scopes}
\usepackage{xcolor}
\begin{document}
\begin{tikzpicture}[every node/.style={circle}, node distance=20mm, >=latex]
\node[](b) at (0,2)[draw,fill,label=left: $a$] {};
\node[](a) at (0,0)[draw,fill,label=left: $b$] {};
\node[](c) at (1,1)[draw,fill,label=below:$c$] {};
\node[](d) at (2,1)[draw,fill,label=below:$d$] {};
\node[](e) at (3,1)[draw,fill,label=below:$e$] {};
\node[](g) at (4,2)[draw,fill,label=right:$f$] {};
\node[](f) at (4,0)[draw,fill,label=right:$g$] {};
\draw[-] (a) to node {}(c);
\draw[-] (b) to node {}(c);
\draw[-] (c) to node {}(d);
\draw[-] (d) to node {}(e);
\draw[-] (e) to node {}(f);
\draw[-] (e) to node {}(g);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1508.07951 | arxiv | 2016-04-26T02:09:38 | |
A simple graph | \documentclass{elsarticle}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{amssymb}
\usepackage{colortbl}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\tikzstyle{noeud}=[draw, circle, minimum height=0.55cm, minimum
width=0.55cm, inner sep=0pt]
\node[noeud] (A) at (-2, 2) {$a$};
\node[noeud] (B) at (-2, 0) {$b$};
\node[noeud] (C) at (0, 2) {$c$};
\node[noeud] (D) at (0, 0) {$d$};
\node[noeud] (E) at (1, 1) {$e$};
\node[noeud] (F) at (-1, -1) {$f$};
\draw[-, >=stealth ] (A) -> (C);
\draw[-, >=stealth ] (A) -> (D);
\draw[-, >=stealth ] (A) -> (B);
\draw[-, >=stealth ] (D) -> (B);
\draw[-, >=stealth ] (F) -> (B);
\draw[-, >=stealth ] (D) -> (E);
\draw[-, >=stealth ] (C) -> (E);
\draw[-, >=stealth ] (F) to[bend right=45] (E);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.02726 | arxiv | 2016-09-12T02:03:19 | |
IDEAL characterization of local isometry classes of regular FLRW spacetimes (Theorem~thm_FLRW_class, Table~tab_FLRW_class). | \documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows}
\usepackage[colorlinks=true,linkcolor=blue,citecolor=red,urlcolor=Violet,bookmarksdepth=subsection,final]{hyperref}
\newcommand{\FLRW}{\mathit{FLRW}}
\newcommand{\CSC}{\mathit{CSC}}
\begin{document}
\begin{tikzpicture}[auto]
\node[rectangle, draw,
text centered, minimum height=24pt](init){$(M,g), \; \dim M = m+1$};
%%
\node[signal, signal to=east and west, draw, text centered, node distance=1.2cm, below of=init](Ricci){$(\nabla\mathcal{R})^2 < 0$};
%%
\node[signal, signal to=east and west, draw, text centered, node distance= 1.2cm, below of=Ricci](Ricci2){$(\nabla\mathcal{B})^2 < 0$};
\node[signal, signal to=east and west, draw, text centered, node distance= 3.3cm, right of=Ricci2](CCCdesitter){$R - \frac{k}{2} (g\odot g)= 0$};
\node[node distance=1.6cm, right of=CCCdesitter](pointright){};
\node[node distance=1.6cm, left of=CCCdesitter](pointleft){};
\node[node distance=1.7cm, left of=Ricci2](pointleftright){};
\node[node distance=4.9cm, left of=Ricci2](pointleftleft){};
%%
\node[rectangle, draw, text width=6em, text centered, minimum height=24pt, below of=pointright, node distance= 1.2cm](Desitter){ $CC_K^m$};
%%
\node[rectangle, draw, text width=7em, text centered, minimum height=24pt, below of=Ricci2, node distance= 1.5cm](UB){$U:= U_{\mathcal{B}}$};
\node[rectangle, draw, text width=7em, text centered, minimum height=24pt, left of=UB, node distance= 3.5cm](UR){ $U:= U_{\mathcal{R}}$};
\node[signal, signal to=east and west, draw, text centered, node distance=3cm, text width=13em, below of=CCCdesitter](ifESU){$W_{ijkh} = 0 $\\
$R_i^j \left(R_{jk} - (m-1) K g_{jk}\right) = 0 $ \\
$\mathcal{R} - m (m-1) K = 0$ \\
$\nabla_i R_{jk} = 0$ };
%%
\node[signal, signal to=east and west, draw, text centered, node distance=4.3cm, below of=UB](main){$\zeta=0$};
\node[rectangle, draw, text width=4em, text centered, minimum height=24pt, below of=main, node distance= 3cm](nothing){not FLRW};
\node[rectangle, draw, text width=6em, text centered, minimum height=24pt, below of=pointright, node distance= 4.8cm](ESU){$ESU_K^m$};
\node[rectangle, draw, text width=4em, text centered, minimum height=24pt, below of=pointleft, node distance= 4.8cm](nothing2){not FLRW};
%%
\node[signal, signal to=east and west, draw, text width=10em, text centered, node distance=6cm, below of=UR](constant){$\mathfrak{P}_{ij} = 0, \quad \mathfrak{D}_{ij} = 0$\\ $\mathfrak{Z}_{ijkh} =0$ };
\node[signal, signal to=east and west, draw, text width=10em, text centered, node distance=4.5cm, below of=ifESU](PD){$\mathfrak{C}_{ijkh}=0$\\ $\nabla_i U_j - \frac{\nabla_i \zeta}{2\zeta}U_j = \xi g_{ij}$};
%%
\node[signal, signal to=east and west, draw, text width=10em, text centered, node distance=2.7cm, below of=constant](FLRW){$\eta=-\kappa P(\xi^2)$\\ $\xi\in J$};
\node[signal, signal to=east and west, draw, text width=10em, text centered, node distance=1.3cm, below of=FLRW](FLRW-P){$\kappa P(u) = \frac{(m+1)}{2} (u-K)$};
\node[signal, signal to=east and west, draw, text width=10em, text centered, node distance=2.7cm, below of=PD](PD2){$\xi^2+ \zeta= \kappa E(\zeta)$\\ $\zeta\in J$};
\node[signal, signal to=east and west, draw, text width=10em, text centered, node distance=1.3cm, below of=PD2](PD2-E){$\kappa E(u) = K + \Omega |u|^{\frac{m+1}{2}}$};
%%
\node[rectangle, draw, text width=6em, text centered, minimum height=24pt, below of=pointleftleft, node distance= 12.7cm](flatFLRW){$\FLRW^{m,0}_{P,J}$ };
\node[rectangle, draw, text width=6em, text centered, minimum height=24pt, below of=pointleftright, node distance= 12.7cm](flatFLRW-J){$\CSC^{m,0}_{K,J}$ };
\node[rectangle, draw, text width=6em, text centered, minimum height=24pt, below of=pointleft, node distance= 12.7cm](genFLRW){$\FLRW^m_{E,J}$ };
\node[rectangle, draw, text width=6em, text centered, minimum height=24pt, below of=pointright, node distance= 12.7cm](genFLRW-J){$\CSC^m_{K,\Omega,J}$ };
%%%%%% paths %%%%%%
\path[draw, -latex'] (init)--(Ricci);
%%
\path[draw, -latex'] (Ricci)--node {no}(Ricci2);
\path[draw, -latex'] (Ricci2)--node {no}(CCCdesitter);
%%
\path[draw, -latex'] (CCCdesitter)--node [pos=.8]{yes}(Desitter);
\path[draw, -latex'] (CCCdesitter)--node {no}(ifESU);
%%
\path[draw, -latex'] (Ricci)-|node[pos=.2] {yes}(UR);
\path[draw, -latex'] (Ricci2)--node {yes}(UB);
%%
\path[draw, -latex'] (UR)|-(main);
\path[draw, -latex'] (UB)--(main);
%%
\path[draw, -latex'] (PD)--node {no}(nothing);
\path[draw, -latex'] (constant)--node [swap]{no}(nothing);
\path[draw, -latex'] (ifESU)--node[left] {no} (nothing2);
\path[draw, -latex'] (ifESU)--node[pos=1] {yes}(ESU);
\path[draw, -latex'] (main)--node [swap]{yes}(constant);
\path[draw, -latex'] (main)--node {no}(PD);
\path[draw, -latex'] (PD)--node {yes}(PD2);
\path[draw, -latex'] (constant)--node {yes}(FLRW);
%%
\path[draw, -latex'] (PD2)--node [swap]{no}(nothing);
\path[draw, -latex'] (PD2)--node {yes}(PD2-E);
\path[draw, -latex'] (PD2-E)--node[pos=.8] {yes}(genFLRW-J);
\path[draw, -latex'] (PD2-E)--node [left]{no}(genFLRW);
\path[draw, -latex'] (FLRW)--node {no}(nothing);
\path[draw, -latex'] (FLRW)--node {yes}(FLRW-P);
\path[draw, -latex'] (FLRW-P)--node[pos=.8] {yes}(flatFLRW-J);
\path[draw, -latex'] (FLRW-P)--node [left]{no}(flatFLRW);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.05542 | arxiv | 2017-05-24T02:02:55 | |
Pair Hidden Markov model as proposed by Mackay \& Kondrak MackayKondrak2005. The states of the model are depicted as the circles. The arrows show the possible transitions between the states. <, , , _M, _XY> represent the transition probabilities. | \documentclass[11pt,a4paper]{article}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage[utf8]{inputenc}
\usetikzlibrary{arrows,automata,shapes}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=3cm,
semithick, scale=0.8, every node/.style={transform shape}]
\tikzstyle{every state}=[fill=none,draw=black,text=black, align=center]
\node[state] (A) {\textbf{M}\\[-0.7em]$p_{o_{i}o'_{j}}$};
\node[state] (B) [above right of=A] {\textbf{X}\\[-0.7em]$q_{o_i}$};
\node[state] (C) [below right of=A] {\textbf{Y}\\[-0.7em]$q_{o'_j}$};
\node[state] (D) [left of=A, node distance = 3.7cm, label={[xshift = -10mm,
yshift=-6mm]\textbf{Begin}}, scale=0.55, ultra thick] { };
\node[state] (E) [right of=A, node distance = 4.7 cm, label={[xshift = 9mm,
yshift=-5.5mm]\textbf{End}}, scale=0.55, ultra thick] { };
\node (dummy2) [below left of = C, node distance=2.7cm, xshift=10mm] {};
\path (A) edge [bend right] node[pos=0.3] {\footnotesize{$\delta$}} (B)
edge [bend left ] node[below, pos=0.3] {\footnotesize{$\delta$}} (C)
edge node[pos=0.85]{\footnotesize{$\tau_M$}} (E)
edge [loop left] node[below, yshift=-2mm]{\footnotesize{$1\!-\!2\delta\!-\!\tau_M$}} (A)
(B) edge [loop above] node {\footnotesize{$\epsilon$}} (B)
edge [bend left] node[xshift=-3mm] {\footnotesize{$\tau_{XY}$}} (E)
edge [bend right] node[above, pos=0.45,
xshift=-8mm]{\footnotesize{$1\!-\!\epsilon\!-\!\lambda\!-\!\tau_{XY}$}} (A)
edge [bend left, dashed] node[pos=0.75, right]{\footnotesize{$\lambda$}} (C)
(C) edge [bend right] node[xshift=3mm] {\footnotesize{$\tau_{XY}$}} (E)
edge [loop below] node {\footnotesize{$\epsilon$}} (C)
edge [bend left, dashed] node[pos=0.85, left]{\footnotesize{$\lambda$}} (B)
edge [bend left] node[above, pos=0.65,
xshift=-13mm]{\footnotesize{$1\!-\!\epsilon\!-\!\lambda\!-\!\tau_{XY}$}} (A)
(D) edge [bend left = 50] node {\footnotesize{$\delta$}} (B)
edge [bend left] node[pos=0.55] {\footnotesize{$1\!-\!2\delta\!-\!\tau_M$}}
(A)
edge [bend right] node[below]{\footnotesize{$\delta$}} (C);
% (E);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.04938 | arxiv | 2017-02-17T02:04:17 | |
E_P() for GL_3 when M_0=A. | \documentclass[11pt, a4paper]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.6,every node/.style={scale=0.8}]
\draw (0.75,-1.3)--(-0.25,-1.3);
\draw (0.75,-1.3)--(1.25,-0.4);
\draw (1.25,-0.4)--(0.25,1.3);
\draw (0.25,1.3)--(-0.75,1.3);
\draw (-0.75,1.3)--(-1.25,0.4);
\draw (-1.25,0.4)--(-0.25,-1.3);
\draw (4.75,-8.1)--(9.25,-0.4);
\draw (9.25,-0.4)--(4.25,8.1);
\draw (4.25,8.1)--(-4.75,8.1);
\draw (-4.75,8.1)--(-9.25,0.4);
\draw (-9.25,0.4)--(-4.25,-8.1);
\draw (-4.25,-8.1)--(4.75,-8.1);
\draw [blue] (5.25,-7.25)--(4.25,-5.55);
\draw [blue] (4.25,-5.55)--(-4.75,-5.55);
\draw [blue] (-4.75,-5.55)--(-5.25,-6.4);
\draw [red] (3.75,-8.1)--(2.75,-6.4);
\draw [red] (2.75,-6.4)--(7.25,1.25);
\draw [red] (7.25,1.25)--(8.25,1.25);
\draw [blue] (8.75,-1.25)--(7.75,-1.25);
\draw [blue] (7.75,-1.25)--(2.75,7.25);
\draw [blue] (2.75,7.25)--(3.25,8.1);
\draw [red] (5.25,6.4)--(4.75,5.55);
\draw [red] (4.75,5.55)--(-4.25,5.55);
\draw [red] (-4.25,5.55)--(-5.25,7.25);
\draw [blue] (-3.75,8.1)--(-2.75,6.4);
\draw [blue] (-2.75,6.4)--(-7.25,-1.25);
\draw [blue] (-7.25,-1.25)--(-8.25,-1.25);
\draw [red] (-8.75,1.25)--(-7.75,1.25);
\draw [red] (-7.75,1.25)--(-2.75,-7.25);
\draw [red] (-2.75,-7.25)--(-3.25,-8.1);
\node [blue] at (4, 6.8) {$E_{B_{0}}(\Pi)$};
\node [blue] at (0, 6.8) {$E_{P_{1}}(\Pi)$};
\node [blue] at (6,3.6) {$E_{P_{2}}(\Pi)$};
\node [blue] at (0,0) {$\Sigma_{\gamma}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.03202 | arxiv | 2017-01-13T02:02:18 | |
Partition of a_A^G for GL_3. | \documentclass[11pt, a4paper]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.6]
\draw (-2.5,3.17)--(0.5,3.17);
\draw (-4,0.57)--(-1.5,-3.75);
\draw (1.5,-3.75)--(3,-1.15);
\draw (-4,0.57)--(-2.5,3.17);
\draw (-1.5,-3.75)--(1.5,-3.75);
\draw (0.5,3.17)--(3,-1.15);
\draw [red] (-2.5,3.17)--(-2.5, 5.17);
\draw [red] (0.5,3.17)--(0.5, 5.17);
\draw [red] (-1.5,-3.75)--(-1.5, -5.75);
\draw [red] (1.5,-3.75)--(1.5, -5.75);
\draw [red] (-4.23,4.17)--(-2.5,3.17);
\draw [red] (2.23,4.17)--(0.5,3.17);
\draw [red] (-4,0.57)--(-5.75, 1.57);
\draw [red] (-4,0.57)--(-5.75, -0.43);
\draw [red] (-1.5,-3.75)--(-3.23,-4.75);
\draw [red] (1.5,-3.75)--(3.23,-4.75);
\draw [red] (4.73,0.15)--(3,-1.15);
\draw [red] (4.73,-2.15)--(3,-1.15);
\node [blue] at (-2.5, -5.5) {$R_{B^{-}}$};
\node [blue] at (-4.5, -2.6) {$R_{P^{-}}$};
\node [blue] at (3,2) {$R_{P}$};
\node [blue] at (1.4,4.6) {$R_{B}$};
\node [blue] at (0,0) {$D_{0}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.03202 | arxiv | 2017-01-13T02:02:18 | |
Arthur-Kottwitz reduction when applying A__\{3\}^G,M_\{3\}. | \documentclass[11pt, a4paper]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[every node/.style={scale=0.8}]
\draw (4.75,-1.25)--(-4.25,-1.25);
\draw (-4.25,-1.25)--(-5.25,0.45);
\draw (-5.25,0.45)--(-4.75,1.3);
\draw (-4.75,1.3)--(4.25,1.3);
\draw (4.25,1.3)--(5.25,-0.4);
\draw (5.25,-0.4)--(4.75,-1.25);
\draw (3.25,1.3)--(4.25,-0.4);
\draw (4.25,-0.4)--(3.75,-1.25);
\draw [red] (3.3,1.35)--(3.3,3.05);
\draw [red] (3.3,1.35)--(4.8,2.2);
\draw [red] (4.33,-0.4)--(5.83,0.45);
\draw [red] (4.33,-0.4)--(5.83,-1.25);
\draw [red] (3.8,-1.3)--(5.3,-2.15);
\draw [red] (3.8,-1.3)--(3.8,-3);
\draw [red] (3.8,-1.3)--(4.33,-0.4);
\draw [red] (3.3,1.35)--(4.33,-0.4);
\node [blue] at (0, 0) {$\left(A_{\alpha_{\{3\}}}^{G,M_{\{3\}}}\right)^{a}(F_{\gamma})$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.03202 | arxiv | 2017-01-13T02:02:18 | |
Complete the hexagon to a triangle. | \documentclass[11pt, a4paper]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[node distance = 2cm, scale=0.6]
\draw (-5.5, 3.17)--(5.5,3.17);
\draw (-5.5, 3.17)--(0,-6.35);
\draw (0,-6.35)--(5.5,3.17);
\draw (-4,0.57)--(-2.5,3.17);
\draw (-1.5,-3.75)--(1.5,-3.75);
\draw (0.5,3.17)--(3,-1.15);
\node [blue] at (-0.5,0) {$\Pi_{0}$};
\node [blue] at (-4, 2.3) {$T_{1}$};
\node [blue] at (3.5, 1.8) {$T_{2}$};
\node [blue] at (0, -4.7){$T_{3}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.03202 | arxiv | 2017-01-13T02:02:18 | |
Counting points in the non-equivalued case. | \documentclass[11pt, a4paper]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.6, every node/.style={scale=0.7}]
\draw (5.18,3)--(-5.18,3);
\draw (-5.18,3)--(0,-6);
\draw (0,-6)--(5.18,3);
\draw [dashed] (-1.15,-4)--(2.3,-2);
\draw [dashed] (-3.74,0.5)--(0.58,3);
\draw [red] (-4.03,1)--(4.03,1);
\draw [red] (-1.15,-4)--(2.88,3);
\draw [blue] (-1.73,1)--(0,-2);
\draw [blue] (4.6,2)--(4.03,3);
\draw [blue] (-1.15,2)--(2.3,2);
\draw [blue] (0.58,-3)--(2.88,1);
\node [blue] at (0.58,3.5) {$(1,n,0)$};
\node [black] at (0.58,3) {$\bullet$};
\node [blue] at (-5.18,3.5) {$(-2m, 2m+n+1,0)$};
\node [black] at (-5.18,3) {$\bullet$};
\node [blue] at (0,-6.5) {$(-2m,0, 2m+n+1)$};
\node [black] at (0,-6) {$\bullet$};
\node [blue] at (3.7,-2) {$(0,0,n+1)$};
\node [black] at (2.3,-2) {$\bullet$};
\node [blue] at (6.5,3.5) {$(n+1,0,0)$};
\node [black] at (5.18,3) {$\bullet$};
\node [red] at (-6.5,1) {$(-2m,m+n+1,m)$};
\node [red] at (-4.03,1) {$\bullet$};
\node [red] at (6,1) {$(n+1-m,0,m)$};
\node [red] at (4.03,1) {$\bullet$};
\node [red] at (3,3.5) {$(n+1-m,m,0)$};
\node [red] at (2.88,3) {$\bullet$};
\node [red] at (-3.5,-4) {$(-2m,m,m+n+1)$};
\node [red] at (-1.15,-4) {$\bullet$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.03202 | arxiv | 2017-01-13T02:02:18 | |
Counting points in the equivalued case. | \documentclass[11pt, a4paper]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.5, every node/.style={scale=0.7}]
\draw [dashed] (-4.03,-0.33)--(2.88,3.67);
\draw [dashed] (-2.01,-3.83)--(4.03,-0.33);
\draw (6.33,3.67)--(-6.33,3.67);
\draw (-6.33,3.67)--(0,-7.33);
\draw (0,-7.33)--(6.33,3.67);
\draw [red] (-4.03,-0.33)--(4.03,-0.33);
\draw [red] (-1.73,-4.33)--(2.88,3.67);
\draw [blue] (-1.73,-0.33)--(-0.58,-2.33);
\draw [blue] (1.73,-0.33)--(0.58,-2.33);
\draw [blue] (4.03,3.67)--(5.18,1.67);
\draw [blue] (-0.58,1.67)--(1.73,1.67);
\node [blue] at (2.88,4.2) {$(1,n,0)$};
\node [black] at (2.88,3.67) {$\bullet$};
\node [blue] at (-6.33,4.2) {$(-(2n+1), 3n+2,0)$};
\node [black] at (-6.33,3.67) {$\bullet$};
\node [blue] at (0,-8) {$(-(2n+1),0, 3n+2)$};
\node [black] at (0,-7.33) {$\bullet$};
\node [blue] at (6,-0.33) {$(0,0,n+1)$};
\node [black] at (4.03,-0.33) {$\bullet$};
\node [blue] at (6.33,4.2) {$(n+1,0,0)$};
\node [black] at (6.33,3.67) {$\bullet$};
\node [red] at (-7.5,-0.33) {$(-(2n+1),2n+1,n+1)$};
\node [red] at (-4.03,-0.33) {$\bullet$};
\node [red] at (-5,-4.33) {$(-(2n+1),n,2(n+1))$};
\node [red] at (-1.73,-4.33) {$\bullet$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.03202 | arxiv | 2017-01-13T02:02:18 | |
The (G,A)-orthogonal family _n_1,n_2 and its extension to a triangle. | \documentclass[11pt, a4paper]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.6, every node/.style={scale=0.7}]
\draw [dashed] (-0.58,3)--(5.18,3);
\draw [dashed] (2.3,-2)--(5.18,3);
\draw (-0.58,3)--(-5.18,3);
\draw (-5.18,3)--(0,-6);
\draw (0,-6)--(2.3,-2);
\draw (2.3,-2)--(-0.58,3);
\node [blue] at (-0.58,3.5) {$(0,n_{2},0)$};
\node [black] at (-0.58,3) {$\bullet$};
\node [blue] at (-5.18,3.5) {$(-n_{1}, n_{1}+n_{2},0)$};
\node [black] at (-5.18,3) {$\bullet$};
\node [blue] at (0,-6.5) {$(-n_{1},0, n_{1}+n_{2})$};
\node [black] at (0,-6) {$\bullet$};
\node [blue] at (3.7,-2) {$(0,0,n_{2})$};
\node [black] at (2.3,-2) {$\bullet$};
\node [blue] at (5.18,3.5) {$(n_{2},0,0)$};
\node [black] at (5.18,3) {$\bullet$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.03202 | arxiv | 2017-01-13T02:02:18 | |
Counting points for ramified anisotropic gl_3(O)-second case. | \documentclass[11pt, a4paper]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.5, every node/.style={scale=0.7}]
\draw [dashed] (-6.93,-4)--(6.93,4);
\draw [dashed] (0,-8)--(0,8);
\draw [dashed] (-6.93,4)--(6.93,-4);
\node [blue] at (0,0,0){$(0,0,0)$};
\draw (-5.75,8)--(-5.75,-10);
\draw (-5.75,-10)--(9.78,-1);
\draw (9.78,-1)--(10.35,0);
\draw (-5.18,9)--(10.35,0);
\draw (-5.18,9)--(10.35,0);
\draw (-5.18,9)--(-5.75,8);
\draw (-5.18,9)--(-5.18,-9);
\draw (-5.18,-9)--(10.35,0);
\draw (0,6)--(-5.2,3);
\draw (-5.2,-3)--(0,-6);
\draw (5.2,-3)--(5.2,3);
\draw (-0.58,6.33)--(-5.18,3.67);
\draw (-5.18,-3.67)--(-0.58,-6.33);
\draw (5.75,2.67)--(5.75,-2.67);
\node [blue] at (-5, 9.5) {$(0,n_{2},-n_{2})$};
\node [black] at (-5.18, 9) {$\bullet$};
\node [blue] at (-8, 8) {$(-1,n_{2},-n_{2}+1)$};
\node [black] at (-5.75, 8) {$\bullet$};
\node [blue] at (-5.75,-10.5) {$(-n_{2}-1,0,n_{2}+1)$};
\node [black] at (-5.75,-10) {$\bullet$};
\node [blue] at (-5,-9.5) {$(-n_{2},0,n_{2})$};
\node [black] at (-5.18,-9) {$\bullet$};
\node [blue] at (12,-1) {$(n_{2}-1,-n_{2},1)$};
\node [black] at (9.78,-1) {$\bullet$};
\node [blue] at (12,0) {$(n_{2},-n_{2},0)$};
\node [black] at (10.35,0) {$\bullet$};
\node [blue] at (2.5,3.5) {$q^{2(a_{1}-a_{3})}$};
\node [black] at (1.73, 3) {$\bullet$};
\node [blue] at (-2.5,-3.5) {$q^{2(a_{3}-a_{1})-3}$};
\node [black] at (-1.73, -3) {$\bullet$};
\node [blue] at (-2.5,3.5) {$q^{2(a_{2}-a_{3})-1}$};
\node [black] at (-1.73, 3) {$\bullet$};
\node [blue] at (2.5,-3.5) {$q^{2(a_{3}-a_{2})-2}$};
\node [black] at (1.73, -3) {$\bullet$};
\node [blue] at (3,0.5) {$q^{2(a_{1}-a_{2})-1}$};
\node [black] at (3.45, 0) {$\bullet$};
\node [blue] at (-3.5,0.5) {$q^{2(a_{2}-a_{1})-2}$};
\node [black] at (-3.45, 0) {$\bullet$};
\node [blue] at (8,0.5) {$q^{a_{1}-a_{2}+n_{2}}$};
\node [black] at (8.05,0) {$\bullet$};
\node [blue] at (-3.8,6.5) {$q^{a_{2}-a_{3}+n_{2}}$};
\node [black] at (-4.03,7) {$\bullet$};
\node [blue] at (-3.5,-6.5) {$q^{a_{3}-a_{1}+n_{2}-1}$};
\node [black] at (-4.03,-7) {$\bullet$};
\node [blue] at (-1,-8.5) {$q^{a_{3}-a_{1}+n_{2}-1}$};
\node [black] at (-2.3,-8) {$\bullet$};
\node [blue] at (4,-5) {$q^{2n_{2}}$};
\node [black] at (2.88,-5) {$\bullet$};
\node [blue] at (9.5,-2) {$q^{a_{1}-a_{2}+n_{2}}$};
\node [black] at (8.05,-2) {$\bullet$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.03202 | arxiv | 2017-01-13T02:02:18 | |
Counting points for ramified anisotropic gl_3(O)-first case. | \documentclass[11pt, a4paper]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm, amssymb, amscd}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.5, every node/.style={scale=0.7}]
\draw [dashed] (-6.93,-4)--(6.93,4);
\draw [dashed] (0,-8)--(0,8);
\draw [dashed] (-6.93,4)--(6.93,-4);
\node [blue] at (0,0,0){$(0,0,0)$};
\draw (5.2,-9)--(5.2,9);
\draw (-10.4,0)--(5.2,9);
\draw (-10.4,0)--(5.2,-9);
\draw (-10.4,0)--(-9.8,-1);
\draw (4.05,-9)--(-9.8,-1);
\draw (4.05,-9)--(5.2,-9);
\draw (0,6)--(5.2,3);
\draw (5.2,-3)--(0,-6);
\draw (-5.2,-3)--(-5.2,3);
\node [blue] at (5.2, 10) {$(n_{1},0,-n_{1})$};
\node [black] at (5.2, 9) {$\bullet$};
\node [blue] at (7.2, -9) {$(0,-n_{1},n_{1})$};
\node [black] at (5.2, -9) {$\bullet$};
\node [blue] at (4.05, -10) {$(-1,1-n_{1},n_{1})$};
\node [black] at (4.05, -9) {$\bullet$};
\node [blue] at (-12.5,0) {$(-n_{1},n_{1},0)$};
\node [black] at (-10.4,0) {$\bullet$};
\node [blue] at (-11.5,-1.5) {$(-n_{1},n_{1}-1,1)$};
\node [black] at (-9.8,-1) {$\bullet$};
\node [blue] at (2.5,3.5) {$q^{2(a_{1}-a_{3})}$};
\node [black] at (1.73, 3) {$\bullet$};
\node [blue] at (-2.5,-3.5) {$q^{2(a_{3}-a_{1})-3}$};
\node [black] at (-1.73, -3) {$\bullet$};
\node [blue] at (-2.5,3.5) {$q^{2(a_{2}-a_{3})-1}$};
\node [black] at (-1.73, 3) {$\bullet$};
\node [blue] at (2.5,-3.5) {$q^{2(a_{3}-a_{2})-2}$};
\node [black] at (1.73, -3) {$\bullet$};
\node [blue] at (3,0.5) {$q^{2(a_{1}-a_{2})-1}$};
\node [black] at (3.45, 0) {$\bullet$};
\node [blue] at (-3.5,0.5) {$q^{2(a_{2}-a_{1})-2}$};
\node [black] at (-3.45, 0) {$\bullet$};
\node [blue] at (3.46,6.5) {$q^{a_{1}-a_{3}+n_{1}}$};
\node [black] at (3.46, 6) {$\bullet$};
\node [blue] at (3.46,-6.5) {$q^{a_{3}-a_{2}+n_{1}-1}$};
\node [black] at (3.46, -6) {$\bullet$};
\node [blue] at (-6.9,0.5) {$q^{a_{2}-a_{1}+n_{1}-1}$};
\node [black] at (-6.9,0) {$\bullet$};
\node [blue] at (-9,-2.5) {$q^{a_{2}-a_{1}+n_{1}-1}$};
\node [black] at (-8.05,-2) {$\bullet$};
\node [blue] at (-4,-5.5) {$q^{2(a_{3}-a_{1})-3}$};
\node [black] at (-2.88,-5) {$\bullet$};
\node [blue] at (1.3, -8.5) {$q^{a_{3}-a_{2}+n_{1}-1}$};
\node [black] at (2.3,-8) {$\bullet$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.03202 | arxiv | 2017-01-13T02:02:18 | |
PSNR for Lena images depending on the choice of k' and the quantity of noise | \documentclass[a4paper,11pt]{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[utf8]{inputenc}
\begin{document}
\begin{tikzpicture}[scale=.2]
\draw[thin] (0,0) node[left] {\tiny$10$} -- (50,0);
\draw[thin] (0,5) node[left] {\tiny$15$};
\draw[thin] (0,10) node[left] {\tiny$20$};
\draw[thin] (0,15) node[left] {\tiny$25$} ;
\draw[thin] (0,20) node[left] {\tiny$30$};
\draw[thin] (0,25) node[left] {\tiny$35$} -- (50,25);
\draw[thin,black!50] (0,5) -- (50,5);
\draw[thin,black!50] (0,10) -- (50,10);
\draw[thin,black!50] (0,15) -- (50,15);
\draw[thin,black!50] (0,20) -- (50,20);
\draw[thin] (0,-.2) node[below] {\tiny$0\%$} -- (0,25);
\draw[thin] (10,-.2) node[below] {\tiny$10\%$} -- (10,.2);
\draw[thin] (20,-.2) node[below] {\tiny$20\%$} -- (20,.2);
\draw[thin] (30,-.2) node[below] {\tiny$30\%$} -- (30,.2);
\draw[thin] (40,-.2) node[below] {\tiny$40\%$} -- (40,.2);
\draw[thin] (50,-.2) node[below] {\tiny$50\%$} -- (50,25);
% Median
\draw[thick,red] (0,21.35) -- (10,20.38) -- (20,18.21) -- (30,13.37) -- (40,6.45) -- (50,1.92);
% k'=25
\draw[thick,blue] (0,19.62) -- (10,15.31) -- (20,11.52) -- (30,8.73) -- (40,6.52) -- (50,4.8);
\fill[blue] (0,19.62) circle (7pt);
\fill[blue] (10,15.31) circle (7pt);
\fill[blue] (20,11.52) circle (7pt);
\fill[blue] (30,8.73) circle (7pt);
\fill[blue] (40,6.52) circle (7pt);
\fill[blue] (50,4.8) circle (7pt);
% k'=21
\draw[thick,brown] (0,20.4) -- (10,18.07) -- (20,15.21) -- (30,11.81) -- (40,8.67) -- (50,6.12);
\draw[thick,brown] (-.2,20.2) -- (.2,20.6);
\draw[thick,brown] (.2,20.2) -- (-.2,20.6);
\draw[thick,brown] (9.8,17.87) -- (10.2,18.27);
\draw[thick,brown] (10.2,17.87) -- (9.8,18.27);
\draw[thick,brown] (19.8,15.01) -- (20.2,15.41);
\draw[thick,brown] (20.2,15.01) -- (19.8,15.41);
\draw[thick,brown] (29.8,11.61) -- (30.2,12.01);
\draw[thick,brown] (30.2,11.61) -- (29.8,12.01);
\draw[thick,brown] (39.8,8.47) -- (40.2,8.87);
\draw[thick,brown] (40.2,8.47) -- (39.8,8.87);
\draw[thick,brown] (49.8,5.92) -- (50.2,6.32);
\draw[thick,brown] (50.2,5.92) -- (49.8,6.32);
% k'=19
\draw[thick,green!50!black!100] (0,20.31) -- (10,18.37) -- (20,16.52) -- (30,13.61) -- (40,9.97) -- (50,6.49);
\fill[green!50!black!100] (-.2,20.01) -- (0,20.51) -- (.2,20.01);
\fill[green!50!black!100] (9.8,18.17) -- (10,18.57) -- (10.2,18.57);
\fill[green!50!black!100] (19.8,16.32) -- (20,16.72) -- (20.2,16.32);
\fill[green!50!black!100] (29.8,13.41) -- (30,13.81) -- (30.2,13.41);
\fill[green!50!black!100] (39.8,9.77) -- (40,10.17) -- (40.2,9.77);
\fill[green!50!black!100] (49.8,6.29) -- (50,6.69) -- (50.2,6.29);
% k'=17
\draw[thick,yellow!50!black!100] (0,19.98) -- (10,18.35) -- (20,17.09) -- (30,14.88) -- (40,10.61) -- (50,5.69);
\fill[yellow!50!black!100] (-.2,19.78) -- (.2,19.78) -- (.2,20.18) -- (-.2,20.18);
\fill[yellow!50!black!100] (9.8,18.15) -- (10.2,18.15) -- (10.2,18.55) -- (9.8,18.15);
\fill[yellow!50!black!100] (19.8,16.89) -- (20.2,16.89) -- (20.2,17.29) -- (19.8,17.29);
\fill[yellow!50!black!100] (29.8,14.68) -- (30.2,14.68) -- (30.2,15.08) -- (29.8,15.08);
\fill[yellow!50!black!100] (39.8,10.41) -- (40.2,10.41) -- (40.2,10.81) -- (39.8,10.81);
\fill[yellow!50!black!100] (49.8,5.49) -- (50.2,5.49) -- (50.2,5.89) -- (49.8,5.89);
% k'=13
\draw[thick,purple,dashed] (0,19.01) -- (10,18.01) -- (20,16.85) -- (30,12.54) -- (40,5.95) -- (50,1.68);
\fill[purple] (-.2,19.21) -- (-.2,18.81) -- (.2,19.01);
\fill[purple] (9.8,18.21) -- (9.8,17.81) -- (10.2,18.01);
\fill[purple] (19.8,17.05) -- (19.8,16.65) -- (20.2,16.85);
\fill[purple] (29.8,12.74) -- (29.8,12.34) -- (30.2,12.54);
\fill[purple] (39.8,6.15) -- (39.8,5.75) -- (40.2,5.95);
\fill[purple] (49.8,1.88) -- (49.8,1.48) -- (50.2,1.68);
\draw (25,-3) node {\small noise ratio};
\draw (-4,12.5) node[rotate=90] {\small PSNR};
\draw[thick,red] (55,9) -- (57,9) node[right] {\tiny median};
\draw[thick,blue] (55,14) -- (57,14) node[right] {\tiny $k'=25$};
\fill[blue] (56,14) circle (7pt);
\draw[thick,brown] (55,13) -- (57,13) node[right] {\tiny $k'=21$};
\draw[thick,brown] (55.8,12.8) -- (56.2,13.2);
\draw[thick,brown] (56.2,12.8) -- (55.8,13.2);
\draw[thick,green!50!black!100] (55,12) -- (57,12) node[right] {\tiny $k'=19$};
\fill[green!50!black!100] (55.8,11.8) -- (56,12.2) -- (56.2,11.8);
\draw[thick,yellow!50!black!100] (55,11) -- (57,11) node[right] {\tiny $k'=17$};
\fill[yellow!50!black!100] (55.8,10.8) -- (56.2,10.8) -- (56.2,11.2) -- (55.8,11.2);
\draw[thick,purple,dashed] (55,10) -- (57,10) node[right] {\tiny $k'=13$};
\fill[purple] (55.8,10.2) -- (55.8,9.8) -- (56.2,10);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1412.1680 | arxiv | 2015-04-08T02:11:34 | |
(s,t)=12 | \documentclass[envcountsame]{llncs}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{color}
\usetikzlibrary{calc,arrows,positioning}
\usepackage[amsmath]{ntheorem}
\begin{document}
\begin{tikzpicture}[->,>=stealth,auto,node distance=1.7cm,semithick,scale=1,every node/.style={scale=1}]
\tikzstyle{state}=[minimum size=25pt,circle,draw,thick]
\tikzstyle{triangleState}=[minimum size=0pt,regular polygon, regular polygon sides=4,draw,thick]
\tikzstyle{stateNframe}=[]
every label/.style=draw
\tikzstyle{blackdot}=[circle,fill=black, minimum
size=6pt,inner sep=0pt]
\node[state](s){$s$};
\node[state](s1)[below of=s]{$s_1$};
\node[blackdot](m1)[below of=s1]{};
\node[state](s2)[below of=m1,xshift=-1cm]{$s_2$};
\node[state](s3)[below of=m1,xshift=1cm]{$s_3$};
\node[state](s4)[below of=s2,xshift=1cm]{$s_4$};
\node[state](t)[left of=s,xshift=10cm]{$t$};
\node[blackdot](n1)[below of=t]{};
\node[state](t1)[below of=n1,xshift=-1cm]{$t_1$};
\node[state](t2)[below of=n1,xshift=1cm]{$t_2$};
\node[state](t3)[below of=t1]{$t_3$};
\node[state](t4)[below of=t2]{$t_4$};
\node[state](t5)[below of=t3,xshift=1cm]{$t_5$};
\path (s) edge node[right] {$a$} (s1)
(s1) edge[-] node[right] {$b$} (m1)
(m1) edge[dashed] node[left] {$\frac{1}{2}$} (s2)
edge[dashed] node[right] {$\frac{1}{2}$} (s3)
(s2) edge node[left] {$c$} (s4)
(s3) edge node[right] {$d$} (s4)
(t) edge[-] node {$a$} (n1)
(n1) edge[dashed] node[left] {$\frac{1}{2}$} (t1)
edge[dashed] node[right] {$\frac{1}{2}$} (t2)
(t1) edge node[left] {$b$} (t3)
(t2) edge node[right] {$b$} (t4)
(t3) edge node[left] {$c$} (t5)
(t4) edge node[right] {$d$} (t5);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1509.03391 | arxiv | 2015-09-14T02:04:47 | |
The blinker surrounded by a wall of `bricks', which protect it from uncontrolled perturbations from its environment. | \documentclass[11pt,a4paper]{article}
\usepackage{amssymb,fullpage,graphicx,url,amsmath}
\usepackage{tikz,url}
\begin{document}
\begin{tikzpicture}
\draw[step=1cm,gray,very thin] (-3,-3) grid (6,6);
\fill[black!40!white] (1,1) rectangle (2,2);
\fill[black!40!white] (0,1) rectangle (1,2);
\fill[black!40!white] (2,1) rectangle (3,2);
\fill[black] (-2,-2) rectangle (-1,-1);
\fill[black] (-1,-2) rectangle (0,-1);
\fill[black] (0,-2) rectangle (1,-1);
\fill[black] (1,-2) rectangle (2,-1);
\fill[black] (2,-2) rectangle (3,-1);
\fill[black] (3,-2) rectangle (4,-1);
\fill[black] (4,-2) rectangle (5,-1);
\fill[black] (4,-1) rectangle (5,0);
\fill[black] (4,0) rectangle (5,1);
\fill[black] (4,1) rectangle (5,2);
\fill[black] (4,2) rectangle (5,3);
\fill[black] (4,3) rectangle (5,4);
\fill[black] (4,4) rectangle (5,5);
\fill[black] (3,4) rectangle (4,5);
\fill[black] (2,4) rectangle (3,5);
\fill[black] (1,4) rectangle (2,5);
\fill[black] (0,4) rectangle (1,5);
\fill[black] (-1,4) rectangle (0,5);
\fill[black] (-2,4) rectangle (-1,5);
\fill[black] (-2,3) rectangle (-1,4);
\fill[black] (-2,2) rectangle (-1,3);
\fill[black] (-2,1) rectangle (-1,2);
\fill[black] (-2,0) rectangle (-1,1);
\fill[black] (-2,-1) rectangle (-1,0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.01591 | arxiv | 2017-01-09T02:04:45 | |
Beam of 3 propagating particles which implement the turning on and off of the blue target cell 3 times. | \documentclass[11pt,a4paper]{article}
\usepackage{amssymb,fullpage,graphicx,url,amsmath}
\usepackage{tikz,url}
\begin{document}
\begin{tikzpicture}
\draw[step=2cm,black,thin] (0,0) grid (10,10);
\draw[red,thin] (1,0) -- (1,10);
\draw[red,thin] (3,0) -- (3,10);
\draw[red,thin] (5,0) -- (5,10);
\draw[red,thin] (7,0) -- (7,10);
\draw[red,thin] (9,0) -- (9,10);
\draw[red,thin] (0,1) -- (10,1);
\draw[red,thin] (0,3) -- (10,3);
\draw[red,thin] (0,5) -- (10,5);
\draw[red,thin] (0,7) -- (10,7);
\draw[red,thin] (0,9) -- (10,9);
\fill[black!80!white] (1,8) rectangle (2,9);
\fill[black!80!white] (3,6) rectangle (4,7);
\fill[black!80!white] (5,4) rectangle (6,5);
\draw[blue,ultra thick] (7,2) rectangle (8,3);
\draw[thick,->] (11.5,5) -- (12.5,5);
\draw[step=2cm,black,thin] (14,0) grid (24,10);
\draw[red,thin] (15,0) -- (15,10);
\draw[red,thin] (17,0) -- (17,10);
\draw[red,thin] (19,0) -- (19,10);
\draw[red,thin] (21,0) -- (21,10);
\draw[red,thin] (23,0) -- (23,10);
\draw[red,thin] (14,1) -- (24,1);
\draw[red,thin] (14,3) -- (24,3);
\draw[red,thin] (14,5) -- (24,5);
\draw[red,thin] (14,7) -- (24,7);
\draw[red,thin] (14,9) -- (24,9);
\fill[black!80!white] (16,7) rectangle (17,8);
\fill[black!80!white] (18,5) rectangle (19,6);
\fill[black!80!white] (20,3) rectangle (21,4);
\draw[blue,ultra thick] (21,2) rectangle (22,3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.01591 | arxiv | 2017-01-09T02:04:45 | |
Free particle propagation in Schaeffer's physically universal CA: the configuration on the left turns into the one in the middle by applying Rule (2) to the red partitioning. The middle configuration turns into the right one by applying the same rule to the black partitioning. | \documentclass[11pt,a4paper]{article}
\usepackage{amssymb,fullpage,graphicx,url,amsmath}
\usepackage{tikz,url}
\begin{document}
\begin{tikzpicture}
\draw[step=2cm,black,thin] (0,0) grid (4,4);
\draw[red,thin] (1,0) -- (1,4);
\draw[red,thin] (3,0) -- (3,4);
\draw[red,thin] (0,1) -- (4,1);
\draw[red,thin] (0,3) -- (4,3);
\fill[black!80!white] (1,2) rectangle (2,3);
\draw[very thick,->] (5.5,2) -- (6.5,2);
\draw[step=2cm,black,thin] (8,0) grid (12,4);
\draw[red,thin] (9,0) -- (9,4);
\draw[red,thin] (11,0) -- (11,4);
\draw[red,thin] (8,1) -- (12,1);
\draw[red,thin] (8,3) -- (12,3);
\fill[black!80!white] (10,1) rectangle (11,2);
\draw[very thick,->] (13.5,2) -- (14.5,2);
\draw[step=2cm,black,thin] (16,0) grid (20,4);
\draw[red,thin] (17,0) -- (17,4);
\draw[red,thin] (19,0) -- (19,4);
\draw[red,thin] (16,1) -- (20,1);
\draw[red,thin] (16,3) -- (20,3);
\fill[black!80!white] (19,0) rectangle (20,1);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.01591 | arxiv | 2017-01-09T02:04:45 | |
Geometric construction to compute the rate of injectivity: the green points are the elements of , the blue parallelogram is a fundamental domain of and the grey squares are centred on the points of and have radii 1/2. The rate of injectivity is equal to the area of the intersection between the union of the grey squares and the blue parallelogram. | \documentclass[reqno, 11pt]{amsart}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{pgf,tikz}
\usetikzlibrary{decorations.pathreplacing, shapes.multipart, arrows, matrix}
\usepackage[pdftex,colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref}
\begin{document}
\begin{tikzpicture}[scale=1.5]
\clip (-1.2,-.6) rectangle (1.3,1.8);
\foreach\i in {-1,...,2}{
\foreach\j in {-1,...,3}{
\fill[color=gray,opacity = .3] (.866*\i-.5*\j-.5,.859*\i+.659*\j-.5) rectangle (.866*\i-.5*\j+.5,.859*\i+.659*\j+.5);
\draw[color=gray] (.866*\i-.5*\j-.5,.859*\i+.659*\j-.5) rectangle (.866*\i-.5*\j+.5,.859*\i+.659*\j+.5);
}}
\draw[color=blue!40!black,thick] (0,0) -- (.866,.859) -- (.366,1.518) -- (-.5,.659) -- cycle;
\foreach\i in {-2,...,2}{
\foreach\j in {-2,...,2}{
\draw[color=green!40!black] (.866*\i-.5*\j,.859*\i+.659*\j) node {$\bullet$};
}}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1510.00723 | arxiv | 2015-10-06T02:00:35 | |
A setup for head-to-head cyber security combat. | \documentclass[10pt, titlepage, twocolumn]{article}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usepackage{xcolor}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{units}
\newcommand{\drawPlayers}{
\draw (0,3) circle (.5cm);
\draw (0,2)--(0,2.5);
\draw (0,1) -- (0,2);\draw (0,1) -- (1,1);
\draw (1,1)--(0,0);
\draw (0,2) -- (.5,1.8) -- (1,1.8);
\draw (4,3) circle (.5cm);
\draw (4,2)--(4,2.5);
\draw (4,1) -- (4,2);\draw (4,1) -- (3,1);
\draw (3,1)--(4,0);
\draw (4,2) -- (3.5,1.8) -- (3,1.8);
\draw (.75,1.70) -- (1.40,1.70);
\draw (1.40,1.70) -- (1.35, 2.40);
\draw (2.65,1.70) -- (3.30,1.70);
\draw (2.65,1.70) -- (2.70, 2.40);
\draw (.5,1.60) -- (3.5,1.60);
\draw (2,1.60) -- (2,.20);
\draw (2,.20)--(1.5,0);
\draw (2,.20)--(2.5,0);
\draw (1.3,0)--(1.5,0);
\draw (2.5,0)--(2.7,0);
\draw (-0.5,.9)--(.5,.9);
\draw (-0.5, .9) -- (-.5,0);
\draw (.5, .9) -- (.5,0);
\draw (-0.5, .9) -- (-.55,1.2);
\draw (-.55,1.2)--(-.55,2);
\draw (3.5,.9)--(4.5,.9);
\draw (4.5, .9) -- (4.5,0);
\draw (3.5, .9) -- (3.5,0);
\draw (4.5, .9) -- (4.55,1.2);
\draw (4.55,1.2)--(4.55,2);
}
\begin{document}
\begin{tikzpicture}
\centering
\drawPlayers
%
%
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.04874 | arxiv | 2017-03-16T01:06:11 | |
Illustration of the cost-to-go function approximation by SDDP | \documentclass[12 pt]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1,utf8]{inputenc}
\usepackage{amssymb,amsmath}
\usepackage{color}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale =0.7]
\draw[->](0,0)--(0,8); \draw[->](0,0)--(9,0); \draw(10,0) node{$\text{State}$}; \draw(0,8.5) node{$\text{Cost-to-go}$};
\draw [domain=1:9] plot (\x, 8/\x^2);
\draw(4.5,0.)--(0,2.6667); \draw(1,0.5926)--(9,.0006); \draw(0.5625,8)--(2.25,0);
\draw[<-](1.1,8)--(1.5,8); \draw (2,8) node{$V_{t+1}$};
\draw[<-](1.05,6.125)--(1.45,6.125); \draw (1.9,6.125) node{$\hat{V}_{t+1}$};
\draw[->](0.5,3)--(0.5,2.5); \draw (0.7,3.3)node{$H_{t+1}^1$};
\draw[->](1.4,1)--(2,1); \draw (1,1.3)node{$H_{t+1}^2$};
\draw[->](0.5,0.3)--(1.2,.5); \draw (0.5,0.3)node{$H_{t+1}^3$};
\draw[very thick](0.5625,8)--(1.9685,1.5)--(3.8567,0.3812)--(9,.0006);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.08189 | arxiv | 2016-04-28T02:14:41 | |
9-bus system configuration | \documentclass[12 pt]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1,utf8]{inputenc}
\usepackage{amssymb,amsmath}
\usepackage{color}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.9]
\draw (0,0) circle(0.3); \draw(0.,-0.05) node{$\sim$}; \draw(0,-0.5) node{$\text{\tiny{G2}}$}; \draw (0.3,0.)--(0.8,0); \draw[very thick] (0.8,-0.2)--(0.8,0.2); \draw(0.8,-0.4) node{$\tiny{\text{Bus 2}}$}; \draw (0.8,0.)--(1.3,0); \draw (1.45,0) circle (0.15); \draw (1.65,0) circle (0.15); \draw (1.8,0.)--(2.5,0); \draw[very thick] (2.5,-0.2)--(2.5,0.2); \draw(2.5,-0.4) node{$\tiny{\text{Bus 7}}$}; \draw (2.5,0.)--(3.25,0); \draw[very thick] (3.25,-0.2)--(3.25,0.2); \draw(3.25,0.4) node{$\tiny{\text{Bus 8}}$}; \draw (3.25,0.)--(3.95,0); \draw[very thick] (3.95,-0.2)--(3.95,0.2); \draw(3.95,-0.4) node{$\tiny{\text{Bus 9}}$}; \draw (3.95,0.)--(4.65,0); \draw (4.8,0) circle (0.15); \draw (5.0,0) circle (0.15); \draw (5.15,0.)--(5.85,0);
\draw[very thick] (5.85,-0.2)--(5.85,0.2); \draw(5.85,-0.4) node{$\tiny{\text{Bus 3}}$}; \draw (5.85,0.)--(6.45,0); \draw (6.75,0) circle(0.3); \draw(6.75,-0.05) node{$\sim$}; \draw(6.75,-0.5) node{$\text{\tiny{G3}}$};
\draw (2.5,-0.1)--(2.9,-0.1); \draw (2.9,-0.1)--(2.9,-1); \draw[very thick] (2.6,-1)--(3.3,-1); \draw(2.2,-1) node{$\tiny{\text{Bus 5}}$}; \draw (5.85,-0.1)--(5.35,-0.1); \draw (5.35,-0.1)--(5.35,-1); \draw[very thick] (5.05,-1)--(5.75,-1); \draw(6.15,-1) node{$\tiny{\text{Bus 6}}$};
\draw (5.35,-1)--(5.35,-1.7); \draw (2.9,-1)--(2.9,-1.7); \draw (2.9,-1.7)--(3.6,-1.7); \draw (5.35,-1.7)--(4.6,-1.7);
\draw (3.6,-1.7)--(3.6,-2.45); \draw (4.6,-1.7)--(4.6,-2.45); \draw[very thick] (3.4,-2.45)--(4.8,-2.45); \draw(5.2,-2.45) node{$\tiny{\text{Bus 4}}$};
\draw (4.1,-2.45)--(4.1,-3.05); \draw (4.1,-3.2) circle (0.15); \draw (4.1,-3.35) circle(0.15); \draw (4.1,-3.5)--(4.1,-4.1);
\draw[very thick] (3.4,-4.1)--(4.8,-4.1); \draw(5.2,-4.1) node{$\tiny{\text{Bus 1}}$};
\draw (4.1,-4.1)--(4.1,-4.7); \draw (4.1,-5) circle(0.3); \draw(4.1,-5.05) node{$\sim$}; \draw(4.1,-5.5) node{$\text{\tiny{G1}}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.08189 | arxiv | 2016-04-28T02:14:41 | |
A graph with ||=2. With u(v_0)=0, u(v_1)=1 and all energies equal, the underlying number field is Q(5). | \documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts,amsthm,bbm,graphicx,color,tikz}
\begin{document}
\begin{tikzpicture}
\matrix (m) [row sep = 8em, column sep = 5em]
{
\begin{scope}[scale=.5]
\draw (0,0) -- (2,3) -- (0,6) -- (-2,3) --cycle;
\draw (2,3) to (-2,3);
\draw[fill] (0,0) circle (3pt);
\draw[fill] (0,6) circle (3pt);
\draw[fill] (2,3) circle (3pt);
\draw[fill] (-2,3) circle (3pt);
\draw (0,0) node[anchor=north]{$v_0$};
\draw (0,6) node[anchor=south]{$v_1$};
\draw (2,3) node[anchor=west]{$y$};
\draw (-2,3) node[anchor=east]{$x$};
\draw (-1,4.5) node[anchor=south east]{$a$};
\draw (1,4.5) node[anchor=south west]{$b$};
\draw (0,3) node[anchor=south]{$c$};
\draw (-1,1.5) node[anchor=north east]{$d$};
\draw (1,1.5) node[anchor=north west]{$e$};
\end{scope}
&
\begin{scope}[scale=.5]
\draw (0,0) rectangle (6,6);
\draw (0,4.34) to (4.34,4.34);
\draw (4.34,6) to (4.34,1.66);
\draw (1.66,1.66) to (6,1.66);
\draw (1.66,0) to (1.66,4.34);
\begin{scope}[xshift=10cm]
\draw (0,0) rectangle (6,6);
\draw (1.66,4.34) to (6,4.34);
\draw (4.34,4.34) to (4.34,0);
\draw (0,1.66) to (4.34,1.66);
\draw (1.66,1.66) to (1.66,6);
\end{scope}
\draw (8,0) node{$0$};
\draw (8,6) node{$1$};
\draw (8,1.66) node{$\frac 12 - \frac 1 {2\sqrt{5}}$};
\draw (8,4.34) node{$\frac 12 + \frac 1 {2\sqrt{5}}$};
\end{scope}
\\};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1505.05785 | arxiv | 2017-03-14T01:13:02 | |
Illustration for Example~example:common end. | \documentclass[11pt]{amsart}
\usepackage{amsthm,amsmath,amssymb,url}
\usepackage{xcolor}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=5]
\draw (0,1) node[anchor=east]{$a$} -- (1,0) node[anchor=west]{$b$}-- (0,0)node[anchor=east]{$c$} -- cycle;
\filldraw[fill=black!20!white] (0.5,0) -- (0.3333,0.3333) -- (0,0.5) -- (0,0.3333) -- (0.3333,0) -- cycle;
\draw[very thick] (0,1) -- (0.3333,0.3333);
\draw[very thick] (1,0) -- (0.3333,0.3333);
\draw[very thick] (0,0) node{};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.01900 | arxiv | 2016-10-07T02:05:34 | |
Some boundary faces in a portion of an open planar trivalent graph. The boundary region which is a small neighborhood of faces A, B, C, and D is a growth region -- it has five edges meeting the boundary and two which don't. The boundary region which is a small neighborhood of B and C is not a growth region --- it has three edges meeting the boundary and four edges which don't. | \documentclass[12pt]{amsart}
\usepackage{amsmath,amssymb,amsfonts,amsthm}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{tikz-qtree}
\usetikzlibrary{backgrounds}
\begin{document}
\begin{tikzpicture}
\draw[dashed] (2,0) arc (0:180:2cm);
\draw (10:2cm) -- (30:1cm) -- (50:2cm);
\draw (170:2cm) -- (150:1cm) -- (130:2cm);
\draw (30:1cm)--(45:.5cm) -- ++(-90:.5cm);
\draw (150:1cm)--(135:.5cm) -- ++(-90:.5cm);
\draw (45:.5cm)--(90:.5cm)--(135:.5cm);
\draw (90:.5cm)--(90:2cm);
\node at (30:1.6cm) {$D$};
\node at (60:1cm) {$C$};
\node at (120:1cm) {$B$};
\node at (150:1.6cm) {$A$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1501.06869 | arxiv | 2016-07-21T02:07:05 | |
Hasse-diagram of Szondi's signatures | \documentclass{article}
\usepackage{amsmath,amssymb,array,multirow,tikz,tikz-cd,rotating}
\usetikzlibrary{arrows,automata}
\begin{document}
\begin{tikzpicture}
\node (pbbb) at (0,4) {$+!!!$};
\node (pbb) at (0,3) {$+!!$};
\node (pb) at (0,2) {$+!$};
\node (p) at (0,1) {$+$};
\node (n) at (0,0) {$0$};
\node (m) at (0,-1) {$-$};
\node (mb) at (0,-2) {$-!$};
\node (mbb) at (0,-3) {$-!!$};
\node (mbbb) at (0,-4) {$-!!!$};
\draw (mbbb) -- (mbb) -- (mb) -- (m) -- (n) -- (p) -- (pb) -- (pbb) -- (pbbb);
\node (pmub) at (1,1) {$\pm^{!}$};
\node (pm) at (1,0) {$\pm$};
\node (pmlb) at (1,-1) {$\pm_{!}$};
\draw (pmlb) -- (pm) -- (pmub);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1405.0877 | arxiv | 2014-05-06T02:15:50 | |
Graph G and the resulting graph G' | \documentclass[]{llncs}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{backgrounds}
\pgfdeclarelayer{myback}
\pgfsetlayers{background,myback,main}
\begin{document}
\begin{tikzpicture}[]
\tikzstyle{vert}=[circle,draw=black,fill=white,inner sep=1.5pt, minimum size=20]
\node[vert] (a1) at (90 :1) {a};
\node[vert] (a2) at (18 :1) {b};
\node[vert] (a3) at (-54:1) {c};
\node[vert] (a4) at (-126:1) {d};
\node[vert] (a5) at (-198:1) {e};
\draw (a1) -- (a2);
\draw (a2) -- (a3);
\draw (a3) -- (a4);
\draw (a3) -- (a5);
\draw (a4) -- (a5);
\begin{scope}[xshift=6cm]
\node[vert] (a1) at (-0.75, 5) {$a_1$};
\node[vert] (a2) at (-0.75, 4) {$b_1$};
\node[vert] (a3) at (-0.75, 3) {$c_1$};
\node[vert] (a4) at (-0.75, 2) {$d_1$};
\node[vert] (a5) at (-0.75, 1) {$e_1$};
\node[vert] (b1) at (0.75, 5) {$a_2$};
\node[vert] (b2) at (0.75, 4) {$b_2$};
\node[vert] (b3) at (0.75, 3) {$c_2$};
\node[vert] (b4) at (0.75, 2) {$d_2$};
\node[vert] (b5) at (0.75, 1) {$e_2$};
\draw (a1) -- (b2);
\draw (a2) -- (b3);
\draw (a3) -- (b4);
\draw (a3) -- (b5);
\draw (a4) -- (b5);
\draw (b1) -- (a2);
\draw (b2) -- (a3);
\draw (b3) -- (a4);
\draw (b3) -- (a5);
\draw (b4) -- (a5);
\node[vert] (z1) at (-2, -1) {$z_1$};
\node[vert] (z2) at (-1, -1) {$z_2$};
\node[vert] (z3) at ( 0, -1) {$z_3$};
\node[vert] (z4) at ( 1, -1) {$z_4$};
\node[vert] (z5) at ( 2, -1) {$z_5$};
\begin{pgfonlayer}{myback}
\draw (z1) -- (a4);
\draw (z1) -- (a5);
\draw (z1) -- (b4);
\draw (z1) -- (b5);
\end{pgfonlayer}
\draw (z2)+( 65:0.65) -- (z2);
\draw (z2)+( 80:0.65) -- (z2);
\draw (z3)+( 70:0.75) -- (z3);
\draw (z3)+( 75:0.75) -- (z3);
\draw (z3)+( 80:0.75) -- (z3);
\draw (z3)+(110:0.75) -- (z3);
\draw (z3)+(115:0.75) -- (z3);
\draw (z3)+(120:0.75) -- (z3);
\draw (z4)+(100:0.75) -- (z4);
\draw (z4)+(104:0.75) -- (z4);
\draw (z4)+(120:0.75) -- (z4);
\draw (z4)+(124:0.75) -- (z4);
\draw (z5)+(110:0.75) -- (z5);
\draw (z5)+(115:0.75) -- (z5);
\draw (z5)+(130:0.75) -- (z5);
\draw (z5)+(140:0.75) -- (z5);
\node[] (d) at (0.8, 0.10) {$\dots$};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1507.03885 | arxiv | 2015-07-15T02:10:40 | |
The bridge network. | \documentclass[11pt]{article}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}\label{rr}[node distance = 5 cm]
\tikzset{LabelStyle/.style = {semithick,fill= white, text=black}}
\node[scale=0.9,semithick,shape = circle,draw, fill= black, text= white, inner sep =2pt, outer sep= 0pt, minimum size= 5 pt](A) at (0,0) {a};
\node[scale=0.8,semithick,shape = circle,draw, fill= white, text= black, inner sep =2pt, outer sep= 0pt, minimum size= 5 pt](B) at (1.5,1.5) {b};
\node[scale=0.9,semithick,shape = circle,draw, fill= white, text= black, inner sep =2pt, outer sep= 0pt, minimum size= 5 pt](C) at (1.5,-1.5) {c};
\node[scale=0.8,semithick,shape = circle,draw, fill= black, text= white, inner sep =2pt, outer sep= 0pt, minimum size= 5 pt](D) at (3,0) {d};
\draw[semithick] (A) to node[LabelStyle]{1} (B) ;
\draw[semithick] (A) to node[LabelStyle]{2} (C);
\draw[semithick] (B) to node[LabelStyle]{3} (C);
\draw[semithick] (B) to node[LabelStyle]{4} (D);
\draw[semithick] (C) to node[LabelStyle]{5} (D);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1507.04143 | arxiv | 2015-07-16T02:07:17 | |
(Left) With perfect play, the first player wins with any opening move except the corners, which tie. (Right) A more delicate position with black to play. The full strong solution can be explored at http://perfect-pentago.net. | \documentclass[conference]{IEEEtran}
\usepackage[cmex10]{amsmath}
\usepackage{color}
\usepackage{amsfonts,amssymb,amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\definecolor{win} {rgb}{0,1,0};
\definecolor{tie} {rgb}{0,0,1};
\definecolor{loss}{rgb}{1,0,0};
\tikzstyle{kind}=[circle,draw=gray,inner sep=0pt,minimum size=15]
\node at (-2,0) [kind,label=below:win, fill=win] {};
\node at ( 0,0) [kind,label=below:tie, fill=tie] {};
\node at ( 2,0) [kind,label=below:loss,fill=loss] {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1404.0743 | arxiv | 2014-04-07T02:02:53 | |
Each section is a 4D array of functions f_abcd : L \{-1,0,1\}. Each dimension corresponds to all patterns of stones in one of the four quadrants with fixed counts of black and white stones, including only patterns lexicographically minimal under rotation. For each (a,b,c,d) describing the four quadrants of a board, f_abcd gives the loss/tie/win values for all 256 ways to rotate the four quadrants. The order is chosen so that reflected pairs are adjacent so that reflection preserves the block structure. The figure shows 2D slices of the full 4D array. | \documentclass[conference]{IEEEtran}
\usepackage[cmex10]{amsmath}
\usepackage{color}
\usepackage{amsfonts,amssymb,amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[scale=1.1]
\definecolor{tan}{rgb}{.8235,.7059,.549}
\begin{scope}[shift={(0.5,0.5)}]
\fill[white] (0,0) rectangle (6,3);
\draw[step=1] (0,0) grid (6,3);
\end{scope}
\begin{scope}[shift={(0.25,0.25)}]
\fill[white] (0,0) rectangle (6,3);
\draw[step=1] (0,0) grid (6,3);
\end{scope}
\begin{scope}[shift={(0,0)}]
\fill[white] (0,0) rectangle (6,3);
\draw[step=1] (0,0) grid (6,3);
\end{scope}
\node at (0.5,-1.05555555556) {$0$};
\begin{scope}[shift={(0.5,-0.5)},scale=1/9]
\fill[tan] (-3.05,-3.05) rectangle (3.05,3.05);
\fill[darkgray] (-0.05,-3.15) rectangle (0.05,3.15);
\fill[darkgray] (-3.15,-0.05) rectangle (3.15,0.05);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-1.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-1.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-1.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-0.55) circle (0.4);
\end{scope}
\node at (1.5,-1.05555555556) {$1$};
\begin{scope}[shift={(1.5,-0.5)},scale=1/9]
\fill[tan] (-3.05,-3.05) rectangle (3.05,3.05);
\fill[darkgray] (-0.05,-3.15) rectangle (0.05,3.15);
\fill[darkgray] (-3.15,-0.05) rectangle (3.15,0.05);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-1.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-1.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-1.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-0.55) circle (0.4);
\end{scope}
\node at (2.5,-1.05555555556) {$2$};
\begin{scope}[shift={(2.5,-0.5)},scale=1/9]
\fill[tan] (-3.05,-3.05) rectangle (3.05,3.05);
\fill[darkgray] (-0.05,-3.15) rectangle (0.05,3.15);
\fill[darkgray] (-3.15,-0.05) rectangle (3.15,0.05);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-2.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-1.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-1.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-1.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-0.55) circle (0.4);
\end{scope}
\node at (3.5,-1.05555555556) {$3$};
\begin{scope}[shift={(3.5,-0.5)},scale=1/9]
\fill[tan] (-3.05,-3.05) rectangle (3.05,3.05);
\fill[darkgray] (-0.05,-3.15) rectangle (0.05,3.15);
\fill[darkgray] (-3.15,-0.05) rectangle (3.15,0.05);
\filldraw[draw=gray,fill=black,very thin] (-2.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-1.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-1.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-1.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-0.55) circle (0.4);
\end{scope}
\node at (4.5,-1.05555555556) {$4$};
\begin{scope}[shift={(4.5,-0.5)},scale=1/9]
\fill[tan] (-3.05,-3.05) rectangle (3.05,3.05);
\fill[darkgray] (-0.05,-3.15) rectangle (0.05,3.15);
\fill[darkgray] (-3.15,-0.05) rectangle (3.15,0.05);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-2.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-2.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-1.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-1.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-1.55,-0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-2.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,-0.55) circle (0.4);
\end{scope}
\node at (5.35714285714,-0.5) {$\cdot$};
\node at (5.5,-0.5) {$\cdot$};
\node at (5.64285714286,-0.5) {$\cdot$};
\node at (-1.05555555556,0.5) {$0$};
\begin{scope}[shift={(-0.5,0.5)},scale=1/9]
\fill[tan] (-3.05,-3.05) rectangle (3.05,3.05);
\fill[darkgray] (-0.05,-3.15) rectangle (0.05,3.15);
\fill[darkgray] (-3.15,-0.05) rectangle (3.15,0.05);
\filldraw[draw=gray,fill=white,very thin] (-2.55,0.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-2.55,1.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-2.55,2.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-1.55,0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-1.55,1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-1.55,2.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,2.55) circle (0.4);
\end{scope}
\node at (-1.05555555556,1.5) {$1$};
\begin{scope}[shift={(-0.5,1.5)},scale=1/9]
\fill[tan] (-3.05,-3.05) rectangle (3.05,3.05);
\fill[darkgray] (-0.05,-3.15) rectangle (0.05,3.15);
\fill[darkgray] (-3.15,-0.05) rectangle (3.15,0.05);
\filldraw[draw=gray,fill=black,very thin] (-2.55,0.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-2.55,1.55) circle (0.4);
\filldraw[draw=gray,fill=white,very thin] (-2.55,2.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-1.55,0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-1.55,1.55) circle (0.4);
\filldraw[draw=gray,fill=black,very thin] (-1.55,2.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,0.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,1.55) circle (0.4);
\filldraw[draw=gray,fill=tan,very thin] (-0.55,2.55) circle (0.4);
\end{scope}
\node at (-0.5,2.35714285714) {$\cdot$};
\node at (-0.5,2.5) {$\cdot$};
\node at (-0.5,2.64285714286) {$\cdot$};
\node at (.5+0,.5+0) {$f_{00cd}$};
\node at (.5+0,.5+1) {$f_{01cd}$};
\node at (0.5,2.35714285714) {$\cdot$};
\node at (0.5,2.5) {$\cdot$};
\node at (0.5,2.64285714286) {$\cdot$};
\node at (.5+1,.5+0) {$f_{10cd}$};
\node at (.5+1,.5+1) {$f_{11cd}$};
\node at (1.5,2.35714285714) {$\cdot$};
\node at (1.5,2.5) {$\cdot$};
\node at (1.5,2.64285714286) {$\cdot$};
\node at (.5+2,.5+0) {$f_{20cd}$};
\node at (.5+2,.5+1) {$f_{21cd}$};
\node at (2.5,2.35714285714) {$\cdot$};
\node at (2.5,2.5) {$\cdot$};
\node at (2.5,2.64285714286) {$\cdot$};
\node at (.5+3,.5+0) {$f_{30cd}$};
\node at (.5+3,.5+1) {$f_{31cd}$};
\node at (3.5,2.35714285714) {$\cdot$};
\node at (3.5,2.5) {$\cdot$};
\node at (3.5,2.64285714286) {$\cdot$};
\node at (.5+4,.5+0) {$f_{40cd}$};
\node at (.5+4,.5+1) {$f_{41cd}$};
\node at (4.5,2.35714285714) {$\cdot$};
\node at (4.5,2.5) {$\cdot$};
\node at (4.5,2.64285714286) {$\cdot$};
\node at (5.35714285714,0.5) {$\cdot$};
\node at (5.5,0.5) {$\cdot$};
\node at (5.64285714286,0.5) {$\cdot$};
\node at (5.35714285714,1.5) {$\cdot$};
\node at (5.5,1.5) {$\cdot$};
\node at (5.64285714286,1.5) {$\cdot$};
\node at (5.35714285714,2.35714285714) {$\cdot$};
\node at (5.5,2.5) {$\cdot$};
\node at (5.64285714286,2.64285714286) {$\cdot$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1404.0743 | arxiv | 2014-04-07T02:02:53 | |
The first graph considered in Case~3, with (a,b,c)=(3,4,4). | \documentclass[11pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amsthm,enumerate}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage[color=blue!20]{todonotes}
\begin{document}
\begin{tikzpicture}[join=bevel,inner sep=0.6mm]
%main vertices
\node[draw,shape=circle,fill] (x) at (0,0) {};
\draw (x) node[left=0.2cm] {$0$};
\node[draw,shape=circle,fill] (y) at (6,0) {};
\draw (y) node[right=0.2cm] {$1$};
\node[draw,shape=circle,fill] (z) at (3,5.2) {};
\draw (z) node[above=0.2cm] {$1$};
\node[draw,shape=circle,fill] (t) at (3,1.7) {};
\draw (t) node[above right=0.1cm] {$4$};
%inner-vertices on a-side
\node[draw,shape=circle,fill] (a1) at (3,4) {};
\draw (a1) node[left=0.2cm] {$2$};
\node[draw,shape=circle,fill] (a2) at (3,2.9) {};
\draw (a2) node[left=0.2cm] {$3$};
%inner-vertices on b-side
\node[draw,shape=circle,fill] (b1) at (0.75,1.3) {};
\draw (b1) node[left=0.2cm] {$4$};
\node[draw,shape=circle,fill] (b2) at (1.5,2.6) {};
\draw (b2) node[left=0.2cm] {$3$};
\node[draw,shape=circle,fill] (b3) at (2.25,3.9) {};
\draw (b3) node[left=0.2cm] {$2$};
%inner-vertices on b'-side
\node[draw,shape=circle,fill] (bp1) at (4.5,0.85) {};
\draw (bp1) node[above=0.2cm] {$0$};
%inner-vertices on c-side
\node[draw,shape=circle,fill] (c1) at (0.75,0.425) {};
\draw (c1) node[above=0.2cm] {$1$};
\node[draw,shape=circle,fill] (c2) at (1.5,0.85) {};
\draw (c2) node[below=0.2cm] {$2$};
\node[draw,shape=circle,fill] (c3) at (2.25,1.275) {};
\draw (c3) node[above=0.2cm] {$3$};
%inner-vertices on c'-side
\node[draw,shape=circle,fill] (cp1) at (4.5,2.6) {};
\draw (cp1) node[right=0.2cm] {$0$};
\draw[-,line width=0.4mm] (x)--(y)--(z)--(x)--(t)--(y) (t)--(z);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.03685 | arxiv | 2016-10-13T02:04:05 | |
A k-Sun graph | \documentclass[11pt]{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture} [scale=1]
\filldraw (-5.5+1.45 + 0.2,1.25 + 1.5 + 0.2 - 10.5) circle (2.1pt);
\filldraw (-5.5 - 1.45 - 0.2,1.25 + 1.5 + 0.2 - 10.5) circle (2.1pt);
\filldraw (-5.5 + 1.43 + 0.882,1.25 + 0.464 -1.1 - 10.5) circle (2.1pt);
\filldraw (-5.5 - 1.43 - 0.882,1.25 + 0.464 -1.1 - 10.5) circle (2.1pt);
\filldraw (-5.5 + 0.2,1.25 - 1.21 -1.2 - 10.5) circle (2.1pt);
\filldraw (-5.5,1.25 + 1.5 - 10.5) circle (2.1pt);
\filldraw (-5.5 + 1.43,1.25 + 0.464 - 10.5) circle (2.1pt);
\filldraw (-5.5 - 1.43,1.25 + 0.464 - 10.5) circle (2.1pt);
\filldraw (-5.5 + 0.882,1.25 - 1.21 - 10.5) circle (2.1pt);
\filldraw (-5.5 - 0.882,1.25 - 1.21 - 10.5) circle (2.1pt);
\draw[-,thick] (-5.5,1.25 + 1.5 - 10.5) -- (-5.5 + 1.43,1.25 + 0.464
- 10.5); \draw[-,thick] (-5.5 + 1.43,1.25 + 0.464 - 10.5) -- (-5.5 -
1.43,1.25 + 0.464 - 10.5); \draw[-,thick] (-5.5 - 1.43,1.25 + 0.464
- 10.5) -- (-5.5 + 0.882,1.25 - 1.21 - 10.5); \draw[-,thick] (-5.5 +
0.882,1.25 - 1.21 - 10.5) -- (-5.5 - 0.882,1.25 - 1.21 - 10.5);
\draw[-,thick] (-5.5 - 0.882,1.25 - 1.21 - 10.5) -- (-5.5,1.25 + 1.5
- 10.5);
\draw[-,thick] (-5.5+1.45 + 0.2,1.25 + 1.5 + 0.2 - 10.5)--(-5.5,1.25
+ 1.5 - 10.5); \draw[-,thick] (-5.5+1.45 + 0.2,1.25 + 1.5 + 0.2 -
10.5)--(-5.5 + 1.43,1.25 + 0.464 - 10.5); \draw[-,thick] (-5.5 -
1.45 - 0.2,1.25 + 1.5 + 0.2 - 10.5)--(-5.5,1.25 + 1.5 - 10.5);
\draw[-,thick] (-5.5 - 1.45 - 0.2,1.25 + 1.5 + 0.2 - 10.5)--(-5.5 -
1.43,1.25 + 0.464 - 10.5); \draw[-,thick] (-5.5 + 1.43 + 0.882,1.25
+ 0.464 -1.1 - 10.5)--(-5.5 + 0.882,1.25 - 1.21 - 10.5);
\draw[-,thick] (-5.5 + 1.43 + 0.882,1.25 + 0.464 -1.1 - 10.5)--(-5.5
+ 1.43,1.25 + 0.464 - 10.5); \draw[-,thick] (-5.5 - 1.43 -
0.882,1.25 + 0.464 -1.1 - 10.5)--(-5.5 - 0.882,1.25 - 1.21 - 10.5) ;
\draw[-,thick] (-5.5 - 1.43 - 0.882,1.25 + 0.464 -1.1 - 10.5)--(-5.5
- 1.43,1.25 + 0.464 - 10.5); \draw[-,thick] (-5.5 + 0.2,1.25 - 1.21
-1.2 - 10.5)--(-5.5 + 0.882,1.25 - 1.21 - 10.5); \draw[-,thick]
(-5.5 + 0.2,1.25 - 1.21 -1.2 - 10.5)--(-5.5 - 0.882,1.25 - 1.21 -
10.5);
\draw[-,thick] (-5.5,1.25 + 1.5 - 10.5) -- (-5.5 - 1.43,1.25 + 0.464
- 10.5); \draw[-,thick] (-5.5 - 1.43,1.25 + 0.464 - 10.5) -- (-5.5 -
0.882,1.25 - 1.21 - 10.5); \draw[-,thick] (-5.5 - 0.882,1.25 - 1.21
- 10.5) -- (-5.5 + 1.43,1.25 + 0.464 - 10.5); \draw[-,thick] (-5.5 +
1.43,1.25 + 0.464 - 10.5) -- (-5.5 + 0.882,1.25 - 1.21 - 10.5);
\draw[-,thick] (-5.5 + 0.882,1.25 - 1.21 - 10.5) -- (-5.5,1.25 + 1.5
- 10.5);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.06099 | arxiv | 2016-03-22T01:06:21 | |
The relationship between entanglement, discord and coherence in composite quantum states Yao2015a, where ``Ent'' denotes entanglement. The hierarchical relation, C() D() E(), signifies that quantum coherence is a rather ubiquitous manifestation of quantum correlations. | \documentclass[american,aps,pra,reprint, superscriptaddress]{revtex4-1}
\usepackage[unicode=true,pdfusetitle, bookmarks=true,bookmarksnumbered=false,bookmarksopen=false, breaklinks=false,pdfborder={0 0 0},backref=false,colorlinks=false]{hyperref}
\usepackage{graphics,epstopdf,graphicx, amsthm, amsmath, amssymb, times, braket, colortbl, color, bm, framed, cleveref, mathrsfs}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[thick]
%
\tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
\tikzstyle{phase1} = [fill=blue!20,shape=circle,minimum size=12em,inner sep=0pt]
\tikzstyle{phase2} = [fill=yellow,shape=circle,minimum size=6em,inner sep=0pt]
\tikzstyle{phase3} = [fill=green!60,shape=circle,minimum size=3em,inner sep=0pt]
\tikzstyle{surround} = [fill=blue!10,thick,draw=black,rounded corners=2mm]
\tikzstyle{block} = [rectangle, draw, fill=white,
text width=3em, text centered, , minimum height=6em]
%
\node[phase1] (p1) at (5,3) {~};
\node[phase2] (p2) at (5,2.5) {~};
\node[phase3] (p3) at (5,2.2) {~};
\node at (5,4) (e1){Coherence};
\node at (5,2.8) (e2){Discord};
\node at (5,2.2) (e3){\small {Ent}};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.06322 | arxiv | 2016-07-29T02:02:59 | |
Example net. | \documentclass[preprint]{elsarticle}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage[utf8]{inputenc}
\usetikzlibrary{arrows,shapes,snakes,automata,backgrounds,petri,calc,positioning}
\begin{document}
\begin{tikzpicture}[auto]
\node[place,label=$s_1$,tokens=1] (s1) {};
\node[place,label=$r_1$,right= of s1] (r1) {};
\node[place,label=$s_2$,below= of s1,tokens=1] (s2) {};
\node[place,label=$r_2$,right= of s2] (r2) {};
\coordinate (mid) at ($(r1)!0.5!(r2)$);
\node[place,label=$s_3$,right= 2cm of mid] (s3) {};
\node[transition] (t1) at ($(s1)!0.5!(r1)$) {$a$}
edge [pre] node {} (s1)
edge [post] node {} (r1);
\node[transition] (t2) at ($(s2)!0.5!(r2)$) {$b$}
edge [pre] node {} (s2)
edge [post] node {} (r2);
\node[transition,right= of mid] (t3) {$c$}
edge [pre] node {} (r1)
edge [pre] node {} (r2)
edge [post] node {} (s3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1507.06462 | arxiv | 2015-07-24T02:08:45 | |
Grafted metric on surface obtained via plumbing fixture. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.95]
\draw[line width=1pt] (12.65,1) .. controls (14.15,.8) and (13.85,.35) ..(14.65,0);
\draw[line width=1pt] (12.65,-2) .. controls(14.5,-1.8) and (13.85,-1.35) ..(14.65,-1);
\draw[line width=1pt] (12.65,.4) .. controls(13.85,.5) and (14.40,-1.2) ..(12.65,-1.4);
\draw[line width=1pt,color=gray] (12.65,.7) ellipse (.115 and .315);
\draw[line width=1pt,color=gray] (12.65,-1.7) ellipse (.115 and .315);
\draw[line width=1pt,color=gray] (15.65,-0.52) ellipse (.1 and .2);
\draw[line width=1pt] (16.65,-0.52) ellipse (.11 and .2);
\draw[line width=1pt,color=black] (16,-0.525) ellipse (.085 and .115);
\draw[line width=1pt] (14.65,0) .. controls(14.9,-.15) ..(16.05,-0.4);
\draw[line width=1pt] (14.65,-1) .. controls(14.9,-.85) ..(16.05,-0.65);
\draw[line width=1pt] (17,0) .. controls(18,1) and (19,1) ..(20,0);
\draw[line width=1pt] (17,-1) .. controls(18,-2) and (19,-2) ..(20,-1);
\draw[line width=1pt] (20,0) .. controls(20.2,-.15) ..(21,-.15);
\draw[line width=1pt] (20,-1) .. controls(20.2,-.85) ..(21,-.85);
\draw[line width=1pt,color=gray] (21,-.5) ellipse (.15 and .35);
\draw[line width=1pt] (17.75,-.75) .. controls(18.25,-1.15) and (18.75,-1.15) ..(19.25,-.75);
\draw[line width=1pt] (17.75,-.35) .. controls(18.25,0.1) and (18.75,0.1) ..(19.25,-.35);
\draw[line width=1pt] (17.75,-.35) .. controls(17.65,-.475) and (17.65,-.625) ..(17.75,-.75);
\draw[line width=1pt] (19.25,-.35) .. controls(19.35,-.475) and (19.35,-.625) ..(19.25,-.75);
\draw[line width=1pt] (17,0) .. controls(16.5,-.4) ..(16,-0.4);
\draw[line width=1pt] (17,-1) .. controls(16.5,-.65) ..(16,-0.65);
\draw[line width=1pt,color=gray] (16.35,-0.54) ellipse (.075 and .145);
\draw[line width=1pt] (15.25,-0.5) ellipse (.1 and .25);
\draw[line width=1pt,color=black] (16,-0.525) ellipse (.075 and .115);
\draw[thick,style=dashed](16.35,-0.3) --(16.35,1);
\draw[thick,style=dashed](16.65,-0.2)--(16.65,.95);
\draw[thick,style=dashed](15.65,-0.3) --(15.65,1);
\draw[thick,style=dashed](15.25,-0.2)--(15.25,.95);
\draw[thick,style=dashed](16.35,-0.65) --(16.35,-1.5);
\draw[thick, style=dashed](15.65,-0.65)--(15.65,.-1.5);
\draw (16.2,2.5) node[above]{\it Hyperbolic metric on $\mathcal{R}_0$};
\draw[thick,->](18.25,2.5)--(18.25,1);
\draw[thick,->](14,2.5)--(14,1);
\draw (16.2,1.5) node[above]{\it Interpolating metric};
\draw[thick,->](16.5,1.5)--(16.5,0);
\draw[thick,->](15.45,1.5)--(15.45,0);
\draw (16.2,-3) node[above]{\it Metric on hyperbolic annulus};
\draw[thick,->](16,-2)--(16,-1);
\draw (12.15,.5) node[above ] {$\beta_2$} (12.15,-2) node[above ] {$\beta_1$} (21.2,-.2)node [below right ] {$\beta_3$} (16,0.2) node [below ] {$\gamma$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Two annuli having inner radius |t| and outer radius 1 obtained by removing a disc of radius |t| from D_1 and D_2 where t is a complex parameter. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.8]
\draw[thick,color=black] (3,-2.5) ellipse (2 and 2)(3,-1)node{$D_2$};% right circle external
\draw[thick,color=gray] (3,-2.5) ellipse (1 and 1); % right internal circle
\draw[thick,color=gray](3,-2.5)--(4,-2.5)(3.85,-2.35)--(4,-2.5)(3.85,-2.65)--(4,-2.5)(3.5,-2.2)node{$|t|$};
\draw[thick,color=gray] (-3,-2.5) ellipse (2 and 2);% left circle external
\draw[thick,color=black] (-3,-2.5) ellipse (1 and 1); % left internal circle
\draw[thick](-3,-2.5)--(-2,-2.5)(-2.15,-2.35)--(-2,-2.5)(-2.15,-2.65)--(-2,-2.5)(-2.5,-2.2)node{$|t|$}(-3,-1)node{$D_1$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Complete geodesics that are disjoint from b_2,b_3 and orthogonal to b_1. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=1.85]
\draw[line width=1pt] (1,1) .. controls (1.75,1) and (2.25,.25) ..(3.5,.4);
\draw[line width=1pt] (1,-2) .. controls(1.75,-2) and (2.25,-1.25) ..(3.5,-1.2);
\draw[line width=1.5pt,style=dashed] (3.7,-.2) .. controls (2.5,-.15) and (1.75,-.2) ..(1.7,-.35);
\draw[line width=1.5pt] (3.3,-.4) .. controls (2.5,-.45) and (1.75,-.35) ..(1.7,-.35);
\draw[line width=1.5pt] (3.35,0) .. controls (2.5,0) and (1.9,.75) ..(1.7,.8);
\draw[line width=1.5pt,style=dashed] (1.7,.8) .. controls (1.5,.7) and (1.3,0.1) ..(1.5,0.05);
\draw[line width=1.5pt] (1.4,.92) .. controls (1.65,.85) and (1.7,0.1) ..(1.5,0.05);
\draw[line width=1.5pt,style=dashed] (1.4,.92) .. controls (1.2,.7) and (1.15,0.3) ..(1.3,0.2);
\draw[line width=1.5pt] (1.25,.95) .. controls (1.5,.9) and (1.5,0.1) ..(1.3,0.2);
\draw[line width=1.5pt,style=dashed] (1.25,.95) .. controls (1.1,.7) and (1.11,0.5) ..(1.15,0.3);
\draw[line width=1.5pt] (1.05,1) .. controls (1.25,.9) and (1.3,0.5) ..(1.15,0.3);
\draw[line width=1pt] (1,.4) .. controls(2,-.2) and (2,-.8) ..(1,-1.4);
\draw[line width=1.5pt] (3.6,.1)--(3.7,.1);
\draw[line width=1.5pt] (3.65,-.65)--(3.75,-.65);
\draw[line width=1.5pt] (3.3,-.9)--(3.4,-.9);
\draw[gray, line width=1.5pt] (1,.7) ellipse (.115 and .315);
\draw[gray,line width=1.5pt] (1,-1.7) ellipse (.115 and .315);
\draw[gray, line width=1.5pt] (3.5,-.4) ellipse (.2 and .8);
\draw (0.25,.5) node[above right] {$\beta_2$} (0.25,-2) node[above right] {$\beta_3$} (3.6,.5)node [above right ] {$\beta_1$} (3.35,-.15) node[above right] {$z_1$}(3.7,0) node[above right] {$z_2$} (3.7,-.8) node[above right] {$y_2$} (3.35,-1.1) node[above right] {$y_1$} (3.25,-.6) node[above right] {$w_1$} (3.7,-.4)node [above right ] {$w_2$} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Fundamental domain of collar is the region inside the annulus and wedge. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.6]
\draw[<->,line width=.25pt](-3,0)--(11,0);
\draw[->,line width=.25pt](4,0)--(4,5);
\draw[line width=1pt] (1,0) .. controls (2,3) and (6,3) ..(7,0);
\draw[line width=1pt] (-1,0) .. controls (.5,5) and (7.5,5) ..(9,0);
\draw[line width=1pt, color=gray] (1.25,3)node[above left]{$\pi-l$}--(4,0) -- (6.75,3)node[above right]{$l$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Plumbing fixture of two surfaces at punctures p and q. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.65]
\draw[line width=1pt] (-3,1) .. controls (-2.25,1) and (-1.75,.75) ..(-1,0);
\draw[line width=1pt] (-3,-2) .. controls(-2.25,-2) and (-1.75,-1.75) ..(-1,-1);
\draw[line width=1pt] (-3,.4) .. controls(-1.75,.5) and (-1.25,-1.2) ..(-3,-1.4);
\draw[line width=1pt,color=gray] (-3,.7) ellipse (.115 and .315);
\draw[line width=1pt,color=gray] (-3,-1.7) ellipse (.115 and .315);
\draw[line width=.75pt,color=gray] (0,-0.5) ellipse (.115 and .155);
\draw[line width=1pt,color=black] (0.35,-0.5) ellipse (.085 and .115)node [below ] {$\gamma_2$};
\draw[line width=1pt] (-1,0) .. controls(-.7,-.25) ..(1,-0.5)node[above] {$p$};
\draw[line width=1pt] (-1,-1) .. controls(-.75,-.75) ..(1,-0.5);
\draw[line width=1pt] (4,0) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(8,-.15);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(8,-.85);
\draw[line width=1pt,color=gray] (8,-.5) ellipse (.15 and .35);
\draw[line width=1pt] (4.75,-.75) .. controls(5.25,-1.15) and (5.75,-1.15) ..(6.25,-.75);
\draw[line width=1pt] (4.75,-.35) .. controls(5.25,0.1) and (5.75,0.1) ..(6.25,-.35);
\draw[line width=1pt] (4.75,-.35) .. controls(4.65,-.475) and (4.65,-.625) ..(4.75,-.75);
\draw[line width=1pt] (6.25,-.35) .. controls(6.35,-.475) and (6.35,-.625) ..(6.25,-.75);
\draw[line width=1pt] (4,0) .. controls(3.5,-.4) ..(2,-0.5)node[above] {$q$};
\draw[line width=1pt] (4,-1) .. controls(3.5,-.65) ..(2,-0.5);
\draw[line width=.75pt,color=gray] (3.35,-0.525) ellipse (.1 and .145);
\draw[line width=1pt,color=black] (3,-0.525) ellipse (.075 and .115)node [below ] {$\gamma_1$};
\draw (-3.75,.5) node[above ] {$\beta_2$} (-3.75,-2) node[above] {$\beta_1$} (8.2,-.2)node [below right ] {$\beta_3$};
\draw[->,line width =1pt] (9.5,-.5)--(10.5,-.5);
%
\draw[line width=1pt] (12.65,1) .. controls (14.15,.8) and (13.85,.35) ..(14.65,0);
\draw[line width=1pt] (12.65,-2) .. controls(14.5,-1.8) and (13.85,-1.35) ..(14.65,-1);
\draw[line width=1pt] (12.65,.4) .. controls(13.85,.5) and (14.40,-1.2) ..(12.65,-1.4);
\draw[line width=1pt,color=gray] (12.65,.7) ellipse (.115 and .315);
\draw[line width=1pt,color=gray] (12.65,-1.7) ellipse (.115 and .315);
\draw[line width=.75pt,color=gray] (15.65,-0.52) ellipse (.115 and .2);
\draw[line width=1pt,color=black] (16,-0.525) ellipse (.085 and .115)node [below ] {$\gamma$};
\draw[line width=1pt] (14.65,0) .. controls(14.9,-.15) ..(16.05,-0.4);
\draw[line width=1pt] (14.65,-1) .. controls(14.9,-.85) ..(16.05,-0.65);
\draw[line width=1pt] (17,0) .. controls(18,1) and (19,1) ..(20,0);
\draw[line width=1pt] (17,-1) .. controls(18,-2) and (19,-2) ..(20,-1);
\draw[line width=1pt] (20,0) .. controls(20.2,-.15) ..(21,-.15);
\draw[line width=1pt] (20,-1) .. controls(20.2,-.85) ..(21,-.85);
\draw[line width=1pt,color=gray] (21,-.5) ellipse (.15 and .35);
\draw[line width=1pt] (17.75,-.75) .. controls(18.25,-1.15) and (18.75,-1.15) ..(19.25,-.75);
\draw[line width=1pt] (17.75,-.35) .. controls(18.25,0.1) and (18.75,0.1) ..(19.25,-.35);
\draw[line width=1pt] (17.75,-.35) .. controls(17.65,-.475) and (17.65,-.625) ..(17.75,-.75);
\draw[line width=1pt] (19.25,-.35) .. controls(19.35,-.475) and (19.35,-.625) ..(19.25,-.75);
\draw[line width=1pt] (17,0) .. controls(16.5,-.4) ..(16.05,-0.4);
\draw[line width=1pt] (17,-1) .. controls(16.5,-.65) ..(16.05,-0.65);
\draw[line width=.75pt,color=gray] (16.35,-0.54) ellipse (.1 and .15);
\draw[line width=1pt,color=black] (16,-0.525) ellipse (.075 and .115);
\draw (12.15,.5) node[above ] {$\beta_2$} (12.15,-2) node[above ] {$\beta_1$} (21.2,-.2)node [below right ] {$\beta_3$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Dual triangulation of the two-dimensional moduli space. Each co-dimension one face (i.e. an edge) is shared by two polyhedra and each co-dimension two face (i.e. a vertex) is shared by three polyhedra. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}
\draw[line width=2pt] (1.5,-1) -- (2,1);
\draw[line width=2pt] (1.5,-1) -- (2,-1.5);
\draw[line width=2pt] (2,1) -- (-1,2);
\draw[line width=2pt] (-1,2) -- (-1,-1);
\draw[line width=2pt] (-1,-1) -- (-1.5,-1.5);
\draw[line width=2pt] (-1,-1) -- (1.5,-1);
\draw[line width=2pt] (2,1) -- (3,3);
\draw[line width=2pt] (1.75,0) -- (5,1);
\draw[line width=2pt] (-1,2) -- (-3,4);
\draw[line width=2pt] (-3,4) -- (-4,-1);
\draw[line width=2pt] (-4,-1) -- (-1,0);
\draw[line width=2pt] (-3.8,0) -- (-5,3);
\draw[line width=2pt] (-3,4) -- (3,3);
\draw[line width=2pt] (-4,-1) -- (-4.5,-1.5);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Cone with infinite length representing the covering space M_0,4^. Thick gray circle having radius _2 corresponds to the range of twist parameter associated with curve having length _. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.875]
\draw[line width=1pt,->] (.5,.6)--(5,3);
\draw[line width=1pt,->] (.5,.6) --(5,-1.4);
\draw[gray, line width=1.5pt, style=dashed] (3.65,.75) ellipse (.25 and 1.5);
\draw[ line width=1pt] (4.75,.8) ellipse (.25 and 2.07);
\draw[->](3.65,.75)--(3.65,2.25);
\draw (3.75,1) node[above right] {$\frac{\ell_{\gamma}}{2\pi}$} ;
\draw[->](.5,.75)--(3.65,2.4);
\draw (2,2) node[above right] {$\ell_{\gamma}$} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Cutting the surface along curve _1+_2 produces a pair of pants and genus 1 surface with 5 borders. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.9]
\draw[line width=1pt] (1,1) .. controls (1.75,1) and (2.25,.75) ..(2.75,.2);
\draw[line width=1pt] (1,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (1,.4) .. controls(1.7,0) and (1.7,-1) ..(1,-1.4);
\draw[gray,line width=1pt] (1,.7) ellipse (.115 and .315);
\draw[gray,line width=1pt] (1,-1.7) ellipse (.115 and .315);
\draw[line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0.2) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (2.75,0.2) .. controls(3,0.05) and (3.1,0.2) ..(3,1.5);
\draw[line width=1pt] (4,0.2) .. controls(3.8,0.05) and (3.6,0.2) ..(3.7,1.5);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(8,-.15);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(8,-.85);
\draw[gray, line width=1pt] (8,-.5) ellipse (.15 and .35);
\draw[gray, line width=1pt] (3.35,1.5) ellipse (.35 and .15);
\draw[line width=1pt] (4.75,-.75) .. controls(5.25,-1.1) and (5.75,-1.1) ..(6.25,-.75);
\draw[line width=1pt] (4.75,-.35) .. controls(5.25,0.1) and (5.75,0.1) ..(6.25,-.35);
\draw[line width=1pt] (4.75,-.35) .. controls(4.65,-.475) and (4.65,-.625) ..(4.75,-.75);
\draw[line width=1pt] (6.25,-.35) .. controls(6.35,-.475) and (6.35,-.625) ..(6.25,-.75);
\draw[line width =1.2pt, color=gray] [rotate around={160:(3.7,-.2)}] (3.7,-.2) ellipse (1 and .15);
\draw[line width =1.2pt, color=gray] (5.5,.35) ellipse (.15 and .4);
\draw[line width=1pt] (2.2,-.5) ellipse (.25 and .4);
\draw (0.25,.5) node[above right] {$\beta_2$} (0.25,-2) node[above right] {$\beta_3$} (8.2,-.2)node [below right ] {$\beta_4$} (3.2,1.5)node [above right ] {$\beta_1$} (3.5,-.3) node [below right ] {$\alpha_1$} (5.55,.5) node [below right ] {$\alpha_2$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Cone with infinite length representing the covering space M_1,1^. Thick gray circle having radius _2 corresponds to the range of twist parameter associated with curve having length _ | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.875]
\draw[line width=1pt,->] (.5,.6)--(5,3);
\draw[line width=1pt,->] (.5,.6) --(5,-1.4);
\draw[gray, line width=1.5pt, style=dashed] (3.65,.75) ellipse (.25 and 1.5);
\draw[ line width=1pt] (4.75,.8) ellipse (.25 and 2.07);
\draw[->](3.65,.75)--(3.65,2.25);
\draw (3.75,1) node[above right] {$\frac{\ell_{\tilde\gamma}}{2\pi}$} ;
\draw[->](.5,.75)--(3.65,2.4);
\draw (2,2) node[above right] {$\ell_{\tilde\gamma}$} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Cutting the surface along curve =_1+_2. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.875]
\draw[line width=1pt] (1,1) .. controls (1.75,1) and (2.25,.75) ..(3,0);
\draw[line width=1pt] (1,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (1,.4) .. controls(2.75,.2) and (2.75,-1.2) ..(1,-1.4);
\draw[gray, line width=1pt] (1,.7) ellipse (.115 and .315);
\draw[gray, line width=1pt] (1,-1.7) ellipse (.115 and .315);
\draw[line width=1pt] (3,0) .. controls(3.3,-.25) and (3.75,-.25) ..(4,0);
\draw[line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(8,-.15);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(8,-.85);
\draw[gray, line width=1pt] (8,-.5) ellipse (.15 and .35);
\draw[line width=1pt] (4.75,-.75) .. controls(5.25,-1.15) and (5.75,-1.15) ..(6.25,-.75);
\draw[line width=1pt] (4.75,-.35) .. controls(5.25,0.1) and (5.75,0.1) ..(6.25,-.35);
\draw[line width=1pt] (4.75,-.35) .. controls(4.65,-.475) and (4.65,-.625) ..(4.75,-.75);
\draw[line width=1pt] (6.25,-.35) .. controls(6.35,-.475) and (6.35,-.625) ..(6.25,-.75);
\draw[line width =1pt, color=gray] (3.5,-.5) ellipse (1.2 and .15);
\draw[line width =1pt, color=gray] (5.5,-1.39) ellipse (.15 and .35);
\draw (0.25,.5) node[above right] {$\beta_2$} (0.25,-2) node[above right] {$\beta_1$} (8.2,-.2)node [below right ] {$\beta_3$} (3.5,-.25) node [below right ] {$\gamma_1$} (5.55,-1.25) node [below right ] {$\gamma_2$};
\draw[->,line width =1pt] (9,-.5)--(9.8,-.5);
%
\draw[line width=1pt] (11,1) .. controls (11.75,1) and (12.25,.75) ..(13,0);
\draw[line width=1pt] (11,.4) .. controls(12,.2) and (12.4,-.5) ..(12.3,-.5);
\draw[line width=1pt] (9.95,-2.2) .. controls(10.5,-1.4) and (10.4,-1.2) ..(10.4,-1.2);
\draw[line width=1pt] (12.4,-1.2) .. controls(12.3,-1.4) and (12.8,-1.9) ..(13.1,-2.2);
\draw[line width=1pt] (10,-2.85) .. controls(11,-1.75) and (12,-1.75) ..(13,-2.85);
\draw[gray, line width=1pt] (11,.7) ellipse (.115 and .315);
\draw[gray, line width=1pt] (10,-2.5) ellipse (.115 and .315);
\draw[line width=1pt] (13,0) .. controls(13.3,-.25) and (13.75,-.25) ..(14,0);
\draw[line width=1pt] (14,0) .. controls(15,1) and (16,1) ..(17,0);
\draw[line width=1pt] (15.5,-1.75) .. controls(16.2,-1.6) ..(17,-1);
\draw[line width=1pt] (17,0) .. controls(17.2,-.15) ..(18,-.15);
\draw[line width=1pt] (17,-1) .. controls(17.2,-.85) ..(18,-.85);
\draw[gray, line width=1pt] (18,-.5) ellipse (.15 and .35);
\draw[line width=1pt] (15.5,-1.02) .. controls(16.1,-.9) ..(16.25,-.75);
\draw[line width=1pt] (14.7,-.45) .. controls(15.25,0.1) and (15.75,0.1) ..(16.25,-.35);
\draw[line width=1pt] (16.25,-.35) .. controls(16.35,-.475) and (16.35,-.625) ..(16.25,-.75);
\draw[line width =1pt, color=gray] (13.5,-.5) ellipse (1.2 and .15);
\draw[line width =1pt, color=gray] (11.4,-1.2) ellipse (1 and .15);
\draw[line width =1pt, color=gray] (15.5,-1.39) ellipse (.15 and .35);
\draw[line width =1pt, color=gray] (13,-2.475) ellipse (.15 and .35);
\draw (10.25,.5) node[above right] {$\beta_2$} (9,-2.8) node[above right] {$\beta_1$} (18.2,-.2)node [below right ] {$\beta_3$} (13.5,-.5) node [below right ] {$\gamma^1_1$} (14.65,-1.2) node [below right ] {$\gamma^1_2$} (11,-.3) node [below right ] {$\gamma^2_1$} (13.2,-2.2) node [below right ] {$\gamma^2_2$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Cutting the surface along curve _2 produces a pair of pants and a genus 2 surface with 3 borders. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.9]
\draw[line width=1pt] (1,1) .. controls (1.75,1) and (2.25,.75) ..(2.75,.2);
\draw[line width=1pt] (1,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (1,.4) .. controls(1.7,0) and (1.7,-1) ..(1,-1.4);
\draw[gray, line width=1pt] (1,.7) ellipse (.115 and .315);
\draw[gray, line width=1pt] (1,-1.7) ellipse (.115 and .315);
\draw[line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0.2) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (2.75,0.2) .. controls(3,0.05) and (3.1,0.2) ..(3,1.5);
\draw[line width=1pt] (4,0.2) .. controls(3.8,0.05) and (3.6,0.2) ..(3.7,1.5);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(8,-.15);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(8,-.85);
\draw[gray, line width=1pt] (8,-.5) ellipse (.15 and .35);
\draw[gray, line width=1pt] (3.35,1.5) ellipse (.35 and .15);
\draw[line width=1pt] (4.75,-.75) .. controls(5.25,-1.1) and (5.75,-1.1) ..(6.25,-.75);
\draw[line width=1pt] (4.75,-.35) .. controls(5.25,0.1) and (5.75,0.1) ..(6.25,-.35);
\draw[line width=1pt] (4.75,-.35) .. controls(4.65,-.475) and (4.65,-.625) ..(4.75,-.75);
\draw[line width=1pt] (6.25,-.35) .. controls(6.35,-.475) and (6.35,-.625) ..(6.25,-.75);
\draw[line width =1.2pt, color=gray] [rotate around={5:(2.7,.0)}] (2.7,.0) ellipse (1.25 and .08);
\draw[line width=1pt] (2.2,-.6) ellipse (.25 and .4);
\draw (0.25,.5) node[above right] {$\beta_2$} (0.25,-2) node[above right] {$\beta_3$} (8.2,-.2)node [below right ] {$\beta_4$} (3.2,1.5)node [above right ] {$\beta_1$} (2.5,-.1) node [below right ] {$\gamma_2$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Cutting the surface along curve _1+_2 produces a pair of pants, a genus 1 surface with 3 borders and a genus 1 surface with 2 borders. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.9]
\draw[line width=1pt] (1,1) .. controls (1.75,1) and (2.25,.75) ..(2.75,.2);
\draw[line width=1pt] (1,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (1,.4) .. controls(1.7,0) and (1.7,-1) ..(1,-1.4);
\draw[gray, line width=1pt] (1,.7) ellipse (.115 and .315);
\draw[gray,line width=1pt] (1,-1.7) ellipse (.115 and .315);
\draw[gray, line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0.2) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (2.75,0.2) .. controls(3,0.05) and (3.1,0.2) ..(3,1.5);
\draw[line width=1pt] (4,0.2) .. controls(3.8,0.05) and (3.6,0.2) ..(3.7,1.5);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(8,-.15);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(8,-.85);
\draw[gray, line width=1pt] (8,-.5) ellipse (.15 and .35);
\draw[gray, line width=1pt] (3.35,1.5) ellipse (.35 and .15);
\draw[line width=1pt] (4.75,-.75) .. controls(5.25,-1.1) and (5.75,-1.1) ..(6.25,-.75);
\draw[line width=1pt] (4.75,-.35) .. controls(5.25,0.1) and (5.75,0.1) ..(6.25,-.35);
\draw[line width=1pt] (4.75,-.35) .. controls(4.65,-.475) and (4.65,-.625) ..(4.75,-.75);
\draw[line width=1pt] (6.25,-.35) .. controls(6.35,-.475) and (6.35,-.625) ..(6.25,-.75);
\draw[line width =1.2pt, color=gray] (2.8,-.48) ellipse (.15 and .65);
\draw[line width =1.2pt, color=gray] (4.15,.-.46) ellipse (.15 and .68);
\draw[line width=1pt] (2.2,-.5) ellipse (.25 and .4);
\draw (0.25,.5) node[above right] {$\beta_2$} (0.25,-2) node[above right] {$\beta_3$} (8.2,-.2)node [below right ] {$\beta_4$} (3.2,1.5)node [above right ] {$\beta_1$} (2,-1.5) node [above right ] {$\alpha_1$} (4.3,-1.5) node [above right ] {$ \alpha_2$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Triangulation of the two-dimensional moduli space | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}
\node[right=3pt] (0,0) {$p_{ijk}$};
\node at (-2,-.2) {$T_i$};
\node at (0,2) {$T_j$};
\node at (2,-.2) {$T_k$};
\draw[line width=2pt] (0,0) -- node[align=center,below,xshift=-.1cm]{$B_{ij}$} (-2,2);
\draw[line width=2pt] (0,0) -- node[align=center,below,xshift=.2cm]{$B_{jk}$} (2,2);
\draw[line width=2pt] (0,0) -- node[align=center,left]{$B_{ki}$} (0,-2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Curve on one punctured torus. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.5]
%Torus with one border 2
\draw[black, very thick] (14,-.1) to[curve through={(11,-1)..(9,-3)..(4,0)..(9,3)..(11,1)}] (14,.1);
\draw[black, very thick] (9.5,0) to[curve through={(8.5,1)..(7,1)}] (6,0);
\draw[black, very thick] (9.7,.2) to[curve through={(8.5,-.75)..(7,-.75)}] (5.8,.2);
\draw[gray, very thick](14,0) ellipse (.1 and .1);
%B cycle
\draw[ line width=1.5pt](7.55,-2.2) ellipse (.5 and 1.28);
\draw (7.55,-3.5) node[below] {$\tilde\gamma$} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Pair of pants decomposition of genus 2 surface with 3 punctures. P_i, denotes pair of pants with local coordinate z_i inside P_i for i=1,,5. D_i denote the disc around the i^th puncture having unit radius with respect to the local coordinate w_i defined around the i^th puncture for i=1,2,3. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.45]
%Riemann surface
\draw[black, thick] (0,2) to[curve through={(1,2.2)..(3,3)..(8,0) .. (3,-3) ..(0,-2) .. (-3,-3)..(-8,0)..(-3,3)..(-1,2.2)}] (0,2);
\draw[black, thick] (2.5,0) to[curve through={(3.5,1)..(5,1)}] (6,0);
\draw[black, thick] (2.3,.2) to[curve through={(3.5,-.75)..(5,-.75)}] (6.2,.2);
\draw[black, thick] (-2.5,0) to[curve through={(-3.5,1)..(-5,1)}] (-6,0);
\draw[black, thick] (-2.3,.2) to[curve through={(-3.5,-.75)..(-5,-.75)}] (-6.2,.2);
\draw[black, very thick] (-5,2) ellipse (.06 and .06);
\draw[black, very thick] (-5,-2) ellipse (.06 and .06);
\draw[black, very thick] (7,0) ellipse (.06 and .06);
\draw[black, very thick] (5,2.1) ellipse (.5 and 1);
\draw[black, very thick] (5,-1.95) ellipse (.5 and 1.1);
\draw[black, very thick] (-3.2,1.95) ellipse (.5 and 1);
\draw[black, very thick] (-3.2,-1.85) ellipse (.5 and 1.1);
\draw[black, very thick] (0,0) ellipse (.5 and 2);
\draw[black, very thick] (-7,0) ellipse (1 and .75);
\draw[gray, very thick] (-5,2.05) ellipse (.7 and .7);
\draw[gray, very thick] (-5,-1.95) ellipse (.7 and .7);
\draw[gray, very thick] (7,0) ellipse (.7 and .7);
\draw node[above] at (-5,3) {$D_1$};
\draw node[below] at (-5,-3) {$D_2$};
\draw node[right] at (8,0) {$D_3$};
\draw node[below right] at (-7.5,2.3) {$P_1$};
\draw node[above right] at (-7.5,-2.3) {$P_2$};
\draw node[above ] at (1.5,-.7) {$P_4$};
\draw node[above ] at (-1.5,-.7) {$P_3$};
\draw node[below ] at (6.5,-.7) {$P_5$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Vertical segment for a two dimensional moduli space. $s_i(m)$ and $s_j(m)$ are sections over $T_i$ and $T_j$. The definition of a vertical segment involves the choice of a curve $P_{ij}(m,v)$ in $\mathcal{R}(m^*)$ that connects sections $s_i(m^*)$ and $s_j(m^*)$ over $m^*\in B_{ij}$. For a fixed $m^*\in B_{ij}$, as the parameter $v$ changes over the interval $\left[0,1\right]$, the curve connects the two sections $s_i(m^*)$ and $s_j(m^*)$ over $m^*$. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}
\coordinate (1) at (-2,0);
\coordinate (2) at (2,0);
\coordinate (3) at (0,-3.9);
\node[below] at (0,-3.9) {$m^*\in B_{ij}$};
\node[above,yshift=.1cm] at (-2,0) {$s_i(m^*)$};
\node[above,yshift=.1cm] at (2,0) {$s_j(m^*)$};
\filldraw (0,-3.9) circle (1.5pt);
\filldraw (-2,0) circle (1.5pt);
\filldraw (2,0) circle (1.5pt);
\draw[line width=1pt] (-3,0) ellipse (60pt and 39pt) node[left]{$s_i(m)$};
\draw[line width=1pt] (3,0) ellipse (60pt and 39pt) node[right]{$s_j(m)$};
\draw [line width=1pt,style=dashed] (-2,0) to [out=20,in=160] (0,0) node[above]{$P_{ij}(m,v)$} to [out=-20,in=-160] (2,0);
\draw[line width=2pt] (-6,-5) -- (-4,-3) -- (5,-3) -- (3,-5) -- node[align=center,below]{$\mathcal{M}_{g,n}$} cycle;
\draw[line width=1pt] (-3,-4.5) -- (2,-3.5);
\draw[line width=1pt] (3) -- (1);
\draw[line width=1pt] (3) -- (2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Curves _2,_3 and _4 on sphere with four borders. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.6]
\draw[black, very thick] (20,-2) to[curve through={(21,0)}] (20,2);
\draw[black, very thick] (26,-2) to[curve through={(25,0)}] (26,2);
\draw[black,very thick] (20.5,-3) to[curve through={(23,-2)}] (25.5,-3);
\draw[black,very thick] (20.5,3) to[curve through={(23,2)}] (25.5,3);
\draw[gray,very thick](20.25,-2.5) ellipse (.3 and .6);
\draw[gray,very thick](20.25,2.5) ellipse (.3 and .6);
\draw[gray,very thick](25.75,-2.5) ellipse (.3 and .6);
\draw[gray,very thick](25.75,2.5) ellipse (.3 and .6);
\draw node[below] at (23,-2) {$\gamma_4$};
\draw node[below] at (20.5,.5) {$\gamma_2$};
\draw node[below] at (26,1.5) {$\gamma_3$};
\draw node[below right] at (19,-3.5) {$\beta_1$};
\draw node[left] at (27.5,-3.5) {$\beta_2$};
\draw node[left] at (27.5,4) {$\beta_3$};
\draw node[left] at (20.5,4) {$\beta_4$};
%B Cycle
\draw[line width=1.5pt](23,0) ellipse (.5 and 2);
\draw[ line width=1.5pt, rotate around={95:(23,0)}](23,0) ellipse (.5 and 2);
\draw[ line width=1.5pt, rotate around={133:(23,0)}](23,0) ellipse (1 and 3.3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Fenchel-Nielsen coordinate vector fields _i are the twist vector fields associated with curve C_i and Fenchel-Nielsen coordinate vector fields _i are the twist vector fields associated with curve C_i | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.65]
%Torus with two border 3
\draw[black, very thick] (27.5,-4) to[curve through={(25,-2.5)..(20,0)..(25,2.5)}] (27.5,4);
\draw[black, very thick] (25.5,0) to[curve through={(24.5,.5)..(23,.5)}] (22,0);
\draw[black, very thick] (25.7,.2) to[curve through={(24.5,-.5)..(23,-.5)}] (21.8,.2);
\draw[black, very thick] (28,-2.5) to[curve through={(27.5,-1)..(27.5,1)}] (28,2.5);
\draw[gray, very thick](27.75,3.25) ellipse (.5 and .75);
\draw[gray, very thick](27.75,-3.25) ellipse (.5 and .75);
\draw node[below] at (22,-2) {$\tilde C_2$};
\draw node[below] at (28,0.5) {$ C_1$};
\draw node[below] at (19.5,0.5) {$ C_2$};
\draw node[below] at (26.5,-3.5) {$\tilde C_1$};
% Cycles
\draw[very thick,style=dashed](26.5,0) ellipse (.95 and .3);
\draw[very thick,style=dashed](21,0) ellipse (.95 and .3);
\draw[very thick](26.5,0) ellipse (.3 and 3.1);
\draw[ very thick] (27.5,-1.5) to[curve through={(26.5,-2.25)..(25,-1.75)..(20.5,0)..(25,1.75)..(26.5,2.25)}] (27.5,1.5);
\draw[ very thick] (27.55,-1.5) to[curve through={(27.1,-.9)..(25,-.75)..(21.5,0)..(25,.75)..(27.1,.9)}] (27.55,1.5);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Cutting the surface along curve _1,1+_2,1 produces a pair of pants with one puncture and 2 borders, a genus 1 surface with 2 punctures and one border and a genus 1 surface with one puncture and one border. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.9]
\draw[line width=1pt] (0,1) .. controls (1.75,1) and (2.25,.75) ..(2.75,.2);
\draw[line width=1pt] (0,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (0,.9) to[curve through={(.95,-0.05)..(1,-.15)..(1,-.85)..(.95,-.95)}] (0,-1.9);
\draw[gray, line width=1pt] (0,.95) ellipse (.05 and .05);
\draw[gray,line width=1pt] (0,-1.95) ellipse (.05 and .05);
\draw[line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0.2) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (2.75,0.2) .. controls(3,0.05) and (3.1,0.2) ..(3.3,2.5);
\draw[line width=1pt] (4,0.2) .. controls(3.8,0.05) and (3.6,0.2) ..(3.4,2.5);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(9,-.45);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(9,-.55);
\draw[gray, line width=1pt] (9,-.5) ellipse (.05 and .05);
\draw[gray, line width=1pt] (3.35,2.5) ellipse (.05 and .05);
\draw[line width=1pt] (4.5,-.35) .. controls(5.25,-1.1) and (5.75,-1.1) ..(6.5,-.35);
\draw[line width=1pt] (4.65,-.45) .. controls(5.25,0.1) and (5.75,0.1) ..(6.35,-.45);
\draw[line width=1pt] (2,0) .. controls(2.5,-.3) and (2.5,-.8) ..(2,-1.1);
\draw[line width=1pt] (2,0.1) .. controls(1.5,-.3) and (1.5,-.8) ..(2,-1.2);
\draw (0,.75) node[above left] {$\beta_2$} (0,-2.25) node[above left] {$\beta_3$} (9.2,-.2)node [below right ] {$\beta_4$} (3.2,2.5)node [above right ] {$\beta_1$} (2.5,-2) node [above right ] {$\alpha_{1,1}$} (3.6,-2) node [above right ] {$ \alpha_{2,1}$};
\draw[line width =1.2pt, color=gray] (2.8,-.48) ellipse (.15 and .65);
\draw[line width =1.2pt, color=gray] (4.15,.-.46) ellipse (.15 and .68);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Cutting the surface along curve _2 produces a pair of pants with 2 punctures and one border and a genus 2 surface with 2 punctures and one border. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.9]
\draw[line width=1pt] (0,1) .. controls (1.75,1) and (2.25,.75) ..(2.75,.5);
\draw[line width=1pt] (0,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (0,.9) to[curve through={(.95,-0.05)..(1,-.15)..(1,-.85)..(.95,-.95)}] (0,-1.9);
\draw[gray, line width=1pt] (0,.95) ellipse (.05 and .05);
\draw[gray,line width=1pt] (0,-1.95) ellipse (.05 and .05);
\draw[line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0.5) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (2.75,0.5) .. controls(3,0.35) and (3.1,1) ..(3.3,2.5);
\draw[line width=1pt] (4,0.5) .. controls(3.8,0.35) and (3.6,0.2) ..(3.4,2.5);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(9,-.45);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(9,-.55);
\draw[gray, line width=1pt] (9,-.5) ellipse (.05 and .05);
\draw[gray, line width=1pt] (3.35,2.5) ellipse (.05 and .05);
\draw[line width=1pt] (4.5,-.35) .. controls(5.25,-1.1) and (5.75,-1.1) ..(6.5,-.35);
\draw[line width=1pt] (4.65,-.45) .. controls(5.25,0.1) and (5.75,0.1) ..(6.35,-.45);
\draw[line width=1pt] (2,0) .. controls(2.5,-.3) and (2.5,-.8) ..(2,-1.1);
\draw[line width=1pt] (2,0.1) .. controls(1.5,-.3) and (1.5,-.8) ..(2,-1.2);
\draw (0,.75) node[above left] {$\beta_2$} (0,-2.25) node[above left] {$\beta_3$} (9.2,-.2)node [below right ] {$\beta_4$} (3.2,2.5)node [above right ] {$\beta_1$} (0.2,.3) node [below right ] {$\gamma_2$};
\draw[line width =1.2pt, color=gray] [rotate around={8:(2.4,.2)}] (2.4,.2) ellipse (1.5 and .09);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Cutting the surface along curve _1,2+_2,2 produces a pair of pants with one puncture and 2 borders and genus 1 surface with 3 punctures and 2 borders. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.9]
\draw[line width=1pt] (0,1) .. controls (1.75,1) and (2.25,.75) ..(2.75,.2);
\draw[line width=1pt] (0,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (0,.9) to[curve through={(.95,-0.05)..(1,-.15)..(1,-.85)..(.95,-.95)}] (0,-1.9);
\draw[gray, line width=1pt] (0,.95) ellipse (.05 and .05);
\draw[gray,line width=1pt] (0,-1.95) ellipse (.05 and .05);
\draw[line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0.2) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (2.75,0.2) .. controls(3,0.05) and (3.1,0.2) ..(3.3,2.5);
\draw[line width=1pt] (4,0.2) .. controls(3.8,0.05) and (3.6,0.2) ..(3.4,2.5);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(9,-.45);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(9,-.55);
\draw[gray, line width=1pt] (9,-.5) ellipse (.05 and .05);
\draw[gray, line width=1pt] (3.35,2.5) ellipse (.05 and .05);
\draw[line width=1pt] (4.5,-.35) .. controls(5.25,-1.1) and (5.75,-1.1) ..(6.5,-.35);
\draw[line width=1pt] (4.65,-.45) .. controls(5.25,0.1) and (5.75,0.1) ..(6.35,-.45);
\draw[line width=1pt] (2,0) .. controls(2.5,-.3) and (2.5,-.8) ..(2,-1.1);
\draw[line width=1pt] (2,0.1) .. controls(1.5,-.3) and (1.5,-.8) ..(2,-1.2);
\draw (0,.75) node[above left] {$\beta_2$} (0,-2.25) node[above left] {$\beta_3$} (9.2,-.2)node [below right ] {$\beta_4$} (3.2,2.5)node [above right ] {$\beta_1$} (3.5,-.4) node [below right ] {$\alpha_{1,2}$} (5.55,.5) node [below right ] {$ \alpha_{2,2}$};
\draw[line width =1.2pt, color=gray] [rotate around={160:(3.7,-.2)}] (3.7,-.2) ellipse (1 and .15);
\draw[line width =1.2pt, color=gray] (5.5,.35) ellipse (.15 and .4);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
All curves _2, _1,1+_2,1, _1,2+_2,2 intersect each other. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.9]
\draw[line width=1pt] (0,1) .. controls (1.75,1) and (2.25,.75) ..(2.75,.5);
\draw[line width=1pt] (0,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (0,.9) to[curve through={(.95,-0.05)..(1,-.15)..(1,-.85)..(.95,-.95)}] (0,-1.9);
\draw[gray, line width=1pt] (0,.95) ellipse (.05 and .05);
\draw[gray,line width=1pt] (0,-1.95) ellipse (.05 and .05);
\draw[line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0.5) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (2.75,0.5) .. controls(3,0.35) and (3.1,1) ..(3.3,2.5);
\draw[line width=1pt] (4,0.5) .. controls(3.8,0.35) and (3.6,0.2) ..(3.4,2.5);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(9,-.45);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(9,-.55);
\draw[gray, line width=1pt] (9,-.5) ellipse (.05 and .05);
\draw[gray, line width=1pt] (3.35,2.5) ellipse (.05 and .05);
\draw[line width=1pt] (4.5,-.35) .. controls(5.25,-1.1) and (5.75,-1.1) ..(6.5,-.35);
\draw[line width=1pt] (4.65,-.45) .. controls(5.25,0.1) and (5.75,0.1) ..(6.35,-.45);
\draw[line width=1pt] (2,0) .. controls(2.5,-.3) and (2.5,-.8) ..(2,-1.1);
\draw[line width=1pt] (2,0.1) .. controls(1.5,-.3) and (1.5,-.8) ..(2,-1.2);
\draw (0,.75) node[above left] {$\beta_2$} (0,-2.25) node[above left] {$\beta_3$} (9.2,-.2)node [below right ] {$\beta_4$} (3.2,2.5)node [above right ] {$\beta_1$} (0.2,.3) node [below right ] {$\gamma_2$}(2.3,-1.4) node [below right ] {$\alpha_{1,1}$}(3.8,-1.4) node [below right ] {$\alpha_{2,1}$}(3,-.05) node [below right ] {$\alpha_{1,2}$}(4.7,1.3) node [below right ] {$\alpha_{2,2}$};
\draw[line width =1.2pt, color=gray] [rotate around={8:(2.4,.2)}] (2.4,.2) ellipse (1.5 and .09);
\draw[line width =1.2pt, style=dashed] (4.1,-.275) ellipse (.15 and .825);
\draw[line width =1.2pt, style=dashed] (2.6,-.4) ellipse (.13 and 1);
\draw[line width =1.2pt, color=black] (5,.3) ellipse (.2 and .5);
\draw[line width =1.2pt, color=black] [rotate around={60:(3.75,0)}] (3.75,0) ellipse (.15 and 1);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Mapping the fundamental domain of a torus to conformal plane using an automorphic function f(z) that us with respect to the group generated by the transformation z z+1. Functions h_i(w_i) denote the conformal mappings that maps a unit circle on w_i plane with centre at the origin to curve C_i for i=1,2. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.4]
% Polygon
\draw[ thick] (-30,-6)--(-10,-6);
\draw[ thick] (-30,-6)--(-30,6);
\draw[ gray, very thick] (-30,-6)--(-25,0);
\draw[ gray, very thick] (-20,-6)--(-15,0);
\draw[ very thick] (-30,-6)--(-20,-6);
\draw[ very thick] (-25,0)--(-15,0);
\draw node [above] at (-20,1.25) {$\tilde\mathcal{C}_2$};
\draw node [below,right] at (-25,-5) {$\tilde\mathcal{C}_1$};
% Arrow
\draw[ thick,->] (-11,0)--(-9,0);
\draw node at (-10,1) {$f(z)=e^{2\pi \mathrm{i} z}$};
% Complex Plane
\draw[ thick] (-8,0)--(7,0);
\draw[ thick] (-.5,-7)--(-.5,7);
\draw[black, very thick] (-.5,0)ellipse (6 and 6);
\draw[black, very thick] (-.5,0)ellipse (3 and 3);
\draw node [above] at (-5.5,4.5) {$\mathcal{C}_2$};
\draw node [above] at (-2,1) {$\mathcal{C}_1$};
% Copies of complex planes
\draw[ thick] (11,3)--(11,7);
\draw[ thick] (9,5)--(13,5);
\draw[black, thick,->] (9,4.5)--(2.5,1.5);
\draw[black, very thick] (11,5) ellipse (1.5 and 1.5);
\draw[ thick] (11,-3)--(11,-7);
\draw[ thick] (9,-5)--(13,-5);
\draw[black, thick,->] (9,-4.5)--(4.5,-3.5);
\draw[black, very thick] (11,-5) ellipse (1.5 and 1.5);
\draw node [above] at (6,4.5) {$h_1(w_1)=w_1$};
\draw node [above] at (7.5,-3.5) {$h_2(w_2)=-\frac{e^{2\pi\mathrm{i}\tau}}{w_2}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Pair of pants decomposition of genus 2 Riemann surface with four borders. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=1]
\draw[line width=1pt] (1,1) .. controls (1.75,1) and (2.25,.75) ..(2.75,.2);
\draw[line width=1pt] (1,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (1,.4) .. controls(1.7,0) and (1.7,-1) ..(1,-1.4);
\draw[gray,line width=1pt] (1,.7) ellipse (.115 and .315);
\draw[gray,line width=1pt] (1,-1.7) ellipse (.115 and .315);
\draw[line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0.2) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (2.75,0.2) .. controls(3,0.05) and (3.1,0.2) ..(3,1.5);
\draw[line width=1pt] (4,0.2) .. controls(3.8,0.05) and (3.6,0.2) ..(3.7,1.5);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(8,-.15);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(8,-.85);
\draw[gray,line width=1pt] (8,-.5) ellipse (.15 and .35);
\draw[gray,line width=1pt] (3.35,1.5) ellipse (.35 and .15);
\draw[line width=1pt] (4.75,-.75) .. controls(5.25,-1.1) and (5.75,-1.1) ..(6.25,-.75);
\draw[line width=1pt] (4.75,-.35) .. controls(5.25,0.1) and (5.75,0.1) ..(6.25,-.35);
\draw[line width=1pt] (4.75,-.35) .. controls(4.65,-.475) and (4.65,-.625) ..(4.75,-.75);
\draw[line width=1pt] (6.25,-.35) .. controls(6.35,-.475) and (6.35,-.625) ..(6.25,-.75);
\draw[line width =1.4pt, ] (2.85,-.48) ellipse (.15 and .65);
\draw[line width =1.4pt, ] (4.05,-.42) ellipse (.15 and .62);
\draw[line width =1.4pt] (2.25,0.25) ellipse (.1 and .35);
\draw[line width =1.4pt] (2.25,-1.25) ellipse (.1 and .35);
\draw[line width =1.4pt] (1.75,-.55) ellipse (.225 and .1);
\draw[line width =1.4pt] (5.5,0.375) ellipse (.1 and .365);
\draw[line width =1.4pt] (5.5,-1.365) ellipse (.1 and .35);
\draw[line width=1pt] (2.2,-.5) ellipse (.25 and .4);
\draw (0.25,.5) node[above right] {$b_2$} (0.25,-2) node[above right] {$b_3$} (8.2,-.2)node [below right ] {$b_4$} (3.2,1.7)node [above right ] {$b_1$} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Ordered coordinate geodesics and pair of pants. Thick gray curves are the coordinates geodesics. L_1 and L_2 are attaching geodesics and L_3 is handle geodesic. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.9]
\draw[line width=1pt] (1,1) .. controls (1.75,1) and (2.25,.75) ..(3,0);
\draw[line width=1pt] (1,-2) .. controls(1.75,-2) and (2.25,-1.75) ..(3,-1);
\draw[line width=1pt] (1,.4) .. controls(2.75,.2) and (2.75,-1.2) ..(1,-1.4);
\draw[gray,line width=1pt] (1,.7) ellipse (.115 and .315);
\draw[gray,line width=1pt] (1,-1.7) ellipse (.115 and .315);
\draw[line width=1pt] (3,0) .. controls(3.3,-.25) and (3.75,-.25) ..(4,0);
\draw[line width=1pt] (3,-1) .. controls(3.3,-.75) and (3.75,-.75) ..(4,-1);
\draw[line width=1pt] (4,0) .. controls(5,1) and (6,1) ..(7,0);
\draw[line width=1pt] (4,-1) .. controls(5,-2) and (6,-2) ..(7,-1);
\draw[line width=1pt] (7,0) .. controls(7.2,-.15) ..(8,-.15);
\draw[line width=1pt] (7,-1) .. controls(7.2,-.85) ..(8,-.85);
\draw[gray,line width=1pt] (8,-.5) ellipse (.15 and .35);
\draw[line width=1pt] (4.75,-.75) .. controls(5.25,-1.15) and (5.75,-1.15) ..(6.25,-.75);
\draw[line width=1pt] (4.75,-.35) .. controls(5.25,0.1) and (5.75,0.1) ..(6.25,-.35);
\draw[line width=1pt] (4.75,-.35) .. controls(4.65,-.475) and (4.65,-.625) ..(4.75,-.75);
\draw[line width=1pt] (6.25,-.35) .. controls(6.35,-.475) and (6.35,-.625) ..(6.25,-.75);
\draw[line width =1.5pt, color=gray] (3.5,-.5) ellipse (1.2 and .15);
\draw[line width =1.5pt, color=gray] (5.5,.375) ellipse (.15 and .375);
\draw[line width =1.5pt, color=gray] (5.5,-1.39) ellipse (.15 and .35);
\draw (2,.5) node[below right] {$P_2$} (2,-1.5) node[above right] {$P_1$} (6.5,-.5)node [ right ] {$P_3$} (3.5,-.25) node [below right ] {$L_1$} (5.55,-1.25) node [ right ] {$L_2$} (5.55,0.5) node [below right ] {$L_3$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
Correlation functions of a conformal field theory on a hyperbolic Riemann surface can be obtained by gluing path integrals over all the pairs of pants in a pair of pants decomposition of the surface. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=1.5]
\draw[line width=1pt] (.7,.75) .. controls (1.75,.35) and (2.25,.25) ..(2.75,.25);
\draw[line width=1pt] (.7,-1.75) .. controls(1.75,-1.35) and (2.25,-1.25) ..(2.75,-1.25);
\draw[line width=1pt] (.7,.35) to[curve through={(.95,-0.05)..(1,-.15)..(1,-.85)..(.95,-.95)}] (.7,-1.35);
\draw[line width=1pt] (-.5,1.25)--(.2,1.05);
\draw[line width=1pt] (-.5,1.15)--(.2,.65);
\draw[gray, line width=1pt] (-.5,1.2) ellipse (.05 and .05);
\draw[gray, line width=1pt] (-.5,-2.1) ellipse (.05 and .05);
\draw[gray, line width=1pt] (2.75,-0.5) ellipse (.2 and .75);
\draw[gray, line width=1pt] (0.7,.55) ellipse (.1 and .2);
\draw[gray, line width=1pt] (0.7,-1.55) ellipse (.1 and .2);
\draw[gray, line width=1pt] (0.2,.85) ellipse (.1 and .2);
\draw[gray, line width=1pt] (0.2,-1.85) ellipse (.1 and .2);
\draw[line width=1pt] (-.5,-2.15)--(.2,-2.05);
\draw[line width=1pt] (-.5,-2.05)--(.2,-1.65);
\draw (-.5,-1.95) node[below left] {$\beta_1$} ;
\draw (-.5,1.2) node[ left] {$\beta_2$} ;
\draw (9.5,-.95) node[above right] {$\beta_3$} ;
\draw[gray, line width=1pt] (3.5,-0.5) ellipse (.2 and .75);
\draw[line width=1pt] (3.5,.25) .. controls (3.75,.35) and (4.25,.75) ..(4.75,1);
\draw[line width=1pt] (3.5,-1.25) .. controls(3.75,-1.35) and (4.25,-1.75) ..(4.75,-2);
\draw[line width=1pt] (4.75,.25) to[curve through={(4.25,-0.35)..(4.25,-.65)}] (4.75,-1.25);
\draw[gray, line width=1pt] (4.75,.625) ellipse (.175 and .375);
\draw[gray, line width=1pt] (4.75,-1.625) ellipse (.175 and .375);
\draw[gray, line width=1pt] (5.75,.625) ellipse (.175 and .375);
\draw[gray, line width=1pt] (5.75,-1.625) ellipse (.175 and .375);
\draw[line width=1pt] (5.75,.25) to[curve through={(6.5,-0.35)..(6.5,-.65)}] (5.75,-1.25);
\draw[line width=1pt] (8.3,-.3) .. controls (7.5,-.2) and (6.5,.85) ..(5.75,1);
\draw[line width=1pt] (8.3,-.7) .. controls(7.5,-.8) and (6.5,-1.85) ..(5.75,-2);
\draw[gray, line width=1pt] (9.5,-.5) ellipse (.05 and .05);
\draw[gray, line width=1pt] (8.3,-.5) ellipse (.1 and .2);
\draw[gray, line width=1pt] (8.6,-.5) ellipse (.1 and .2);
\draw[line width=1pt] (8.6,-.29)--(9.5,-.45);
\draw[line width=1pt] (8.6,-.715)--(9.5,-.55);
\draw (1.5,-.5) node[ right] {$P_1$} ;
\draw (3.6,-.5) node[ right] {$P_2$} ;
\draw (7.5,-.5) node[ left] {$P_3$} ;
\draw (1,-1.25) node[above left] {$\beta^1_1$} ;
\draw (1,-.5) node[above left] {$\beta^1_2$} ;
\draw (2.25,-1.5) node[below right] {$\beta^1_3$} ;
\draw (3.8,-1.35) node[below left] {$\beta^2_1$} ;
\draw (4.5,.25) node[below right] {$\beta^2_2$} ;
\draw (4.5,-1.0) node[above right] {$\beta^2_3$} ;
\draw (6.25,.25) node[below left] {$\beta^3_1$} ;
\draw (8.3,-.6) node[below ] {$\beta^3_3$} ;
\draw (5.5,-1.25) node[above right] {$\beta^3_2$} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
S and A-move | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.325]
%Torus with one border 1
\draw[black, very thick] (0,-2) to[curve through={(-3,-3)..(-8,0)..(-3,3)..(-1,2.2)}] (0,2);
\draw[black, very thick] (-2.5,0) to[curve through={(-3.5,1)..(-5,1)}] (-6,0);
\draw[black, very thick] (-2.3,.2) to[curve through={(-3.5,-.75)..(-5,-.75)}] (-6.2,.2);
\draw[gray, very thick](0,0) ellipse (.5 and 2);
\draw node[below] at (2,-4) {S-move};
%A Cycle
\draw[ very thick](-4,0) ellipse (3 and 2);
% Arrow
\draw[very thick,->] (1,0)--(3,0);
%Torus with one border 2
\draw[black, very thick] (12,-2) to[curve through={(9,-3)..(4,0)..(9,3)..(11,2.2)}] (12,2);
\draw[black, very thick] (9.5,0) to[curve through={(8.5,1)..(7,1)}] (6,0);
\draw[black, very thick] (9.7,.2) to[curve through={(8.5,-.75)..(7,-.75)}] (5.8,.2);
\draw[gray, very thick](12,0) ellipse (.5 and 2);
%B cycle
\draw[ very thick](7.55,-2) ellipse (.5 and 1.05);
%Sphere with four border 1
\draw[black,very thick] (18,-2) to[curve through={(19,0)}] (18,2);
\draw[black,very thick] (24,-2) to[curve through={(23,0)}] (24,2);
\draw[black,very thick] (18.5,-3) to[curve through={(21,-2)}] (23.5,-3);
\draw[black, very thick] (18.5,3) to[curve through={(21,2)}] (23.5,3);
\draw node[below] at (26,-4) {A-move};
\draw[ gray,very thick](18.25,-2.5) ellipse (.3 and .6);
\draw[gray, very thick](18.25,2.5) ellipse (.3 and .6);
\draw[ gray,very thick](23.75,-2.5) ellipse (.3 and .6);
\draw[gray, very thick](23.75,2.5) ellipse (.3 and .6);
%A Cycle
\draw[ very thick](21,0) ellipse (2 and 1);
% Arrow
\draw[very thick,->] (25,0)--(27,0);
%Sphere with four border 2
\draw[black,very thick] (28,-2) to[curve through={(29,0)}] (28,2);
\draw[black, very thick] (34,-2) to[curve through={(33,0)}] (34,2);
\draw[black,very thick] (28.5,-3) to[curve through={(31,-2)}] (33.5,-3);
\draw[black,very thick] (28.5,3) to[curve through={(31,2)}] (33.5,3);
\draw[ gray,very thick](28.25,-2.5) ellipse (.3 and .6);
\draw[gray, very thick](28.25,2.5) ellipse (.3 and .6);
\draw[ gray,very thick](33.75,-2.5) ellipse (.3 and .6);
\draw[ gray,very thick](33.75,2.5) ellipse (.3 and .6);
%B Cycle
\draw[ very thick](31,0) ellipse (1 and 2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.5]
%Torus with one border 1
\draw[black, very thick] (3,-2) to[curve through={(0,-3)..(-5,0)..(0,3)..(2,2.2)}] (3,2);
\draw[black, very thick] (0.5,0) to[curve through={(-0.5,1)..(-2,1)}] (-3,0);
\draw[black, very thick] (.7,.2) to[curve through={(-0.5,-.75)..(-2,-.75)}] (-3.2,.2);
\draw[gray, very thick](3,0) ellipse (.5 and 2);
\draw node[below] at (-1,-4) {(a)};
\draw node[below] at (-1,-3) {$\beta_1$};
\draw node[below] at (2,-1) {$\beta_2$};
\draw node[below] at (-5,-1) {$\beta_3$};
% Cycles
\draw[very thick](-1,0) ellipse (3 and 2);
\draw[very thick, rotate around ={35:(-1.9,0)}](-1.9,0) ellipse (2.9 and 2.2);
\draw[ very thick](-1.45,-2) ellipse (.5 and 1.05);
%Sphere with four border 1
\draw[black,very thick] (8,-2) to[curve through={(8.5,0)}] (7.1,2);
\draw[black,very thick] (14,-2) to[curve through={(13.5,0)}] (14.7,1.9);
\draw[black,very thick] (8.5,-3) to[curve through={(11,-2)}] (13.5,-3);
\draw[black,very thick] (7.5,3) to[curve through={(9.5,3.3 )}] (10.4,4);
\draw[black,very thick] (11.6,4) to[curve through={(13,3.1)}] (14.5,3);
\draw[gray,very thick](8.25,-2.5) ellipse (.3 and .6);
\draw[gray,very thick](7.25,2.5) ellipse (.3 and .6);
\draw[gray,very thick](11,4) ellipse (.6 and .3);
\draw[gray,very thick](13.75,-2.5) ellipse (.3 and .6);
\draw[gray,very thick](14.75,2.5) ellipse (.3 and .6);
\draw node[below] at (11,-4) {(b)};
\draw node[below] at (14.65,1.8) {$\beta_1$};
\draw node[below] at (12,-2) {$\beta_2$};
\draw node[below] at (7.75,-.25) {$\beta_3$};
\draw node[below] at (10,-2) {$\beta_4$};
\draw node[below] at (7.3,1.85) {$\beta_5$};
%A Cycle
\draw[ very thick](11,-1) ellipse (2.6 and .5);
\draw[ very thick, rotate around={25:(10.2,2)}](10.4,2.2) ellipse (2.5 and .5);
\draw[ very thick, rotate around={-25:(11.6,2)}](11.6,2.2) ellipse (2.5 and .5);
\draw[ very thick, rotate around={25:(9.4,.5)}](9.4,.5) ellipse (.5 and 2.7);
\draw[ very thick, rotate around={-25:(12.6,.5)}](12.6,.5) ellipse (.5 and 2.7);
%Sphere with four border 2
\draw[black, very thick] (20,-2) to[curve through={(21,0)}] (20,2);
\draw[black, very thick] (26,-2) to[curve through={(25,0)}] (26,2);
\draw[black,very thick] (20.5,-3) to[curve through={(23,-2)}] (25.5,-3);
\draw[black,very thick] (20.5,3) to[curve through={(23,2)}] (25.5,3);
\draw[gray,very thick](20.25,-2.5) ellipse (.3 and .6);
\draw[gray,very thick](20.25,2.5) ellipse (.3 and .6);
\draw[gray,very thick](25.75,-2.5) ellipse (.3 and .6);
\draw[gray,very thick](25.75,2.5) ellipse (.3 and .6);
\draw node[below] at (23,-4) {(c)};
\draw node[below] at (23,-2) {$\beta_1$};
\draw node[below] at (20.5,.5) {$\beta_2$};
\draw node[below] at (26,2) {$\beta_3$};
%B Cycle
\draw[ very thick](23,0) ellipse (.5 and 2);
\draw[ very thick, rotate around={95:(23,0)}](23,0) ellipse (.5 and 2);
\draw[ very thick, rotate around={133:(23,0)}](23,0) ellipse (1 and 3.3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | ||
Mapping fundamental domain of Fuchsian uniformization corresponding to a pair of pants to conformal plane. Functions h_i(w_i) denote the conformal mapping that maps a unit circle on w_i plane with centre at the origin to curve C_i for i=1,2,3. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.4]
% Polygon
\draw[ thick] (-30,-6)--(-10,-6);
\draw[black, very thick] (-22,-5) to[curve through={(-20,-4)}] (-18,-5);
\draw[gray, very thick] (-24,-4) to[curve through={(-22.5,-4.5)}] (-22,-5);
\draw[black, very thick] (-27,-2) to[curve through={(-24.5,-3)}] (-24,-4);
\draw[gray, very thick] (-28,0)to[curve through={(-27.5,-.5)}] (-27,-2) ;
\draw[black, very thick] (-28,0)to[curve through={(-20,4.25)}] (-12,0) ;
\draw[gray, very thick] (-13,-2)to[curve through={(-12.5,-.5)}] (-12,0) ;
\draw[black, very thick] (-13,-2)to[curve through={(-15.5,-3)}] (-16,-4) ;
\draw[gray, very thick] (-16,-4) to[curve through={(-17.5,-4.5)}] (-18,-5);
\draw node [above] at (-20,4.25) {$\tilde\mathcal{C}_3$};
\draw node [below,right] at (-15.5,-3) {$\tilde\mathcal{C}^1_2$};
\draw node [below,left] at (-24.5,-3) {$\tilde\mathcal{C}^2_2$};
\draw node [below,right ] at (-12.5,-.5) {$\tilde\mathcal{B}_2$};
\draw node [below] at(-20,-4) {$\tilde\mathcal{C}_1$};
\draw node [below,left ] at (-27.5,-.5) {$\tilde\mathcal{B}_2$};
\draw node [below,right] at (-17.5,-5) {$\tilde\mathcal{B}_1$};
\draw node [below,left ] at (-22,-5) {$\tilde\mathcal{B}_1$};
% Arrow
\draw[ thick,->] (-11,0)--(-9,0);
\draw node at (-10,1) {$f(z)$};
% Complex Plane
\draw[ thick] (-8,0)--(7,0);
\draw[ thick] (-.5,-6)--(-.5,6);
\draw[black, very thick] (-6.5,0) to[curve through={(-5.5,4)..(0,5)..(6,0)..(7,-3)..(0,-5)..(-4,-4)}] (-6.5,0);
\draw[black, very thick] (-4,4) to[curve through={(-3.5,4.45)..(-2,4.5)..(0,4)..(-2,3)..(-3,2)..(-4,3)}] (-4,4);
\draw[black, very thick] (4,-4) to[curve through={(3.5,-4.25)..(2,-4.5)..(0,-4)..(2,-3)..(3,-2)..(4,-3)}] (4,-4);
\draw node [above] at (-5.5,4.5) {$\mathcal{C}_3$};
\draw node [above] at (-2,1) {$\mathcal{C}_2$};
\draw node [above] at (2,-2.5) {$\mathcal{C}_1$};
% Copies of complex planes
\draw[ thick] (11,3)--(11,7);
\draw[ thick] (9,5)--(13,5);
\draw[black, thick,->] (9,4.5)--(2,4.5);
\draw[black, very thick] (11,5) ellipse (1.5 and 1.5);
\draw[ thick] (11,2)--(11,-2);
\draw[ thick] (9,0)--(13,0);
\draw[black, thick,->] (9,0.5)--(0,3.5);
\draw[black, very thick] (11,0) ellipse (1.5 and 1.5);
\draw[ thick] (11,-3)--(11,-7);
\draw[ thick] (9,-5)--(13,-5);
\draw[black, thick,->] (9,-4.5)--(4.5,-3.5);
\draw[black, very thick] (11,-5) ellipse (1.5 and 1.5);
\draw node [above] at (7.5,4.5) {$h_3(w_3)$};
\draw node [above] at (7.5,1) {$h_2(w_2)$};
\draw node [above] at (7.5,-4) {$h_1(w_1)$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
The fundamental domain of Fuchsian uniformization corresponding to the genus 2 surface. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.45]
%Riemann surface
\draw[black,very thick] (0,2) to[curve through={(1,2.2)..(3,3)..(8,0) .. (3,-3) ..(0,-2) .. (-3,-3)..(-8,0)..(-3,3)..(-1,2.2)}] (0,2);
\draw[black, very thick] (2.5,0) to[curve through={(3.5,1)..(5,1)}] (6,0);
\draw[black, very thick] (2.3,.2) to[curve through={(3.5,-.75)..(5,-.75)}] (6.2,.2);
\draw[black,very thick] (-2.5,0) to[curve through={(-3.5,1)..(-5,1)}] (-6,0);
\draw[black,very thick] (-2.3,.2) to[curve through={(-3.5,-.75)..(-5,-.75)}] (-6.2,.2);
%Cycles on Riemann surface
\draw[very thick] (1.5,-2.25) to[curve through={(.5,-1)..(.05,-.25)..(0,0)..(.5,.25)..(1,.25)..}] (2.75,-.25);
\draw[very thick, style=dashed] (2.75,-.25) to[curve through={(3,-2)}] (1.5,-2.25);
\draw[very thick] (-1.5,-2.4) to[curve through={(-.5,-1)..(-.05,-.25)..(0,0)..(-.5,.25)..(-1,.25)..}] (-2.75,-.25);
\draw[very thick, style=dashed] (-2.75,-.25) to[curve through={(-3,-2)}] (-1.5,-2.4);
\draw[very thick] (0,0) to[curve through={(5,2)..(7,0)..(5,-2)}] (0,0) ;
\draw[very thick] (0,0) to[curve through={(-5,2)..(-7,0)..(-5,-2)}] (0,0);
\draw node at (7.5,0) {$\mathcal{A}_1$};
\draw node at (1,-.5) {$\mathcal{B}_1$};
\draw node at (-7.5,0) {$\mathcal{A}_2$};
\draw node at (-1,-.5) {$\mathcal{B}_2$};
% Arrow
\draw[very thick,->] (-11,0)--(-9,0);
\draw node at (-10,.5) {$\pi$};
% Polygon
\draw[very thick] (-30,-6)--(-10,-6);
\draw node at (-9,-6) {$R$};
\draw[black, very thick] (-22,-5) to[curve through={(-20,-4)}] (-18,-5);
\draw[black, very thick] (-24,-4) to[curve through={(-22.5,-4.5)}] (-22,-5);
\draw[black, very thick] (-27,-2) to[curve through={(-24.5,-3)}] (-24,-4);
\draw[black, very thick] (-28,0)to[curve through={(-27.5,-.5)}] (-27,-2) ;
\draw[black, very thick] (-28,0)to[curve through={(-20,4.25)}] (-12,0) ;
\draw[black, very thick] (-13,-2)to[curve through={(-12.5,-.5)}] (-12,0) ;
\draw[black, very thick] (-13,-2)to[curve through={(-15.5,-3)}] (-16,-4) ;
\draw[black,very thick] (-16,-4) to[curve through={(-17.5,-4.5)}] (-18,-5);
\draw node [above] at (-20,4.25) {$\tilde\mathcal{A}_2$};
\draw node [below,right] at (-15.5,-3) {$\tilde\mathcal{A}_1$};
\draw node [below,left] at (-24.5,-3) {$\tilde\mathcal{A}_2$};
\draw node [below,right ] at (-12.5,-.5) {$\tilde\mathcal{B}_1$};
\draw node [below] at(-20,-4) {$\tilde\mathcal{A}_1$};
\draw node [below,left ] at (-27.5,-.5) {$\tilde\mathcal{B}_2$};
\draw node [below,right] at (-17.5,-5) {$\tilde\mathcal{B}_1$};
\draw node [below,left ] at (-22,-5) {$\tilde\mathcal{B}_2$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | |
\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\usepackage{epsfig,amsfonts,amssymb,setspace}
\usepackage{tikz-cd}
\usetikzlibrary{arrows, matrix}
\begin{document}
\begin{tikzpicture}[scale=.4]
%Torus with two border 1
\draw[black, very thick] (2.5,-4) to[curve through={(0,-2.5)..(-5,0)..(0,2.5)}] (2.5,4);
\draw[black,very thick] (0.5,0) to[curve through={(-0.5,.5)..(-2,.5)}] (-3,0);
\draw[black,very thick] (.7,.2) to[curve through={(-0.5,-.5)..(-2,-.5)}] (-3.2,.2);
\draw[black, very thick] (3,-2.5) to[curve through={(2.5,-1)..(2.5,1)}] (3,2.5);
\draw[gray, very thick](2.75,3.25) ellipse (.5 and .75);
\draw[gray,very thick](2.75,-3.25) ellipse (.5 and .75);
\draw node[below] at (-3,-.5) {$\alpha_3$};
\draw node[below] at (1,-3) {$\epsilon_1$};
% Cycles
\draw[very thick](1.4,0) ellipse (.5 and 3);
\draw[ very thick](-4,0) ellipse (.95 and .8);
\draw[very thick,<->](3.5,0)--(6.5,0);
\draw[very thick,<->](0,-4)--(0,-7);
\draw node[below] at (5,0) {\bf A};
\draw node[right] at (0,-5.5) {\bf S};
%Torus with two border 2
\draw[black, very thick] (14.5,-4) to[curve through={(12,-2.5)..(7,0)..(12,2.5)}] (14.5,4);
\draw[black, very thick] (12.5,0) to[curve through={(11.5,.5)..(10,.5)}] (9,0);
\draw[black, very thick] (12.7,.2) to[curve through={(11.5,-.5)..(10,-.5)}] (8.8,.2);
\draw[black, very thick] (15,-2.5) to[curve through={(14.5,-1)..(14.5,1)}] (15,2.5);
\draw[gray,very thick](14.75,3.25) ellipse (.5 and .75);
\draw[gray, very thick](14.75,-3.25) ellipse (.5 and .75);
\draw node[below] at (9,-.5) {$\alpha_3$};
\draw node[below] at (15.5,0) {$\alpha_1$};
% Cycles
\draw[very thick](13.5,0) ellipse (.95 and .8);
\draw[ very thick](8,0) ellipse (.95 and .8);
\draw[very thick,<->](16.5,0)--(19.5,0);
\draw node[below] at (18,0) {\bf A};
%Torus with two border 3
\draw[black,very thick] (27.5,-4) to[curve through={(25,-2.5)..(20,0)..(25,2.5)}] (27.5,4);
\draw[black, very thick] (25.5,0) to[curve through={(24.5,.5)..(23,.5)}] (22,0);
\draw[black, very thick] (25.7,.2) to[curve through={(24.5,-.5)..(23,-.5)}] (21.8,.2);
\draw[black, very thick] (28,-2.5) to[curve through={(27.5,-1)..(27.5,1)}] (28,2.5);
\draw[gray, very thick](27.75,3.25) ellipse (.5 and .75);
\draw[gray, very thick](27.75,-3.25) ellipse (.5 and .75);
\draw node[below] at (22,-1.75) {$\alpha_3$};
\draw node[below] at (29,.5) {$\alpha_1$};
\draw[very thick,<->](26,-4)--(26,-7);
\draw node[left] at (26,-5.5) {\bf S};
% Cycles
\draw[very thick](26.5,0) ellipse (.95 and .3);
\draw[ very thick] (27.5,-1.5) to[curve through={(26.5,-2.25)..(25,-1.75)..(20.5,0)..(25,1.75)..(26.5,2.25)}] (27.5,1.5);
\draw[ very thick] (27.55,-1.5) to[curve through={(27.1,-.9)..(25,-.75)..(21.5,0)..(25,.75)..(27.1,.9)}] (27.55,1.5);
%Torus with two border 1
\draw[black,very thick] (2.5,-16) to[curve through={(0,-14.5)..(-5,-12)..(0,-9.5)}] (2.5,-8);
\draw[black,very thick] (0.5,-12) to[curve through={(-0.5,-11.5)..(-2,-11.5)}] (-3,-12);
\draw[black, very thick] (.7,-11.8) to[curve through={(-0.5,-12.5)..(-2,-12.5)}] (-3.2,-11.8);
\draw[black,very thick] (3,-14.5) to[curve through={(2.5,-13)..(2.5,-11)}] (3,-9.5);
\draw[gray,very thick](2.75,-8.75) ellipse (.5 and .75);
\draw[gray, very thick](2.75,-15.25) ellipse (.5 and .75);
\draw node[below] at (-3,-12.5) {$\alpha_3$};
\draw node[below] at (1,-15) {$\epsilon_1$};
% Cycles
\draw[very thick](1.6,-12) ellipse (.3 and 3.1);
\draw[ very thick](-1.2,-12) ellipse (2.25 and .8);
\draw[very thick,<->](3.5,-12)--(6.5,-12);
\draw node[below] at (5,-12) {\bf A};
%Torus with two border 2
\draw[black,very thick] (14.5,-16) to[curve through={(12,-14.5)..(7,-12)..(12,-9.5)}] (14.5,-8);
\draw[black, very thick] (12.5,-12) to[curve through={(11.5,-11.5)..(10,-11.5)}] (9,-12);
\draw[black, very thick] (12.7,-11.8) to[curve through={(11.5,-12.5)..(10,-12.5)}] (8.8,-11.8);
\draw[black, very thick] (15,-14.5) to[curve through={(14.5,-13)..(14.5,-11)}] (15,-9.5);
\draw[gray, very thick](14.75,-8.75) ellipse (.5 and .75);
\draw[gray, very thick](14.75,-15.25) ellipse (.5 and .75);
\draw node[below] at (9,-12.5) {$\alpha_2$};
\draw node[below] at (15.5,-10) {$\epsilon_2$};
% Cycles
\draw[ very thick, rotate around={25:(11.3,-11.5)}](11.3,-11.55) ellipse (3.5 and 1.7);
\draw[ very thick](10.8,-12) ellipse (2.25 and .8);
\draw[very thick,<->](16.5,-12)--(19.5,-12);
\draw node[below] at (18,-12) {\bf A};
%Torus with two border 3
\draw[black, very thick] (27.5,-16) to[curve through={(25,-14.5)..(20,-12)..(25,-9.5)}] (27.5,-8);
\draw[black, very thick] (25.5,-12) to[curve through={(24.5,-11.5)..(23,-11.5)}] (22,-12);
\draw[black, very thick] (25.7,-11.8) to[curve through={(24.5,-12.5)..(23,-12.5)}] (21.8,-11.8);
\draw[black, very thick] (28,-14.5) to[curve through={(27.5,-13)..(27.5,-11)}] (28,-9.5);
\draw[gray,very thick](27.75,-8.75) ellipse (.5 and .75);
\draw[gray,very thick](27.75,-15.25) ellipse (.5 and .75);
\draw node[below] at (22,-14) {$\alpha_3$};
\draw node[below] at (24,-11.25) {$\alpha_1$};
% Cycles
\draw[very thick](23.75,-12) ellipse (2.25 and .7);
\draw[ very thick] (27.5,-13.5) to[curve through={(26.5,-14.25)..(25,-13.75)..(20.5,-12)..(25,-10.25)..(26.5,-9.75)}] (27.5,-10.5);
\draw[ very thick] (27.55,-13.5) to[curve through={(27.1,-12.9)..(25,-12.85)..(21,-12)..(25,-11.2)..(27.1,-11.1)}] (27.55,-10.5);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.10563 | arxiv | 2017-03-31T02:07:52 | ||
An example of PhaseCode. Bins 1, 3, 5, 6 are singletons with singleton balls 1, 3, 5, 5, which can be found in the first iteration of PhaseCode algorithm. Then, the algorithm finds a strong doubleton: bin 2, and the relative phases between balls 1 and 3. In the next iteration, the algorithm finds a resolvable multiton bin 4 and colors ball 5. After that, no more balls can be colored. The algorithm stops and successfully finds all the non-zero components. | \documentclass[11pt]{article}
\usepackage[cmex10]{amsmath}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsmath,amssymb,euscript,mathrsfs,amsthm}
\usepackage{graphicx,color,subfig}
\usepackage{tikz}
\usetikzlibrary{automata,arrows,shapes,snakes,automata,backgrounds,petri}
\usepackage[latin1]{inputenc}
\usepackage{color}
\begin{document}
\begin{tikzpicture}[node distance=0.7cm,>=stealth',bend angle=45,auto]
\tikzstyle{ball}=[circle,thick,draw=blue!75,fill=blue!20,minimum size=3mm]
\tikzstyle{emptyball}=[circle,thick,draw=black,fill=white,minimum size=3mm]
\tikzstyle{bin}=[rectangle,thick,draw=black,fill=white,minimum size=3mm]
\begin{scope}
\node [ball] (L1) {1};
\node [emptyball] (L2) [below of=L1] {2};
\node [ball] (L3) [below of=L2] {3};
\node [emptyball] (L4) [below of=L3] {4};
\node [ball] (L5) [below of=L4] {5};
\node [emptyball] (L6) [below of=L5] {6};
\node [bin] (R1) [right of=L1, xshift=2.0cm] {1};
\node [bin] (R2) [right of=L2, xshift=2.0cm] {2};
\node [bin] (R3) [right of=L3, xshift=2.0cm] {3};
\node [bin] (R4) [right of=L4, xshift=2.0cm] {4};
\node [bin] (R5) [right of=L5, xshift=2.0cm] {5};
\node [bin] (R6) [right of=L6, xshift=2.0cm] {6};
\path (L1) edge [left] (R1);
\path (L1) edge [left] (R2);
\path (L1) edge [left] (R4);
\path (L2) edge [left, dashed] (R2);
\path (L2) edge [left, dashed] (R4);
\path (L2) edge [left, dashed] (R5);
\path (L3) edge [left] (R2);
\path (L3) edge [left] (R3);
\path (L3) edge [left] (R4);
\path (L4) edge [left, dashed] (R3);
\path (L4) edge [left, dashed] (R4);
\path (L4) edge [left, dashed] (R6);
\path (L5) edge [left] (R4);
\path (L5) edge [left] (R5);
\path (L5) edge [left] (R6);
\path (L6) edge [left, dashed] (R1);
\path (L6) edge [left, dashed] (R3);
\path (L6) edge [left, dashed] (R6);
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1606.00531 | arxiv | 2016-06-03T02:05:16 | |
This figure gives an explicit example of minimal dominating sets, which are not maximal independent and an example of when _odd(G) < i_odd(G). | \documentclass[10pt]{amsart}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{shapes,positioning}
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture} [every loop/.style={}]
\node [draw,circle] (A) at (4,0) {1};
\node [draw,circle] (B) at (2,0) {2};
\node [draw,circle] (C) at (0,0) {3};
\node [draw,circle] (D) at (1,1) {4};
\node [draw,circle] (E) at (2,2) {5};
\node [draw,circle] (F) at (3,1) {6};
\draw[line width=1pt] (C) edge (D);
\draw[line width=1pt] (D) edge (E);
\draw[line width=1pt] (E) edge (F);
\draw[line width=1pt] (A) edge (F);
\draw[line width=1pt] (A) edge (B);
\draw[line width=1pt] (B) edge (C);
\draw[line width=1pt] (B) edge (D);
\draw[line width=1pt] (B) edge (F);
\draw[line width=1pt] (D) edge (F);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1505.02268 | arxiv | 2015-05-12T02:06:15 | |
The figure above characterizes a family of graphs produced by n vertices each only adjacent to u_1 and u_2, and the edge u_1u_2. This family of graphs is an example where the bounds in Proposition prop:EasyBounds, Proposition prop:CyDomBound and Proposition prop:CyIRBound are tight. In fact, up to an arbitrary subdivision of the edge u_1u_2 and vertices not contained in a cycle, this family characterizes when the lower bounds of these propositions are tight. | \documentclass[10pt]{amsart}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{shapes,positioning}
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture}[every loop/.style={}]
\draw (0,0) circle (.3) node (A) {$u_1$}
(4,0) circle (.3) node (B) {$u_2$}
(2,1.5) circle (.3) node (C) {$v_1$}
(2,3.1) circle (.3) node (D) {$v_n$};
\node at (2,2.4) {$\vdots$};
\draw[line width=.5pt] (A) edge (B);
\draw[line width=.5pt] (A) edge (C);
\draw[line width=.5pt] (A) edge (D);
\draw[line width=.5pt] (B) edge (C);
\draw[line width=.5pt] (B) edge (D);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1505.02268 | arxiv | 2015-05-12T02:06:15 | |
A de Bruijn torus for d=5, k=3, n=2, and G=Z/5Z, accompanied by some valid block patterns. | \documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale= 0.5 ]
\draw[step=1,help lines] (0,3) grid (14,6);
\draw[step=1,ultra thick, draw=red] (0,6) to (2,6) to (2,5) to (1,5) to (1,3) to (0,3) to (0,6);
\draw[step=1,ultra thick, draw=red] (3,6) to (4,6) to (4,5) to (5,5) to (5,4) to (4,4) to (4,3) to (3,3) to (3,6);
\draw[step=1,ultra thick, draw=red] (6,3) to (6,4) to (7,4) to (7,6) to (8,6) to (8,3) to (6,3);
\draw[step=1,ultra thick, draw=red] (9,6) to (10,6) to (10,5) to (11,5) to (11,3) to (10,3) to (10,4) to (9,4) to (9,6);
\draw[step=1,ultra thick, draw=red] (12,6) to (14,6) to (14,5) to (13,5) to (13,4) to (12,4) to (12,6);
\draw[step=1,ultra thick, draw=red] (13,3) to (13,4) to (14,4) to (14,3) to (13,3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1505.04065 | arxiv | 2015-11-24T02:20:18 | |
Solution to problem from Figure DBGEx. | \documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale= 0.5 ]
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (0,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (0,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (1,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (1,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (2,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (2,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (5,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (5,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (8,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (8,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (9,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (9,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (10,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (10,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,9) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,9) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,9) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,9) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,9) {};
\draw[step=1,help lines] (0,0) grid (12,10);
\node[draw=red,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,6) {};
\node[draw=red,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (5,6) {};
\node[draw=red,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (8,6) {};
\node[draw=red,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (5,3) {};
\node[draw=red,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (8,0) {};
\draw[step=1,ultra thick, draw=blue] (4,0) to (4,7) to (9,7) to (9,0) to (4,0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1505.04065 | arxiv | 2015-11-24T02:20:18 | |
De Bruijn grid and pattern to be located with corresponding connection graph. | \documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[-,>=stealth',auto,node distance=2cm,
thick,main node/.style={circle,draw,font=\sffamily\bfseries}, scale= 0.5 ]
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (0,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (0,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (1,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (1,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (2,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (2,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (5,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (5,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (8,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (8,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (9,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (9,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (10,2) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (10,6) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (3,9) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (4,9) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (6,9) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (7,9) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,0) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,1) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,3) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,4) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,5) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,7) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,8) {};
\node[fill=black,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (11,9) {};
\draw[step=1,help lines] (0,0) grid (12,10);
\node[draw=red,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (14,8) {};
\node[draw=red,fill=black,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (15,8) {};
\node[draw=red,fill=black,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (18,8) {};
\node[draw=red,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (15,5) {};
\node[draw=red,ultra thick,inner sep=0.25cm,outer sep=0pt,anchor=south west] at (18,2) {};
\draw[step=1,help lines] (14,2) grid (19,9);
\node[] at (14.5,9.5) {$a$};
\node[] at (13.5,8.5) {$a$};
\node[] at (13.5,5.5) {$\overline{a}$};
\node[] at (13.5,2.5) {$\overline{a}$};
\node[] at (15.5,9.5) {$\overline{a}$};
\node[] at (18.5,9.5) {$\overline{a}$};
\node[main node] (1) at (20,8.5) {};
\node[main node] (2) at (21,8.5) {};
\node[main node] (3) at (23,8.5) {};
\node[main node] (4) at (21,5.5) {};
\node[main node] (5) at (23,2.5) {};
\path[every node/.style={font=\sffamily\footnotesize}]
(1) edge node [left] {} (2)
(2) edge node [left] {} (3)
(2) edge node [left] {} (4)
(3) edge node [right] {} (5)
;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1505.04065 | arxiv | 2015-11-24T02:20:18 | |
The MDP Client | \documentclass[conference,final]{IEEEtran}
\usepackage{amssymb}
\usepackage{pgf}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,positioning,calc}
\newcommand{\var}[1]{\textsf{#1}}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=5.5cm,
semithick]
\tikzstyle{every state}=[circle, minimum width=30pt, fill=white,draw=black,text=black]
\tikzstyle{ghost}=[fill=white, draw=none,text=black]
\node[state] (A) {$0$};
\node[state] (B) [above right = 2.5cm and 4cm of A] {$1$};
\node[state] (C) [below right = 2.5cm and 4cm of A] {$1$};
\node[state] (D) [left = 2cm of A] {$2$};
\node[ghost] (E) [above left = 3.5cm of A] {};
\node[ghost] (F) [right = 4cm of A] {$\vdots$};
\tikzstyle{lblabove}=[sloped,above,midway,align=center]
\tikzstyle{lblbelow}=[sloped,below,midway,align=center]
\path (A) edge node[lblabove] {$\{ p_1 \} ~ \var{ctr}_c < n \wedge \var{s}_c' = 1$}
(B)
edge node[lblabove] {$\{ p_m \} ~ \var{ctr}_c < n \wedge \var{s}_c' = m$}
(C)
edge node[lblabove] {$\var{ctr}_c = n$} (D)
(B) edge [bend left] node[lblbelow] {$\var{ctr}_c^1 \ge c$}
(A)
edge [bend right] node[align=center, sloped, midway, above] {$[busy] \var{ctr}_c^1 < c \wedge$\\$\var{ctr}_c' = \var{ctr}_c+1 \wedge {\var{ctr}'}_c^1 = {\var{ctr}'}_c^1 + 1$}
(A)
(C) edge [bend left] node[lblbelow] {$[busy] \var{ctr}_c^m < c \wedge$\\$\var{ctr}'_c = \var{ctr}_c+1 \wedge {\var{ctr}'}_c^m = {\var{ctr}'}_c^m + 1$}
(A)
edge [bend right] node[lblabove] {$\var{ctr}_c^m \ge c$}
(A)
(E) edge node[near start,align=center] {$\forall l. \var{ctr}_c^l = 0 \wedge$\\$\var{ctr}_c=0 \wedge$\\$\var{s}_c=0$}
(A);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1605.05930 | arxiv | 2016-06-30T02:08:19 | |
Model graph and its model matrix | \documentclass[11pt,oneside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.05] \draw[fill] (0,0) circle [radius=1]; \draw[fill] (10,0) circle [radius=1]; \draw[fill] (20,0) circle [radius=1]; \draw[fill] (30,0) circle [radius=1]; \draw[fill] (40,0) circle [radius=1]; \draw[fill] (50,0) circle [radius=1]; \draw[fill] (60,0) circle [radius=1]; \draw (20,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (30,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (40,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (50,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (60,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (30,0) arc [radius=15, start angle=5, end angle= 175]; \draw (40,0) arc [radius=15, start angle=5, end angle= 175]; \draw (50,0) arc [radius=15, start angle=5, end angle= 175]; \draw (60,0) arc [radius=15, start angle=5, end angle= 175]; \draw (0,0) -- (60,0); \end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.03189 | arxiv | 2017-04-12T02:05:11 | |
Random linear graph and its random matrix | \documentclass[11pt,oneside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.05] \draw[fill] (0,0) circle [radius=1]; \draw[fill] (10,0) circle [radius=1]; \draw[fill] (20,0) circle [radius=1]; \draw[fill] (30,0) circle [radius=1]; \draw[fill] (40,0) circle [radius=1]; \draw[fill] (50,0) circle [radius=1]; \draw[fill] (60,0) circle [radius=1]; \draw (20,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (30,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (40,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (50,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (60,0) arc [radius=11.4, start angle=25, end angle= 155]; \draw (40,0) arc [radius=15, start angle=5, end angle= 175]; \draw (10,0) -- (50,0); \end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.03189 | arxiv | 2017-04-12T02:05:11 | |
The text is represented by a feature allocation where each block represents a paragraph. | \documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{fit}
\usetikzlibrary{backgrounds}
\usetikzlibrary{matrix,positioning}
\usepackage[utf8]{inputenc}
\begin{document}
\begin{tikzpicture}[scale=0.98]
\draw (-5,1.5) node (v1) {} circle (0.1);
\draw (-4,1.5) node (v3) {} circle (0.1);
\draw (-3,1.5) node (v8) {} circle (0.1);
\draw (-2,1.5) node (v11) {} circle (0.1);
\node at (-1,1.5) {$\dots$};
\draw (-0.5,1.5) circle (0.1);
\draw (-5,0) node (v2) {} circle (0.1);
\draw (-4.5,0) node (v4) {} circle (0.1);
\draw (-4,0) node (v5) {} circle (0.1);
\draw (-3.5,0) node (v6) {} circle (0.1);
\draw (-3,0) node (v7) {} circle (0.1);
\draw (-2.5,0) node (v9) {} circle (0.1);
\draw (-2,0) node (v10) {} circle (0.1);
\draw (-1.5,0) node (v12) {} circle (0.1);
\node at (-1,0) {$\dots$};
\draw (-0.5,0) circle (0.1);
\draw (v1) edge (v2);
\draw (v3) edge (v4);
\draw (v3) edge (v5);
\draw (v3) edge (v6);
\draw (v3) edge (v7);
\draw (v8) edge (v2);
\draw (v8) edge (v9);
\draw (v8) edge (v10);
\draw (v11) edge (v7);
\draw (v11) edge (v12);
\node at (-1,0.8) {$\dots$};
\node[align=left] at (-2.75,-0.4) {$a$\hspace{6.60pt} $b$\hspace{6.60pt} $c$\hspace{6.60pt} $d$\hspace{6.60pt} $e$\hspace{6.60pt} $f$\hspace{6.60pt} $g$\hspace{6.60pt} $h$\hspace{18pt} $x$};
\node[align=left] at (-2.60,1.8) {$B_1$\hspace{13pt} $B_2$\hspace{13pt} $B_3$\hspace{13pt} $B_4$\hspace{28pt} $B_{|F|}$};
\node at (3.90,1.5) {Entropy:\hspace{5pt} $H(F)\ =\ \sum_{i=1}^{|F|}\ \frac{|B_i|}{n} \log \frac{n}{|B_i|}$};
\node at (4.55,0.7) {Projection:\hspace{5pt} $PROJ(F,S)\ =\ \{B\cap S\}_{B\in F} \backslash \{\emptyset\}$};
\node at (3.80,-0.1) {Projection entropy:\hspace{5pt} $H(PROJ(F,S))$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1410.6830 | arxiv | 2014-10-28T01:00:54 | |
Comparing co-occurence and projection entropy in their values for 2 and 3 elements | \documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{fit}
\usetikzlibrary{backgrounds}
\usetikzlibrary{matrix,positioning}
\usepackage[utf8]{inputenc}
\begin{document}
\begin{tikzpicture}[yscale=0.75,xscale=0.85]
\draw (-6,1.8) ellipse (1 and 0.7);
\draw (-5,1.8) ellipse (1 and 0.7);
\draw (-2.3,3.2) ellipse (1 and 1);
\draw (-1.3,3.2) ellipse (1 and 1);
\draw (-1.8,2.3) ellipse (1 and 1);
\node at (-5.5,1.8) {$1$};
\node at (-6.5,1.8) {$0$};
\node at (-4.5,1.8) {$0$};
\node at (-3.9,1.2) {$0$};
\node at (-1.8,2.9) {$1$};
\node at (-1.8,3.6) {$0$};
\node at (-2.4,2.6) {$0$};
\node at (-1.2,2.6) {$0$};
\node at (-2.7,3.4) {$0$};
\node at (-0.9,3.4) {$0$};
\node at (-1.8,1.9) {$0$};
\node at (-6.2,2.8) {$a\in B$};
\node at (-4.7,2.8) {$b\in B$};
\node at (-2.5,4.5) {$a\in B$};
\node at (-1,4.5) {$b\in B$};
\node at (-1.8,1) {$c\in B$};
\node at (-0.4,2.1) {$0$};
\draw (1.65,1.8) ellipse (1.1 and 0.7);
\draw (2.95,1.8) ellipse (1.1 and 0.7);
\draw (5.6,3.2) ellipse (1.2 and 1);
\draw (7,3.2) ellipse (1.2 and 1);
\draw (6.3,2.3) ellipse (1.2 and 1);
\node at (2.3,1.8) {$0$};
\node at (1.25,1.8) {{\tiny $\frac{1}{2}\log\frac{2}{1}$}};
\node at (3.35,1.8) {{\tiny $\frac{1}{2}\log\frac{2}{1}$}};
\node at (4,1.2) {$0$};
\node at (6.3,2.9) {$0$};
\node at (6.3,3.45) {{\tiny $\frac{2}{3}\log\frac{3}{2}$}};
\node at (5.6,2.45) {{\tiny $\frac{2}{3}\log\frac{3}{2}$}};
\node at (7,2.45) {{\tiny $\frac{2}{3}\log\frac{3}{2}$}};
\node at (5.1,3.4) {{\tiny $\frac{1}{3}\log\frac{3}{1}$}};
\node at (7.5,3.4) {{\tiny $\frac{1}{3}\log\frac{3}{1}$}};
\node at (6.3,1.9) {{\tiny $\frac{1}{3}\log\frac{3}{1}$}};
\node at (1.6,2.8) {$a\in B$};
\node at (3.1,2.8) {$b\in B$};
\node at (5.6,4.5) {$a\in B$};
\node at (7.1,4.5) {$b\in B$};
\node at (6.3,1) {$c\in B$};
\node at (7.8,2.1) {$0$};
\node at (-5.8,4.5) {Co-occurence of elements};
\node at (2.4,4.5) {Projection entropy};
\node at (-6,3.9) {$\sum_i [S\subset B_i] $};
\node at (2.4,3.9) {$H(PROJ(F,S))$};
\node at (6.3,0.3) {{\footnotesize $S=\{a,b,c\}$}};
\node at (2.5,0.3) {{\footnotesize $S=\{a,b\}$}};
\node at (-1.7,0.3) {{\footnotesize $S=\{a,b,c\}$}};
\node at (-5.5,0.3) {{\footnotesize $S=\{a,b\}$}};
\node (v1) at (0.2,4.8) {};
\node (v2) at (0.2,-0.2) {};
\draw[dashed] (v1) edge (v2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1410.6830 | arxiv | 2014-10-28T01:00:54 | |
The time-dependent function of variances for real-time measurements. | \documentclass[journal]{IEEEtran}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=1.5}
\begin{document}
\begin{tikzpicture}
\begin{axis}[axis lines=center, axis equal image, enlargelimits=true,
y label style={at={(0.0,1.1)}}, x label style={at={(1.02,-0.12)}},
xlabel={$t$},
ylabel={$\sigma^2$},
label style={font=\footnotesize},
xtick={1, 2},
xticklabels={$t_{\mathrm{rt}}$, $t_{\mathrm{ps}}$},
ytick={0.2,1},
yticklabels={$\sigma_{\mathrm{rt}}^2$, $\sigma_{\mathrm{ps}}^2$},
tick label style={font=\footnotesize},
ymin = 0, ymax = 1.2,
xmin = 0, xmax = 3.3]
\addplot [black, no markers, thick] coordinates {(0,1) (1,1) (1,0.2) (2,1) (3.2,1)};
\addplot [black, no markers, dashed, very thin] coordinates {(0,0.2) (1,0.2)};
\addplot [black, no markers, dashed, very thin] coordinates {(2,1) (2,0)};
\addplot [black, no markers, dashed, very thin] coordinates {(1,1) (1,0)};
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1705.01376 | arxiv | 2017-05-04T02:05:39 | |
Long-running process life-cycle with partially actice and partially terminated states. | \documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes}
\usetikzlibrary{positioning,calc}
\usetikzlibrary{arrows,decorations.markings}
\begin{document}
\begin{tikzpicture}
\node [draw, ultra thick, circle, fill=blue!05!white, minimum size=60, align=center] (active) at (0,0) {Partially\\Active};
\node [draw, ultra thick, dashed, circle, fill=blue!05!white, minimum size=60, align=center] (term) at (0,-4) {Partially\\Terminated};
\node [draw, circle, fill=black, minimum size=20] (init) at (0,3.5) {};
\node [draw, circle, ultra thick, fill=white, minimum size=35] (endouter) at (3.5,0) {};
\node [draw, circle, fill=black, minimum size=20] (end) at (3.5,0) {};
\draw[very thick, decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=latex]{>}}},postaction={decorate}] (init) -- (active) node [midway, left, fill=white] {1};
\draw[very thick, decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=latex]{>}}},postaction={decorate}] (active) -- (term) node [midway, left, fill=white] {2};
\draw[very thick, decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=latex]{>}}},postaction={decorate}] (term.west) -- +(-1,0) -- node [midway, left, fill=white] {3} +(-1,4) -- (active.west) ;
\draw[very thick, decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=latex]{>}}},postaction={decorate}] (active) -- (endouter) node [midway, above, fill=white] {4};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.07642 | arxiv | 2016-04-27T02:11:04 |
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