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Mapping to r_1r_2 random variables in a node with data x_u | \documentclass[10pt,twosided,a4paper,draft,onecolumn]{article}
\usepackage{tikz}
\usetikzlibrary{matrix,arrows,decorations.pathmorphing}
\usepackage{graphicx,color}
\usepackage{amsmath,amsfonts,amssymb,mathrsfs,wasysym,stackrel,amsthm}
\begin{document}
\begin{tikzpicture}[>=latex]
\tikzstyle{every node} = [circle,fill=gray]
\node (a) at (2.5,2) {$x_u$};
\node (b) at (0,0) {$y_u^1$};
\node (c) at (5,0) {$y_u^{r_1}$};
%
\node (d) at (-1.5,-1.5) {$z_u^{1,1}(0)$};
\node (e) at (1.5,-1.5) {$z_u^{1,r_2}(0)$};
\node (f) at (3.5,-1.5) {$z_u^{r_1,1}(0)$};
\node (g) at (6.5,-1.5) {$z_u^{r_1,r_2}(0)$};
%%
\draw [->] (a) -- (b) node[pos=.5,sloped,above,fill=white] {$\phi_1$};;
\draw [->] (a) -- (c)node[pos=.5,sloped,above,fill=white] {$\phi_{r_1}$};;
\draw [->] (b) -- (d);
\draw [->] (b) -- (e);
\draw [->] (c) -- (f);
\draw [->] (c) -- (g);
\fill[black] (1,0) circle (0.3ex);
\fill[black] (2,0) circle (0.3ex);
\fill[black] (3,0) circle (0.3ex);
\fill[black] (4,0) circle (0.3ex);
\fill[black] (-0.5,-1.5) circle (0.3ex);
\fill[black] (0.5,-1.5) circle (0.3ex);
\fill[black] (4.5,-1.5) circle (0.3ex);
\fill[black] (5.5,-1.5) circle (0.3ex);
\fill[black] (2.5,-1.5) circle (0.3ex);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1210.6134 | arxiv | 2012-10-24T02:02:18 |
|
A cross-sectional view of a collar neighborhood of F in the knot complement X_K, where F_ represent F 1, respectively. In addition, the point P_+(resp. P_-) is the intersection point of the meridian Z and F_+(resp. F_-). | \documentclass[11pt, oneside]{amsart}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\draw [ultra thick] (2,2) -- (9,2);
\draw [ultra thick] (2,4) -- (9,4);
\draw [ultra thick] (10.5,3) circle [radius=1.8];
\draw [->, ultra thick, cyan] (9,2) to [out=298, in=180] (10.5,1) to [out=0, in=270] (12.6,3);
\draw [ultra thick, cyan](12.6,3) to [out=90, in=0] (10.5,5) to [out=180, in=62] (9,4);
\draw [dashed, thick] (2,3) -- (10.5,3);
\draw [ultra thick] (12,2.18) -- (12,2) -- (12.18,2);
\node[right] at (10.5,3) {$K$};
\node[left] at (2,2) {$F_-$};
\node[left] at (2,3) {$F$};
\node[left] at (2,4) {$F_+$};
\node[above left] at (9,4) {$P_+$};
\node[below left] at (9,2) {$P_-$};
\node[cyan] at (13, 3) {$C$};
\node [below left] at (12,2.3) {$Z$};
\draw [fill=black] (10.5,3) circle [radius=0.1];
\draw [fill=black] (9,2) circle [radius=0.1];
\draw [fill=black] (9,4) circle [radius=0.1];
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1311.3291 | arxiv | 2014-07-02T02:12:28 |
|
Hasse-diagram of Szondi's signatures | \documentclass{article}
\usepackage{amsmath,amssymb,array,multirow,tikz,tikz-cd}
\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/1403.2000 | arxiv | 2014-05-06T19:50:29 |
|
Schematic of the LHCb detector showing the path of charged particles from a D^0 K^-^+^-^+ decay and its charge conjugate. In this case, the raw asymmetry will be dominated by the material interaction effects of the charged kaon, but when the pion tracking efficiency is measured, this cancels between the numerator and the denominator. | \documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{trees}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale=0.7,
% Set the overall layout of the tree
level/.style={level distance=3.15cm, line width=0.4mm},
level 2/.style={sibling angle=60},
level 3/.style={sibling angle=60},
level 4/.style={level distance=1.4cm, sibling angle=60}
]
\node[draw=none,fill=none] at (-7.80, 0.8){$D^0$} ;
\node[draw=none,fill=none] at (-1.8, 1.5){$K^-$} ;
\node[draw=none,fill=none] at (-1.8, 1.0){$\pi^-$} ;
\node[draw=none,fill=none] at (-1.8, -2.6){$\pi^+$} ;
\node[draw=none,fill=none] at (-1.8, -2.1){$\pi^+$} ;
\filldraw[draw=black,fill=lightgray] (-9.0,-0.3) rectangle
(-7.5,0.3);
\draw[blue,very thick] (-8.5,0.0) -- (-1.8,3.0) ;
\draw[blue,very thick] (-8.5,0.0) -- (-1.8,-3.0) ;
\draw[blue] (-8.5,0.0) -- (-1.8,0.0) ;
\draw[very thick, ->] (-9, -3.5) -- (-7.5, -3.5);
\draw[very thick, ->] (-9, -3.5) -- (-9, -2.0);
\node[draw=none,fill=none] at (-9.30, -2.5){$x$} ;
\node[draw=none,fill=none] at (-8.0, -3.8){$z$} ;
\node[circle, fill=red,inner sep=1pt,minimum size=1pt] at
(-8.0, 0.1){};
\node[circle, fill=red,inner sep=2pt,minimum size=2pt] at (-8.5, 0.0){};
\filldraw[draw=black,fill=blue] (-7.0,2.5) rectangle (-5.5,1.0);
\filldraw[draw=black,fill=blue] (-7.0,-2.5) rectangle
(-5.5,-1.0);
\filldraw[draw=black,fill=green] (-5.0,-2.0) rectangle
(-4.4,2.0);
\filldraw[draw=black,fill=yellow] (-4.0,-2.6) rectangle
(-3.4,2.6);
\filldraw[draw=black,fill=orange] (-3.0,-2.8) rectangle
(-2.4,2.8);
\draw[dotted] (-8.5,0.0) -- (-8.0,0.1) ;
\draw[dotted, thick] (-8.0,0.1) parabola(-2,-2.6);
\draw[dotted, thick] (-8.0,0.1) parabola(-2,-2.1);
\draw[dotted, thick] (-8.0,0.1) parabola(-2,1.0);
\draw[dotted, thick] (-8.0,0.1) parabola(-2,1.5);
\node[draw=red,fill=none, font=\huge,red] at (0.0, 2.0){${\cal C}$} ;
\draw[thick,red, style=->] (-0.5,1.3) -- (0.5,1.3) ;
%-------------------------------------------
\node[draw=none,fill=none] at (1.20, 0.8){$\bar{D^0}$} ;
\node[draw=none,fill=none] at (7.2, 1.5){$\pi^-$} ;
\node[draw=none,fill=none] at (7.2, 2.0){$\pi^-$} ;
\node[draw=none,fill=none] at (7.2, -1.6){$\pi^+$} ;
\node[draw=none,fill=none] at (7.2, -2.6){$K^+$} ;
\filldraw[draw=black,fill=lightgray] (0.0,-0.3) rectangle
(1.5,0.3);
\draw[blue,very thick] (0.5,0.0) -- (7.2,3.0) ;
\draw[blue,very thick] (0.5,0.0) -- (7.2,-3.0) ;
\draw[blue] (0.5,0.0) -- (7.2,0.0) ;
\node[circle, fill=red,inner sep=1pt,minimum size=1pt] at
(1.1, 0.1){};
\node[circle, fill=red,inner sep=2pt,minimum size=2pt] at (0.5, 0.0){};
\filldraw[draw=black,fill=blue] (2.0,2.5) rectangle (3.5,1.0);
\filldraw[draw=black,fill=blue] (2.0,-2.5) rectangle
(3.5,-1.0);
\filldraw[draw=black,fill=green] (4.0,-2.0) rectangle
(4.6,2.0);
\filldraw[draw=black,fill=yellow] (5.0,-2.6) rectangle
(5.6,2.6);
\filldraw[draw=black,fill=orange] (6.0,-2.8) rectangle
(6.6,2.8);
\draw[dotted] (0.5,0.0) -- (1.1,0.1) ;
\draw[dotted, thick] (1.1,0.1) parabola(7,-2.6);
\draw[dotted, thick] (1.1,0.1) parabola(7,-1.6);
\draw[dotted, thick] (1.1,0.1) parabola(7,1.5);
\draw[dotted, thick] (1.1,0.1) parabola(7,2.0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1311.5745 | arxiv | 2013-11-25T02:07:02 |
|
Discipline inclusions for considering the context of a message. | \documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[leqno]{amsmath}
\usepackage{amssymb}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{pgf,pgfarrows,pgfnodes}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{shapes}
\usetikzlibrary{decorations.text}
\usetikzlibrary{trees}
\usetikzlibrary{snakes}
\usetikzlibrary{plotmarks}
\usetikzlibrary{fit}
\begin{document}
\begin{tikzpicture}[scale=.5]
% 1, 4.25
\fill[yellow!50] (1,1) ellipse [x radius=6.25cm,y radius=3.25cm];
\fill [decorate,decoration={text along path,text=Semantics, text align=fit to path}]
(-.3,3.6) arc (100:80:8cm);
\fill[yellow] (1,1) ellipse [x radius=5cm,y radius=2.5cm];
\fill [decorate,decoration={text along path,text={Semiology, hermeneutics}, text align=fit to path}]
(-2,2.5) arc (110:70:9cm);
\fill[green!50] (1,1) ellipse [x radius=3.5cm,y radius=1.75cm];
\fill [decorate,decoration={text along path,text=Rhetorics, text align=fit to path}]
(-.5,2) arc (105:75:6cm);
\fill[green!80!black] (1,1) ellipse [x radius=2cm,y radius=1cm];
\draw (1,1) node {Pragmatics, context};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1207.6224 | arxiv | 2012-07-27T02:03:05 |
|
A comb-like order | \documentclass{amsart}
\usepackage{amsmath, amssymb, amsthm}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\begin{scope}[scale=0.5]
\coordinate [label=left:$i_1$] (i1) at (0,0);
\coordinate [label=right:$i_2$] (i2) at (1,0);
\coordinate [label=left:$i_3$] (i3) at (0.5,1);
\coordinate [label=right:$i_4$] (i4) at (1.5,1);
\coordinate [label=left:$i_5$] (i5) at (1,2);
\coordinate [label=left:$i_{2m -1}$] (j3) at (1.5,3);
\coordinate [label=right:$i_{2m}$] (j2) at (2.5,3);
\coordinate [label=left:$i_{2m + 1}$] (j1) at (2,4);
\draw (i1) -- (i5);
\draw (i3) -- (i2);
\draw (i5) -- (i4);
\draw[style=dotted] (i5) -- (j3);
\draw (j3) -- (j1);
\draw (j1) -- (j2);
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1304.0026 | arxiv | 2013-04-02T02:00:36 |
|
Left and Right intervals | \documentclass[notitlepage,a4paper]{article}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
\matrix (m) [matrix of math nodes,row sep=3em,column sep=1em,minimum width=1em]
{
Level \; h=k & \qquad & I \left [1, \; p_k^2 \right ]_{h=k} & \cup & I \left [p_k^2+1, \; m_k \right ]_{h=k} & = & I \left [1, \; m_k \right ]_{h=k} \\
Level \; h=h^\prime & \qquad & I \left [1, \; p_k^2 \right ]_{h=h^\prime} & \cup & I \left [p_k^2+1, \; m_k \right ]_{h=h^\prime} & = & I \left [1, \; m_k \right ]_{h=h^\prime} \\
Level \; h=1 & \qquad & I \left [1, \; p_k^2 \right ]_{h=1} & \cup & I \left [p_k^2+1, \; m_k \right ]_{h=1} & = & I \left [1, \; m_k \right ]_{h=1}\\
};
\path[loosely dotted]
(m-2-1) edge (m-1-1)
(m-3-1) edge (m-2-1)
(m-2-3) edge (m-1-3)
(m-3-3) edge (m-2-3)
(m-2-5) edge (m-1-5)
(m-3-5) edge (m-2-5)
(m-2-7) edge (m-1-7)
(m-3-7) edge (m-2-7);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1207.4802 | arxiv | 2014-05-16T02:13:16 |
|
The zero sets of the polynomials in eq-cad-intro and some projections on the x-axis (solid dots). | \documentclass[a4paper]{report}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{automata,arrows}
\begin{document}
\begin{tikzpicture}[scale=1.2]
% Axes
\draw[->] (-2.5, 0) -- (2.5,0) node[right] {$x$};
\draw[->] (0, -2.2) -- (0,2.2) node[above] {$y$};
% x^3 - y^2 = 0
\draw[domain=0:1.5,samples=50] plot (\x,{sqrt(\x*\x*\x)});
\draw[domain=0:1.5,samples=50] plot (\x,{-sqrt(\x*\x*\x)});
% x^2 + y^2 - 2 < 0
\draw (0,0) circle (1.41);
% cad
\draw[dotted] (1,-2) -- (1, 2);
\draw[dotted] (1.41,-2) -- (1.41,2);
\draw[dotted] (-1.41,-2) -- (-1.41,2);
\draw[fill] (-1.41, 0) circle (0.05);
\draw[fill] (0, 0) circle (0.05);
\draw[fill] (1, 0) circle (0.05);
\draw[fill] (1.41, 0) circle (0.05);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1401.5351 | arxiv | 2014-01-22T02:10:17 |
|
Geometric interpretation. Top: input feature pairs x_i, x_i' R^p are segments for y_i=0 and arrows for y_i\{-1,1\}. The level curves of the ranking function r( x)=|| x||_2^2 are grey, and differences |r( x')-r( x)| 1 are considered insignificant (y_i=0). Middle: in the enlarged feature space, the ranking function is linear: r( x)= w^( x). Bottom: two symmetric hyperplanes w^( x_i')-( x_i)\{-1,1\} are used to classify the difference vectors. | \documentclass{article}
\usepackage[table]{xcolor}
\usepackage{tikz}
\usepackage{amsmath,amssymb,amsthm}
\begin{document}
\begin{tikzpicture}[x=1pt,y=1pt]
\definecolor[named]{fillColor}{rgb}{1.00,1.00,1.00}
\path[use as bounding box,fill=fillColor,fill opacity=0.00] (0,0) rectangle (224.04,578.16);
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (224.04,578.16);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 14.40,409.44) --
(212.04,409.44) --
(212.04,578.16) --
( 14.40,578.16) --
( 14.40,409.44);
\end{scope}
\begin{scope}
\path[clip] ( 0.00,385.44) rectangle (224.04,578.16);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.00] at (113.22,398.64) {input feature $ x_{i,1}$};
\node[text=drawColor,rotate= 90.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.00] at ( 10.80,493.80) {input feature $ x_{i,2}$};
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (224.04,578.16);
\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= 1.00] at (221.64,493.80) {Original feature space $\mathbf x\in\mathbb R^p$};
\end{scope}
\begin{scope}
\path[clip] ( 14.40,409.44) rectangle (212.04,578.16);
\definecolor[named]{drawColor}{rgb}{0.50,0.50,0.50}
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( 87.24,469.12);
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 85.48,471.55) -- ( 84.58,472.80);
\node[text=drawColor,rotate=-54.13,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.60] at ( 83.81,470.34) { 1 };
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\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 70.72,468.99) -- ( 70.22,470.08);
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\definecolor[named]{drawColor}{rgb}{1.00,0.50,0.00}
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\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round,fill=fillColor] (110.86,123.07) circle ( 1.50);
\definecolor[named]{drawColor}{rgb}{0.60,0.31,0.64}
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\definecolor[named]{drawColor}{rgb}{1.00,0.50,0.00}
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\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round,fill=fillColor] (116.24,107.02) circle ( 1.50);
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round,fill=fillColor] (128.48, 82.90) circle ( 1.50);
\definecolor[named]{drawColor}{rgb}{0.30,0.69,0.29}
\definecolor[named]{fillColor}{rgb}{0.30,0.69,0.29}
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round,fill=fillColor] ( 81.15, 30.25) circle ( 1.50);
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (224.04,578.16);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 14.40, 24.00) --
(212.04, 24.00) --
(212.04,192.72) --
( 14.40,192.72) --
( 14.40, 24.00);
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (224.04,192.72);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.00] at (113.22, 13.20) {difference feature ${x'}_{i,1}^2-x_{i,1}^2$};
\node[text=drawColor,rotate= 90.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.00] at ( 10.80,108.36) {difference feature ${x'}_{i,2}^2-x_{i,2}^2$};
\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (224.04,578.16);
\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= 1.00] at (221.64,108.36) {Difference of enlarged features $\Phi(\mathbf x')-\Phi(\mathbf x)$};
\end{scope}
\begin{scope}
\path[clip] ( 14.40, 24.00) rectangle (212.04,192.72);
\definecolor[named]{drawColor}{rgb}{0.75,0.75,0.75}
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 14.40, 81.98) -- (212.04, 81.98);
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 76.96, 24.00) -- ( 76.96,192.72);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 14.40,175.02) -- (189.42, 0.00);
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 14.40,114.06) -- (128.46, 0.00);
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 82.42,154.55) circle ( 2.25);
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 53.70, 85.65) circle ( 2.25);
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 81.15, 30.25) circle ( 2.25);
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.80] at ( 52.58, 37.31) {$\Phi(\mathbf x_{20}')-\Phi(\mathbf x_{20})$};
\definecolor[named]{drawColor}{rgb}{0.60,0.31,0.64}
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.00] at (107.44, 55.01) {$y_i=0$};
\definecolor[named]{drawColor}{rgb}{1.00,0.50,0.00}
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.00] at (137.92,125.11) {$y_i=1$};
\definecolor[named]{drawColor}{rgb}{0.30,0.69,0.29}
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.00] at ( 37.34, 64.15) {$y_i=-1$};
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.80] at ( 52.58,104.36) {$\Phi(\mathbf x_{11}')-\Phi(\mathbf x_{11})$};
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.80] at (113.54,156.18) {$\Phi(\mathbf x_{1}')-\Phi(\mathbf x_{1})$};
\node[text=drawColor,rotate=-45.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.70] at ( 81.82, 50.26) {$\mathbf w^\intercal [ \Phi(\mathbf x') - \Phi(\mathbf x) ] = -1$};
\node[text=drawColor,rotate=-45.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.70] at (142.78, 50.26) {$\mathbf w^\intercal [ \Phi(\mathbf x') - \Phi(\mathbf x) ] = 1$};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1401.8008 | arxiv | 2014-02-03T02:00:54 |
|
Timed automaton . | \documentclass[runningheads,a4paper]{llncs}
\usepackage{amsmath,wasysym}
\usepackage{tikz}
\usetikzlibrary{automata,fit,positioning}
\begin{document}
\begin{tikzpicture}[shorten >=1pt,node distance=3cm,on
grid,auto,every node/.style={shape=rectangle}]
\node[draw] (q0) {\footnotesize $q_0$};
\node[draw] (q1) [right=of q0] {\footnotesize $q_1$};
\node[draw] (q2) [right=of q1] {\footnotesize $q_2$};
\node[draw] (q3) [right=of q2] {\footnotesize $q_3$};
\node (fakeinit) [node distance=1cm,left=of q0] {};
\begin{scope}[->]
\draw (fakeinit) edge (q0);
\draw (q0) edge node {\footnotesize $x\leq 5$} (q1);
\draw (q1) edge (q2);
\draw (q2) edge [bend right=20] node [swap] {\footnotesize
$y\geq 5,\ x:=0$} (q1);
\draw (q2) edge node {\footnotesize $x\leq 14,\ y:=0$} (q3);
\draw (q0) edge [bend right=16] node[swap] {\footnotesize $y\geq
10^6$} (q3);
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1110.3704 | arxiv | 2011-10-18T02:10:40 |
|
Plate notation of LDA. | \documentclass[10pt, twocolumn]{amsart}
\usepackage{amssymb}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{arrows,backgrounds}
\usepackage{xcolor}
\begin{document}
\begin{tikzpicture}[scale=0.7]
\tikzstyle{post}=[->,shorten >=0pt,>=stealth',thick]
\foreach \x/\y in {-2.2/1.5, 1.6/1.5, 4/1.5, 6.4/5.1,
3/5.1} {
\draw[thick] (\x, \y) circle (0.8);
}
\draw[thick, fill=gray] (6.4,1.5) circle (0.8);
\draw[very thick] (0, -0.8) rectangle (8, 3.2);
\draw[very thick] (2.9, 0) rectangle (7.5, 2.8);
\draw[very thick] (5, 3.6) rectangle (8, 6.4);
\node at (1.6, 1.5) {$\theta$};
\node at (4, 1.5) {$z$};
\node at (6.4, 1.5) {$w$};
\node at (-2.2, 1.5) {$\alpha$};
\node at (6.4, 5.1) {$\varphi$};
\node at (3, 5.1) {$\beta$};
\node at (7.7, -0.4) {$M$};
\node at (7.2, 0.4) {$N$};
\node at (7.7, 4) {$K$};
\foreach \x/\y in {-1.4/0.8, 2.4/3.2, 4.8/5.6} {
\draw[->, post] (\x, 1.5) -- (\y, 1.5);
}
\draw[->, post] (3.8, 5.1) -- (5.6, 5.1);
\draw[->, post] (6.4, 4.3) -- (6.4, 2.3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1307.0317 | arxiv | 2013-07-02T02:03:26 |
|
Plate notation of parameterized distribution q. | \documentclass[10pt, twocolumn]{amsart}
\usepackage{amssymb}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{arrows,backgrounds}
\usepackage{xcolor}
\begin{document}
\begin{tikzpicture}[scale=0.7]
\tikzstyle{post}=[->,shorten >=0pt,>=stealth',thick]
\draw[very thick] (0, 0) rectangle (2.8, -5.2);
\draw[very thick] (-2.6, 0.5) rectangle (3.8, -5.7);
\draw[very thick] (4.3, 0) rectangle (7.1 , -5.2);
\foreach \x/\y/\name in {1.3/-1.3/$\psi$, 1.3/-3.9/$z$, -1.3/-1.3/$\gamma$,
-1.3/-3.9/$\theta$, 5.6/-1.3/$\lambda$, 5.6/-3.9/$\varphi$
}{
\draw[thick] (\x, \y) circle (0.8);
\node at (\x, \y) {\name};
}
\node at (2.4, -4.8) {$N$};
\node at (6.7, -4.8) {$K$};
\node at (3.4, -5.2) {$M$};
\foreach \x/\y/\z/\u in {1.3/-2.1/1.3/-3.1,
-1.3/-2.1/-1.3/-3.1,
5.6/-2.1/5.6/-3.1
}
{
\draw[->, post] (\x, \y) -- (\z, \u);
}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1307.0317 | arxiv | 2013-07-02T02:03:26 |
|
A quantum circuit for producing a GHZ state using Hadamard gates and controlled phase gates. | \documentclass[english,10pt,a4paper,nofootinbib,twocolumn]{revtex4}
\usepackage{amsmath,amssymb,amsfonts,amsthm}
\usepackage[colorlinks=true,linkcolor=blue,citecolor=blue]{hyperref}
\usepackage{tikz}
\usetikzlibrary{backgrounds,fit,decorations.pathreplacing}
\usetikzlibrary{circuits.logic.US}
\newcommand{\fullket}[1]{\ensuremath{\left|#1\right\rangle}}
\begin{document}
\begin{tikzpicture}[thick]
%
% `operator' will only be used by Hadamard (H) gates here.
% `phase' is used for controlled phase gates (dots).
% `surround' is used for the background box.
\tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
\tikzstyle{phase} = [fill,shape=circle,minimum size=5pt,inner sep=0pt]
\tikzstyle{surround} = [fill=blue!10,thick,draw=black,rounded corners=2mm]
%
% Qubits
\node at (0,0) (q1) {\fullket{0}};
\node at (0,-1) (q2) {\fullket{0}};
\node at (0,-2) (q3) {\fullket{0}};
%
% Column 1
\node[operator] (op11) at (1,0) {H} edge [-] (q1);
\node[operator] (op21) at (1,-1) {H} edge [-] (q2);
\node[operator] (op31) at (1,-2) {H} edge [-] (q3);
%
% Column 3
\node[phase] (phase11) at (2,0) {} edge [-] (op11);
\node[phase] (phase12) at (2,-1) {} edge [-] (op21);
\draw[-] (phase11) -- (phase12);
%
% Column 4
\node[phase] (phase21) at (3,0) {} edge [-] (phase11);
\node[phase] (phase23) at (3,-2) {} edge [-] (op31);
\draw[-] (phase21) -- (phase23);
%
% Column 5
\node[operator] (op24) at (4,-1) {H} edge [-] (phase12);
\node[operator] (op34) at (4,-2) {H} edge [-] (phase23);
%
% Column 6
\node (end1) at (5,0) {} edge [-] (phase21);
\node (end2) at (5,-1) {} edge [-] (op24);
\node (end3) at (5,-2) {} edge [-] (op34);
%
% Bracket
\draw[decorate,decoration={brace},thick] (5,0.2) to
node[midway,right] (bracket) {$\frac{\fullket{000}+\fullket{111}}{\sqrt{2}}$}
(5,-2.2);
%
% Background Box
%
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1307.0096 | arxiv | 2013-07-02T02:01:05 |
|
The scheme X | \documentclass{amsart}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[utf8]{inputenc}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=0.5cm,y=0.5cm]
\foreach \x in {-1,1,2,3,4,5,6,7,8,9}
\foreach \y in {-1,1,2,3,4,5,6,7,8}
\clip(-1,0) rectangle (10,10);
\fill [color=black] (1,1) circle (2pt);
\fill [color=black] (2,1) circle (2pt);
\fill [color=black] (3,1) circle (2pt);
\fill [color=black] (1,2) circle (2pt);
\fill [color=black] (2,2) circle (2pt);
\fill [color=black] (3,2) circle (2pt);
\fill [color=black] (4,2) circle (2pt);
\fill [color=black] (1,3) circle (2pt);
\fill [color=black] (2,3) circle (2pt);
\fill [color=black] (3,3) circle (2pt);
\fill [color=black] (4,3) circle (2pt);
\fill [color=black] (5,3) circle (2pt);
\fill [color=black] (1,4) circle (2pt);
\fill [color=black] (2,4) circle (2pt);
\fill [color=black] (3,4) circle (2pt);
\fill [color=black] (4,4) circle (2pt);
\fill [color=black] (5,4) circle (2pt);
\fill [color=black] (6,5) circle (2pt);
\fill [color=black] (1,6) circle (2pt);
\fill [color=black] (2,6) circle (2pt);
\fill [color=black] (5,6) circle (2pt);
\fill [color=black] (6,6) circle (2pt);
\fill [color=black] (1,7) circle (2pt);
\fill [color=black] (2,7) circle (2pt);
\fill [color=black] (4,7) circle (2pt);
\fill [color=black] (5,7) circle (2pt);
\fill [color=black] (6,7) circle (2pt);
\fill [color=black] (3,8) circle (2pt);
\fill [color=black] (7,8) circle (2pt);
\fill [color=black] (8,8) circle (2pt);
\fill [color=black] (9,8) circle (2pt);
\draw (1,0.5) -- (1,8.5);
\draw[color=black] (1,9.5) node {\footnotesize $C_0$};
\draw (2,0.5) -- (2,8.5);
\draw[color=black] (2,9.5) node {\footnotesize $C_1$};
\draw (3,0.5) -- (3,8.5);
\draw[color=black] (3,9.5) node {\footnotesize $C_2$};
\draw (4,1.5) -- (4,8.5);
\draw[color=black] (4,9.5) node {\footnotesize $C_3$};
\draw (5,2.5) -- (5,8.5);
\draw[color=black] (5,9.5) node {\footnotesize $C_4$};
\draw (6,4.5) -- (6,8.5);
\draw[color=black] (6,9.5) node {\footnotesize $C_5$};
\draw (7,7.5) -- (7,8.5);
\draw[color=black] (7,9.5) node {\footnotesize $C_6$};
\draw (8,7.5) -- (8,8.5);
\draw[color=black] (8,9.5) node {\footnotesize $C_7$};
\draw (9,7.5) -- (9,8.5);
\draw[color=black] (9,9.5) node {\footnotesize $C_8$};
\draw (0.5,1) -- (3.5,1);
\draw[color=black] (-0.5,1) node {\footnotesize $R_7$};
\draw (0.5,2) -- (4.5,2);
\draw[color=black] (-0.5,2) node {\footnotesize $R_6$};
\draw (0.5,3) -- (5.5,3);
\draw[color=black] (-0.5,3) node {\footnotesize $R_5$};
\draw (0.5,4) -- (5.5,4);
\draw[color=black] (-0.5,4) node {\footnotesize $R_4$};
\draw (0.5,5) -- (6.5,5);
\draw[color=black] (-0.5,5) node {\footnotesize $R_3$};
\draw (0.5,6) -- (6.5,6);
\draw[color=black] (-0.5,6) node {\footnotesize $R_2$};
\draw (0.5,7) -- (6.5,7);
\draw[color=black] (-0.5,7) node {\footnotesize $R_1$};
\draw (0.5,8) -- (9.5,8);
\draw[color=black] (-0.5,8) node {\footnotesize $R_0$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1009.4095 | arxiv | 2010-09-22T02:02:13 |
|
Hasse-diagram of Szondi's signatures | \documentclass{article}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{amsmath,amssymb,array,marvosym,multirow,rotating,pgf,tikz,stmaryrd,chemarrow,colortbl,listings}
\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/1403.6048 | arxiv | 2014-03-25T01:14:19 |
|
To count the number of ranked topologies for the tree above, we multiply the counts in the 3 levels. In the lowest level we have 3 lineages reducing to 1 (root of lowest calibration), 5 lineages reducing to 3 and 2 free lineages not reducing. So, the total number of topologies is R_3^1 R_5^2 R_2^2 2+5+2 - (1+3+2)1,2,0 = 3 (10 6) 1 3!1!2!0! = 540 Note that in the binomial we use one less lineage (2 instead of 3) for the calibrated clade, since its position as root is fixed. In the second level we have 3 lineages reducing to 1, and 3 free lineages reducing to 2, giving R_3^1 R_3^2 2+3 - (1+2)1,1 = 3 3 2!1!1! = 9 and in the last level 3 lineages to 1 in 3 ways. So, the total number is 540 9 3 = 12960. | \documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{shapes,positioning}
\begin{document}
\begin{tikzpicture}[scale=0.6,node distance = .5cm,auto,transform shape]
\tikzstyle{tip} = [text centered]
\tikzstyle{internal} = [green]
\tikzstyle{calibrated} = [thick, red, fill]
\tikzstyle{line}=[draw,blue,thick]
\tikzstyle{hline}=[densely dotted, thick]
\node[tip] (c1) at (0,0) {A};
\node[tip] (c2) at (1,0) {B};
\node[tip] (c4) at (2,0) {C};
\node[tip] (c6) at (3,0) {D};
\node[tip] (c7) at (4,0) {E};
\node[tip] (c9) at (5,0) {F};
\node[tip] (c10) at (6,0) {G};
\node[tip] (c12) at (7,0) {H};
\node[tip] (c15) at (8,0) {I};
\node[tip] (c16) at (9,0) {K};
\node (c0) at (4.5,7.0) {};
\node (c3) at (0.642857142857,1.0) {};
\node (c5) at (1.28571428571,2.0) {};
\node (c8) at (3.47571428571,1.5) {};
\node (c11) at (5.11714285714,1.0) {};
\node (c13) at (5.29285714286,2.5) {};
\node (c14) at (4.26857142857,4.0) {};
\node (c17) at (7.23214285714,2.75) {};
\node (c18) at (4.98214285714,6.25) {};
\draw[internal] (c0) circle (3pt);
\draw[internal] (c3) circle (3pt);
\draw[calibrated] (c5) circle (3pt);
\draw[internal] (c8) circle (3pt);
\draw[internal] (c11) circle (3pt);
\draw[internal] (c13) circle (3pt);
\draw[calibrated] (c14) circle (3pt);
\draw[internal] (c17) circle (3pt);
\draw[internal] (c18) circle (3pt);
\draw[line] (c1) -- (c3);
\draw[line] (c2) -- (c3);
\draw[line] (c3) -- (c5);
\draw[line] (c4) -- (c5);
\draw[line] (c5) -- (c0);
\draw[line] (c6) -- (c8);
\draw[line] (c7) -- (c8);
\draw[line] (c8) -- (c14);
\draw[line] (c9) -- (c11);
\draw[line] (c10) -- (c11);
\draw[line] (c11) -- (c13);
\draw[line] (c12) -- (c13);
\draw[line] (c13) -- (c14);
\draw[line] (c14) -- (c18);
\draw[line] (c15) -- (c17);
\draw[line] (c16) -- (c17);
\draw[line] (c17) -- (c18);
\draw[line] (c18) -- (c0);
\draw[hline] (0,7.0) -- (9,7.0);
\draw[hline] (0,2.0) -- (9,2.0);
\draw[hline] (0,4.0) -- (9,4.0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1311.4921 | arxiv | 2013-11-21T02:02:03 |
|
Parent of monophyletic clade of size n. | \documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{shapes,positioning}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\node at (-0.4, 4) {$h$};
\draw[dashed] (0,4) -- (6, 4);
\draw[densely dotted] (0,3) -- (6, 3);
\node at (1.0, -0.4) {$n$};
\node at (5.0, -0.4) {$l$};
\node at (3.5, 3) {$i$};
\node at (3, 4) {$k$};
% Leve 1 forests
\draw[thick, blue] (1.5,3) -- (3,6);
\draw[thick, blue] (4,0) -- (2,4);
\draw[thick, blue] (6,0) -- (3,6);
\draw[thick, blue, dashed] (4,0) -- (6,0);
% Level 2 forests
\draw[thick, green] (0,0) -- (2,4);
\draw[thick, green, dashed] (0,0) -- (2,0);
\draw[thick, green] (2,0) -- (1.5,3);
\fill[white] (2,4) circle (3pt);
\draw[thick, green] (2,4) circle (3pt);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1311.4921 | arxiv | 2013-11-21T02:02:03 |
|
Monophyletic clade of size n and root with n+m taxa. | \documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{shapes,positioning}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\node at (-0.4,6) {$h_0$};
\node at (-0.4, 3) {$h$};
\node at (3.5, 3) {$k$};
\draw[dashed] (0,6) -- (6, 6);
\draw[dashed] (0,3) -- (6, 3);
\node at (0.0, -0.4) {1};
\node at (1.0, -0.4) {$\dots$};
\node at (2.0, -0.4) {$n$};
\node at (4.0, -0.4) {$n+1$};
\node at (5.0, -0.4) {$\dots$};
\node at (6.0, -0.4) {$n+m$};
% Leve 1 forests
\draw[thick, blue] (1.5,3) -- (3,6);
\draw[thick, blue] (4,0) -- (2,4);
\draw[thick, blue] (6,0) -- (3,6);
\draw[thick, blue, dashed] (4,0) -- (6,0);
% Level 2 forests
\draw[thick, green] (0,0) -- (1.5,3);
\draw[thick, green, dashed] (0,0) -- (2,0);
\draw[thick, green] (2,0) -- (1.5,3);
\fill[white] (1.5,3) circle (3pt);
\draw[thick, green] (1.5,3) circle (3pt);
\fill[white] (3,6) circle (3pt);
\draw[thick, blue] (3,6) circle (3pt);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1311.4921 | arxiv | 2013-11-21T02:02:03 |
|
Two nested monophyletic clades of size n and n+m taxa in a n + m + l taxa tree (l > 0). | \documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{shapes,positioning}
\begin{document}
\begin{tikzpicture}[scale=0.5]
\node at (-0.4,6) {$h_1$};
\node at (-0.4, 3) {$h_2$};
\draw[dashed] (0,6) -- (9, 6);
\draw[dashed] (0,3) -- (9, 3);
\node at (3.5, 3) {$m_1$};
\node at (6.5, 3) {$l_1$};
\node at (5, 6) {$l_2$};
\node at (1.0, -0.4) {$n$};
\node at (5.0, -0.4) {$m$};
\node at (8.0, -0.4) {$l$};
% Leve 1 forests
\draw[thick, blue] (1.5,3) -- (3,6);
\draw[thick, blue] (4,0) -- (2,4);
\draw[thick, blue] (6,0) -- (3,6);
\draw[thick, blue, dashed] (4,0) -- (6,0);
% Level 2 forests
\draw[thick, green] (0,0) -- (1.5,3);
\draw[thick, green, dashed] (0,0) -- (2,0);
\draw[thick, green] (2,0) -- (1.5,3);
\draw[thick, red] (3,6) -- (4.5,9);
\draw[thick, red] (4.5,9) -- (9,0);
\draw[thick, red, dashed] (9,0) -- (7,0);
\draw[thick, red] (3.5,7) -- (7,0);
\fill[white] (1.5,3) circle (3pt);
\draw[thick, green] (1.5,3) circle (3pt);
\fill[white] (3,6) circle (3pt);
\draw[thick, blue] (3,6) circle (3pt);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1311.4921 | arxiv | 2013-11-21T02:02:03 |
|
Finite state machine illustrating the first strategy set, _1, of the S_i strategies. The action to perform is in the node, and transitions are taken on the basis of the opponent's action in the previous round (or based on the previous round number t). All strategies start in the left node (C), except S_0 that starts with defection in the right node (D). S_i cooperates conditionally for i rounds after which it starts to defect. | \documentclass[10pt,a4paper]{article}
\usepackage{color}
\usepackage{amsmath}
\usepackage{pgf}
\usepackage{tikz}
\usetikzlibrary{arrows,automata}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=3.5cm,semithick]
\tikzstyle{every state}=[circle,draw]
\node[state, label=220:$S_{i \in \{1..N\}}$] (C) {$C$};
\node[state, label=300:$S_0$] (D) [right of=C] {$D$};
\path (C) edge node {$D \lor (t \geq i)$} (D) (C) edge [loop above, distance=2.5cm, out=130, in=50, looseness=0.8] node {$C \land (t < i)$} (C) (D) edge [loop above, distance=2.5cm, out=130, in=50, looseness=0.8] node {} (D);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1301.1710 | arxiv | 2013-01-10T02:00:23 |
|
Finite state machine illustrating the extended strategy set _2 consisting of the strategies S_i,CC_i, and DC_i. S_i are the conditional cooperators as described in Figure~fig_statespace0. The Convincers are denoted CC_i and the Followers DC_i. Strategies start in the state at which the name is placed. The strategies CC_i start with at least two rounds of cooperation, which may trigger DC_i to switch from defection to cooperation. After that the latter two strategies act as the conditional cooperators S_i. | \documentclass[10pt,a4paper]{article}
\usepackage{color}
\usepackage{amsmath}
\usepackage{pgf}
\usepackage{tikz}
\usetikzlibrary{arrows,automata}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=3.5cm,semithick]
\tikzstyle{every state}=[circle,draw]
\node[state, label=220:$S_{i \in \{1..N\}}$] (C) {$C$};
\node[state, label=left:$CC_{i \in \{2..N\}}$] (A) [left of=C] {$C$};
\node[state, label=left:$DC_{i \in \{2..N\}}$] (B) [below of=C] {$D$};
\node[state, label=300:$S_0$] (D) [right of=C] {$D$};
\path (A) edge node {} (C) (B) edge node {$C$} (C) (B) edge node {$D$} (D) (C) edge node {$D \lor (t \geq i)$} (D) (C) edge [loop above, distance=2.5cm, out=130, in=50, looseness=0.8] node {$C \land (t < i)$} (C) (D) edge [loop above, distance=2.5cm, out=130, in=50, looseness=0.8] node {} (D);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1301.1710 | arxiv | 2013-01-10T02:00:23 |
|
Birth/death steps for the product rule (PR) in the Achlioptas' model of percolation. In this example, edge e_2 was born before edge e_1, since |C_11||C_12| > |C_21||C_22|. Therefore, when e_1 and e_2 are selected during a death step, e_2 is discarded aftere_1. This death step specification ensures that births and deaths constitute genuine reverse PR operations. | \documentclass[8pt,apl,superscriptaddress,pdftex,dvipsnames,twocolumn]{revtex4-1}
\usepackage{amsmath,amsthm,amssymb,amsfonts}
\usepackage[dvipsnames]{xcolor}
\usepackage{pgf,tikz}
\usetikzlibrary{snakes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\usetikzlibrary{patterns}
\usetikzlibrary{fit}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[font=\small,scale=.8,show background rectangle]
%%% C11
\draw[rounded corners=10pt,thick]
(-2.75,1.0) -- (-2.75,2.0) -- (-0.25,2.0) -- (-0.25,1.0) -- cycle;
%%% C12
\draw[rounded corners=10pt,thick]
(-2.75,-1.0) -- (-2.75,-2.0) -- (-0.5,-2.0) -- (-0.5,-1.0) -- cycle;
%%% C21
\draw[rounded corners=10pt,thick]
(+2.75,1.0) -- (+2.75,2.0) -- (+1.0,2.0) -- (+1.0,1.0) -- cycle;
%%% C22
\draw[rounded corners=10pt,thick]
(+2.75,-1.0) -- (+2.75,-2.0) -- (+1.10,-2.0) -- (+1.10,-1.0) -- cycle;
%%%%%%%%%%%%%%%%%%%
%%% Gt.
\draw[rounded corners=10pt,thick]
(-3.5,+2.5) -- (-3.5,-2.5) -- (+3.5,-2.5) -- (+3.5,+2.5) -- cycle;
%%% Points Location.
\draw(-1.5,1.5) node(v11){};
\draw(-1.5,-1.5) node(v12){};
\draw(1.5,1.5) node(v21){};
\draw(1.5,-1.5) node(v22){};
% %%% Points filling.
\fill[fill=black](v11) circle (2.0pt);
\fill[fill=black](v12) circle (2.0pt);
\fill[fill=black](v21) circle (2.0pt);
\fill[fill=black](v22) circle (2.0pt);
% %%% Edges.
\draw[semithick,dashed] (v11) -- (v12) node[pos=0.5,anchor=west]{$e_{1}$};
\draw[semithick] (v21) -- (v22) node[pos=0.5,anchor=east]{$e_{2}$};
%%% Node Labels.
\draw(v11) node[anchor=east]{$v_{11}$};
\draw(v12) node[anchor=east]{$v_{12}$};
\draw(v21) node[anchor=west]{$v_{21}$};
\draw(v22) node[anchor=west]{$v_{22}$};
%%% Labels.
\draw(+3.5,-2.5)node[anchor=north west]{$G_{t}$};
\draw(-2.5,1.0)node[anchor=north east]{$C_{11}$};
\draw(-2.5,-1.0)node[anchor=south east]{$C_{12}$};
\draw(+2.5,1.0)node[anchor=north west]{$C_{21}$};
\draw(+2.5,-1.0)node[anchor=south west]{$C_{22}$};
%%% Labels.
\draw[gray!10] (-4.5,-3.0) -- (+4.5,-3.0);
\draw[gray!10] (-4.5,+3.0) -- (+4.5,+3.0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1401.3518 | arxiv | 2014-01-16T02:07:26 |
|
Directed Acyclic Graph (DAG) representation of the hidden Markov process combining a latent stochastic graph process in the first row denoted by G_t, with an observed stochastic graph process contaminated by noise in the second row, denoted by G^_t. Directed arrows indicate probabilistic dependence, such that the distribution of the observed G_t^ depends on the value taken by the latent graph, G_t. | \documentclass[8pt,apl,superscriptaddress,pdftex,dvipsnames,twocolumn]{revtex4-1}
\usepackage{amsmath,amsthm,amssymb,amsfonts}
\usepackage[dvipsnames]{xcolor}
\usepackage{pgf,tikz}
\usetikzlibrary{snakes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\usetikzlibrary{patterns}
\usetikzlibrary{fit}
\usetikzlibrary{calc}
\newcommand{\as}{^\ast}
\begin{document}
\begin{tikzpicture}[font=\small,scale=1.0,show background rectangle]
% Observed (Boxes)
\draw (-2.0,0)node[draw,minimum size=1.0cm](x1){$G\as_{t-1}$};
\draw (0,0) node[draw,minimum size=1.0cm](x2){$G\as_{t}$};
\draw (2.0,0) node[draw,minimum size=1.0cm](x3){$G\as_{t+1}$};
% Latent (Circles)
\draw (-2.0,2.0)node[draw,circle,minimum size=1.0cm](l1){$G_{t-1}$};
\draw (0,2.0) node[draw,circle,minimum size=1.0cm](l2){$G_{t}$};
\draw (2.0,2.0) node[draw,circle,minimum size=1.0cm](l3){$G_{t+1}$};
% Arrows
\draw[thick,->,dashed] (-3.5,2.0) -- (l1);
\draw[thick,->] (l1) -- (l2);
\draw[thick,->] (l2) -- (l3);
\draw[thick,->] (l1) -- (x1);
\draw[thick,->] (l2) -- (x2);
\draw[thick,->] (l3) -- (x3);
\draw[thick,->,dashed] (l3) -- (+3.5,2.0);
% Frame
\draw[color=gray!10](-3.2,-.8)--(3.2,-.8);
\draw[color=gray!10](-3.2,+2.8)--(3.2,+2.8);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1401.3518 | arxiv | 2014-01-16T02:07:26 |
|
Illustration of subroutine SUB | \documentclass[a4paper]{llncs}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{tkz-berge}
\begin{document}
\begin{tikzpicture}
\draw (0,0) circle (100pt);
\draw[very thick] (60:100pt) ++(0,0) arc (60:100:100pt);
\draw (60:95pt) -- (60:105pt);
\draw (60:110pt) node [rotate=60,anchor=west] {$k$};
\draw (100:95pt) -- (100:105pt);
\draw (100:110pt) node [rotate=110,anchor=west]{$k+(b-a)$};
\fill (70:100pt) circle (2pt);
\draw (70:110pt) node [rotate=70,anchor=west] {rightmost 1};
\fill (95:100pt) circle (2pt);
\draw (95:110pt) node [rotate=95,anchor=west] {leftmost 1};
\filldraw[fill=blue!80,draw=blue!80,opacity=0.5] (185:100pt) -- (70:100pt) arc (70:30:100pt) -- cycle;
\filldraw[fill=blue!80,draw=blue!80,opacity=0.5] (250:100pt) -- (95:100pt) arc (95:135:100pt) -- cycle;
\filldraw[fill=blue!20,draw=blue!80,opacity=0.3,style=dashed] (215:100pt) -- (60:100pt) arc (60:100:100pt) -- cycle;
\draw[very thick,draw=blue!100] (185:100pt) ++(0,0) arc (185:250:100pt);
\draw (185:95pt) -- (185:105pt);
\draw (185:110pt) node [rotate=5,anchor=east] {$u$};
\draw (250:95pt) -- (250:105pt);
\draw (250:110pt) node [rotate=70,anchor=east] {$v$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1305.1021 | arxiv | 2013-05-07T02:02:01 |
|
The graph CS(20) | \documentclass[a4paper]{llncs}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{tkz-berge}
\begin{document}
\begin{tikzpicture}
\grCirculant[RA=2.7,prefix=]{20}{1,4,9}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1305.1021 | arxiv | 2013-05-07T02:02:01 |
|
The graph CI(20,4,6) | \documentclass[a4paper]{llncs}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{tkz-berge}
\begin{document}
\begin{tikzpicture}
\grCirculant[RA=3,prefix=]{20}{4,5,6}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1305.1021 | arxiv | 2013-05-07T02:02:01 |
|
Proof of inference node | \documentclass[conference]{llncs}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usepackage{amsmath, amsfonts, amssymb}
\begin{document}
\begin{tikzpicture}[-, main node/.style={circle,fill=white!25,draw,node distance=2.5cm},minimum width=3pt]
\node[main node] (1) {i};
\node[main node] (2) [below left of=1] {k};
\node[main node] (3) [below right of=1] {j};
\node[main node] (4) [below left of=2] {l};
\node[main node] (5) [below right of=2] {m};
\path[every node/.style={font=\sffamily\small}]
(1) edge node [left] {} (2)
edge node [right] {} (3)
(2) edge node [left] {} (4)
edge node [right] {} (5)
;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1403.6237 | arxiv | 2014-04-01T02:09:13 |
|
The LTT of the list =3,9,5,7,8,4,6. The up and down nodes are indicated by a dashed grey line. The layer number is 3. The team of 3 is a list 4,5,9. The team of 5 is a list with a single element 7. The team of 4 is 6,8. These teams form their own team trees at layer 1. | \documentclass[envcountsame]{llncs}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{xcolor}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning, calc, decorations.markings,shapes.multipart,chains}
\begin{document}
\begin{tikzpicture}[tnode/.style={thin,circle,draw},level distance=1cm,emph/.style={edge from parent/.style={black,thick,draw}},norm/.style={edge from parent/.style={black,thin,draw}}]
\node[tnode](root1){3}
child[emph] {
node[tnode](first3){3}
child[emph] {
node[tnode](3){3}
child {
node[tnode](three){3}
}
child[norm] {
node[tnode](mark1){9}
}
}
child[norm] {
node[tnode](first5){5}
child[emph] {
node[tnode]{5}
}
child[norm] {
node[tnode](first7){7}
}
}
}
child {
node[tnode](root3){4}
child[emph] {
node[tnode](first4){4}
child[norm] {
node[tnode](first8){8}
}
child[emph] {
node[tnode](mark2){4}
}
}
child {
node[tnode](first16){6}
}
};
\tikzstyle{level 1}=[sibling distance=4cm]
\tikzstyle{level 2}=[sibling distance=2cm]
\node[tnode, below=of mark1](root2){4}
child[emph] {
node[tnode](four){4}
child[emph] {
node[tnode](second4){4}
}
child[norm] {
node[tnode](second5){5}
}
}
child {
node[tnode](second9){9}
};
\draw[dashed,very thick] (-8,-3.75) to (6,-3.75);
\node[above left=of 3]{\Large Layer 0};
\node[tnode, below=of first7](root5){7};
\node[above left=of four,yshift=-0.5cm,xshift=1cm]{\Large Layer 1};
\node[tnode, below=of mark2](root4){6}
child[emph] {
node[tnode](second6){6}
}
child[norm] {
node[tnode](second8){8}
};
\draw[dashed,very thick] (-8,-7) to (6,-7);
\node[tnode, below=of second5, yshift=0.5cm,xshift=0.75cm](third5root){5}
child[emph]{
node[tnode](third5leaf){5}}
child[norm]{
node[tnode](third9){9}};
\node[above left=of third5leaf,yshift=-0.5cm,xshift=1.3cm]{\Large Layer 2};
\node[tnode, below=of root4,yshift=-1.75cm](third8){8};
\draw[dashed,very thick] (-8,-9.25) to (6,-9.25);
\node[tnode, below=of third5root, yshift=-1cm](fourth9){9};
\node[left=of fourth9,xshift=-0.6cm]{\Large Layer 3};
\path[-,gray,dashed]
(second4) edge[bend left=23] node {} (root1)
(second5) edge[bend right=30] node {} (first3)
(second9) edge[bend right=30] node {} (3)
(root5) edge[bend left=30] node {} (first5)
(second6) edge[bend right=25] node {} (root3)
(second8) edge[bend right=30] node {} (first4)
(four) edge[bend left=20] node {} (third5leaf)
(third5root) edge[bend left=20] node{} (fourth9)
(root2) edge[bend left=20] node {} (third9)
(root4) edge[bend left=20] node {} (third8);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.2712 | arxiv | 2014-04-21T02:03:32 |
|
A tournament tree of a list =3,6,9,2,4,7,8. Edges in principal paths are bolded. | \documentclass[envcountsame]{llncs}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{xcolor}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning, calc, decorations.markings,shapes.multipart,chains}
\begin{document}
\begin{tikzpicture}[decoration={markings,mark=at position 3cm with {\arrow[black]{stealth}}},path/.style={*->,>=stealth,postaction=decorate},
list/.style={rectangle split, rectangle split parts=2,draw,rectangle split horizontal,minimum width=1.5cm, on chain}, start chain]
\node[circle,draw,minimum size=20pt,thin]{\Large 2}
child[very thick]{node[circle,draw,minimum size=20pt,thin]{\Large 2}
child[thin]{node[circle,draw,minimum size=20pt]{\Large 3}
child[very thick]{node[circle,draw,minimum size=20pt,thin](base){\Large 3}}
child{node[circle,draw,minimum size=20pt]{\Large 6}}}
child[very thick]{node[circle,draw,minimum size=20pt,thin]{\Large 2}
child[thin]{node[circle,draw,minimum size=20pt]{\Large 9}}
child[very thick]{node[circle,draw,minimum size=20pt,thin]{\Large 2}}}}
child{node[circle,draw,minimum size=20pt]{\Large 4}
child[very thick]{node[circle,draw,minimum size=20pt,thin]{\Large 4}
child[very thick]{node[circle,draw,minimum size=20pt,thin]{\Large 4}}
child[thin]{node[circle,draw,minimum size=20pt,thin]{\Large 7}}}
child{node[circle,draw,minimum size=20pt]{\Large 8}}};
\node [
list,
below=of base,
yshift=0.5cm
] (3) {\Large 3};
\node[left=of 3](label){\huge $\ell:$};
\node [
list,
right=of 3
] (12) {\Large 6};
\node [
list,
right=of 12
] (16) {\Large 9};
\node [
list,
right=of 16,
xshift=0.1cm
] (2) {\Large 2};
\node [
list,
right=of 2,
xshift=0.1cm
] (4) {\Large 4};
\node [
list,
right=of 4,
xshift=0.2cm
] (7) {\Large 7};
\node [
list,
right=of 7,
xshift=0.5cm
] (13) {\Large 8};
\node [
draw,
on chain,
inner sep=6.5pt,
right=of 13,
] (end){};
\draw(end.north east) -- (end.south west);
\draw(end.north west) -- (end.south east);
\draw[path] let \p1 = (3.two), \p2 = (3.center) in (\x1,\y2) -- (12);
\draw[path] let \p1 = (12.two), \p2 = (12.center) in (\x1,\y2) -- (16);
\draw[path] let \p1 = (16.two), \p2 = (16.center) in (\x1,\y2) -- (2);
\draw[path] let \p1 = (2.two), \p2 = (2.center) in (\x1,\y2) -- (4);
\draw[path] let \p1 = (4.two), \p2 = (4.center) in (\x1,\y2) -- (7);
\draw[path] let \p1 = (7.two), \p2 = (7.center) in (\x1,\y2) -- (13);
\draw[path] let \p1 = (13.two), \p2 = (13.center) in (\x1,\y2) -- (end);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.2712 | arxiv | 2014-04-21T02:03:32 |
|
Example of modeling over four automatically identified frames as possible key postures. | \documentclass[a4paper,11pt]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{pgf}
\usepackage{tikz}
\usetikzlibrary{automata,positioning,shapes,arrows}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto, font=\scriptsize]
\tikzstyle{every state}=[circle, fill=blue!65, draw=none, text=white,
text width=.2cm, inner sep=0pt, minimum size=10pt, node distance=1.75cm]
\tikzstyle{invisible}=[fill=none,draw=none,text=black, node distance=.4cm]
\node[state] (s0) {$\vdots$};
\node[invisible] (s0tag1) [below=0.05cm of s0] {$\mathbb{R}^\nearrow_{\mathbb{L}}$};
\node[invisible] (s0tag2) [below of=s0tag1] {$\Xi^\mathbb{L}_{\mathtt{TORSE}}$};
\node[invisible] (s0tag3) [below of=s0tag2] {$\Xi^\mathbb{R}_{\mathtt{R\_SIDEOFBODY}}$};
\node[invisible] (s0tag4) [below of=s0tag3] {$\neg\mathcal{F}^{\mathbb{R}}_{\mathtt{L\_CONFIG}}$};
\node[invisible] (s0tag5) [below of=s0tag4] {$\neg\mathcal{F}^{\mathbb{L}}_{\mathtt{FIST\_CONFIG}}$};
\node[invisible] (s0tag6) [below of=s0tag5] {$\neg\mathcal{T}^{\mathbb{R}}_{\mathbb{L}}$};
\node[invisible] (s0tag7) [below of=s0tag6] {$\vdots$};
\node[state] (s1) [right of=s0] {$\vdots$};
\node[invisible] (s1tag1) [below=0.05cm of s1] {$\mathbb{R}^\leftarrow_{\mathbb{L}}$};
\node[invisible] (s1tag2) [below of=s1tag1] {$\Xi^\mathbb{L}_{\mathtt{L\_SIDEOFBODY}}$};
\node[invisible] (s1tag3) [below of=s1tag2] {$\Xi^\mathbb{R}_{\mathtt{R\_SIDEOFBODY}}$};
\node[invisible] (s1tag4) [below of=s1tag3] {$\mathcal{F}^{\mathbb{R}}_{\mathtt{KEY\_CONFIG}}$};
\node[invisible] (s1tag5) [below of=s1tag4] {$\mathcal{F}^{\mathbb{L}}_{\mathtt{KEY\_CONFIG}}$};
\node[invisible] (s1tag6) [below of=s1tag5] {$\neg\mathcal{T}^{\mathbb{R}}_{\mathbb{L}}$};
\node[invisible] (s1tag7) [below of=s1tag6] {$\vdots$};
\path[->] (s0) edge node {$\nearrow_{\mathbb{L}}$} (s1);
\path[->] (s1) edge[loop above, distance=.5cm] node {$\leftrightsquigarrow_\mathbb{D} \cap \leftrightsquigarrow_\mathbb{G}$} (s1);
\node[state] (s2) [right of=s1] {$\vdots$};
\node[invisible] (s2tag1) [below=0.05cm of s2] {$\mathbb{R}^\leftarrow_{\mathbb{L}}$};
\node[invisible] (s2tag2) [below of=s2tag1] {$\Xi^\mathbb{L}_{\mathtt{CENTEROFBODY}}$};
\node[invisible] (s2tag3) [below of=s2tag2] {$\Xi^\mathbb{R}_{\mathtt{R\_SIDEOFHEAD}}$};
\node[invisible] (s2tag4) [below of=s2tag3] {$\mathcal{F}^{\mathbb{R}}_{\mathtt{BEAK\_CONFIG}}$};
\node[invisible] (s2tag5) [below of=s2tag4] {$\mathcal{F}^{\mathbb{L}}_{\mathtt{INDEX\_CONFIG}}$};
\node[invisible] (s2tag6) [below of=s2tag5] {$\neg\mathcal{T}^{\mathbb{R}}_{\mathbb{L}}$};
\node[invisible] (s2tag7) [below of=s2tag6] {$\vdots$};
\path[->] (s1) edge node {$\swarrow_{\mathbb{L}}$} (s2);
\node[state] (s3) [right of=s2] {$\vdots$};
\node[invisible] (s3tag1) [below=0.05cm of s3] {$\mathbb{R}^\leftarrow_{\mathbb{L}}$};
\node[invisible] (s3tag2) [below of=s3tag1] {$\Xi^\mathbb{L}_{\mathtt{L\_SIDEOFBODY}}$};
\node[invisible] (s3tag3) [below of=s3tag2] {$\Xi^\mathbb{R}_{\mathtt{R\_SIDEOFBODY}}$};
\node[invisible] (s3tag4) [below of=s3tag3] {$\mathcal{F}^{\mathbb{R}}_{\mathtt{OPENPALM\_CONFIG}}$};
\node[invisible] (s3tag5) [below of=s3tag4] {$\mathcal{F}^{\mathbb{L}}_{\mathtt{OPENPALM\_CONFIG}}$};
\node[invisible] (s3tag6) [below of=s3tag5] {$\neg\mathcal{T}^{\mathbb{R}}_{\mathbb{L}}$};
\node[invisible] (s3tag7) [below of=s3tag6] {$\vdots$};
\path[->] (s2) edge node {$\nearrow_{\mathbb{L}}$} (s3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1403.6636 | arxiv | 2014-03-27T01:08:32 |
|
RDF extraction from OMDoc markup in a wiki page | \documentclass[runningheads]{llncs}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usepackage[pdfpagescrop={91 71 521 721},a4paper=false,pdftex,pdfstartview=FitV,plainpages=false,pdfpagelabels,colorlinks=true,linkcolor=NavyBlue,citecolor=NavyBlue,urlcolor=NavyBlue,hypertexnames=true]{hyperref}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}
\node[text width=3.7cm,draw] (page) at (0,0) {<omdoc>\\
~~<proof id="pyth-proof"\\
~~~~for="pythagoras">\\
~~~~\ldots</proof>\\
</omdoc>};
\node (rdfdummy) at (4,0) {};
\draw[->,dashed] (page) -- node [below] {extraction} node[above] {RDF} (rdfdummy);
\begin{scope}[xshift=5cm,xscale=3,yscale=.8,>=latex,font=\scriptsize]
\tikzstyle abox=[font=\scriptsize,draw,minimum height=2.5ex,rounded corners];
\tikzstyle tbox=[font=\scriptsize\bfseries\itshape,draw,minimum height=2.5ex];
\node[abox] (pp) at (0,0) {pyth-proof};
\node[abox] (pt) at (1,0) {pythagoras};
\node[tbox] (P) at (0,1) {\bfseries Proof};
\node[tbox] (T) at (1,1) {\bfseries Theorem};
\draw[-open triangle 60] (pp) -- node[left=.4em] {type} (P);
\draw[-open triangle 60] (pt) -- node[right=.5em] {type} (T);
\draw[->] (pp) -- node[below=-.3ex] {proves} (pt);
\draw[->] (P) -- node[below=-.3ex,font=\scriptsize\bfseries\itshape] {proves} (T);
\end{scope}
\node[text width=5.25cm,draw,anchor=west] (triples) at (4,-.8) {\scriptsize
<pyth-proof, rdf:type, omdoc:Proof>\\
<pyth-proof, omdoc:proves, pythagoras>};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1003.5196 | arxiv | 2010-03-29T02:01:59 |
|
Mutual information and variation of information. The total information H(X,Y) = H(X|Y) + I(X:Y) + H(Y|X). | \documentclass[9pt,technote]{IEEEtran}
\usepackage{amsmath,amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw (-1cm,0) circle(2cm);
\draw (1cm,0) circle(2cm);
\draw (0,0cm) node[fill=white] {$I(X:Y)$};
\draw (1.8cm,0cm) node[fill=white] {$H(Y|X)$};
\draw (-1.8cm,0cm) node[fill=white] {$H(X|Y)$};
\path(1cm,0) ++ (60:2.2cm) node[rotate=-25] {$H(Y)$};
\path(-1cm,0) ++ (120:2.2cm) node[rotate= 25] {$H(X)$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1110.2515 | arxiv | 2013-08-05T02:03:55 |
|
Kripke structure part corresponding to the fragment C_i with C_i = x_j . | \documentclass[a4paper,oneside]{scrartcl}
\usepackage{amsmath, amssymb}
\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,positioning}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.8cm,
thick]
\node[state] (C1) {$c_i$};
\node[state] (x1_) [below left of=C1, label=left:{$p_j$}] {$s_j^0$};
\node[state] (x1) [below right of=C1, label=right:{$p_j,q$}] {$s_j^1$};
\path (C1) edge [bend left] node {}(x1);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1104.1034 | arxiv | 2012-01-30T02:02:34 |
|
Kripke structure construction in the proof of nor vee | \documentclass[a4paper,oneside]{scrartcl}
\usepackage{amsmath, amssymb}
\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,positioning}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.2cm,thick]
\node[state] (c1) [label=225:{$p_1$, $q_2$}] {$c_{1}$};
\node[state] (c2) [right of=c1,label=225:{$p_2$, $q_3$}] {$c_{2}$};
\node[state] (c3) [right of=c2,label=225:{$q_1$, $p_4$}] {$c_{3}$};
\node (cx) [right of=c3] {$\dots$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1104.1034 | arxiv | 2012-01-30T02:02:34 |
|
Kripke structure corresponding to \,=\,( x_1 x_2 x_3)(x_2 x_3 x_4)(x_1 x_2) | \documentclass[a4paper,oneside]{scrartcl}
\usepackage{amsmath, amssymb}
\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,positioning}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.0cm,
thick]
\node[state] (C1) {$s_1$};
\node[color=white, state] (C1_) [right of=C1] {$s_1$};
\node[state] (C2) [right of=C1_] {$s_2$};
\node[color=white, state] (C2_) [right of=C2] {$s_1$};
\node[state] (C3) [right of=C2_] {$s_3$};
\node[state] (s1x1) [below of=C1, label=left:{}] {$r_1^1$};
\node[state] (s2x1_) [below left of=C2] {$\overline r_2^1 $};
\node[state] (s2x1) [below right of=C2, label=left:$p_1$] {$r_2^1$};
\node[color=lightgray, state] (s3x1) [below of=C3, label=left:$p_1$] {$r_3^1$};
\node[state] (s1x2) [below of=s1x1, label=left:$p_2$] {$r_1^2$};
\node[state] (s2x2) [below left of=s2x1, label=left:$p_2$] {$r_2^2$};
\node[color=lightgray, state] (s3x2) [below of=s3x1] {$r_3^2$};
\node[color=lightgray, state] (s1x3) [below of=s1x2, label=left:$p_3$] {$r_1^3$};
\node[state] (s2x3) [below of=s2x2] {$r_2^3$};
\node[state] (s3x3_) [below left of=s3x2] {$\overline r_3^3 $};
\node[state] (s3x3) [below right of=s3x2, label=left:$p_3$] {$r_3^3$};
\node[state] (s1x4) [below right of=s1x3, label=left:$p_4$] {$r_1^4$};
\node[state] (s1x4_) [below left of=s1x3, label=left:$$] {$\overline r_1^4 $};
\node[color=lightgray, state] (s2x4) [below of=s2x3, label=left:$p_4$] {$r_2^4$};
\node[state] (s3x4) [below of=s3x3, label=left:$p_4$] {$r_3^4$} ;
\node[state] (s3x4_) [below of=s3x3_, label=left:$$] {$\overline r_3^4 $};
\path (C1) edge node {}(s1x1)
(s1x1) edge node {}(s1x2)
(s1x2) edge node {}(s1x3)
(s1x3) edge node {}(s1x4_)
edge node {}(s1x4)
(C2) edge node {}(s2x1)
edge node {}(s2x1_)
(s2x1) edge node {}(s2x2)
(s2x1_) edge node {}(s2x2)
(s2x2) edge node {}(s2x3)
(s2x3) edge node {}(s2x4)
(C3) edge node {}(s3x1)
(s3x1) edge node {}(s3x2)
(s3x2) edge node {}(s3x3)
(s3x2) edge node {}(s3x3_)
(s3x3_) edge node {}(s3x4_)
(s3x3) edge node {}(s3x4);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1104.1034 | arxiv | 2012-01-30T02:02:34 |
|
Kripke structure construction in the proof of Theorem diamond-vee-boundedThe underlying formula contains the clauses C_1= p_2, C_2=p_2 p_3 and C_3= p_1 | \documentclass[a4paper,oneside]{scrartcl}
\usepackage{amsmath, amssymb}
\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,positioning}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.2cm,thick]
\node[state] (c1) [label=left:{$q$}] {$c_{1,1}$};
\node[state] (c2) [right of=c1,label=left:{$q$}] {$c_{2,1}$};
\node[state] (c3) [right of=c2] {$c_{3,1}$};
\node[state] (c12) [below of=c1] {$c_{1,2}$};
\node[state] (c22) [below of=c2,label=left:{$p_2$}] {$c_{2,2}$};
\node[state] (c32) [below of=c3,label=left:{$q$}] {$c_{3,2}$};
\node[state] (c13) [below of=c12,label=left:{$q$}] {$c_{1,3}$};
\node[state] (c23) [below of=c22,label=below:{$\vdots$}] {$c_{2,3}$};
\node[state] (c33) [below of=c32,label=left:{$q$}] {$c_{3,3}$};
\node (cx) [right of=c32] {$\dots$};
\node[state] (x2) [below of=c23,label=left:{$q$}] {$x_{2,1}$};
\node[state] (x1) [left of=x2,label=left:{$q,p_1$}] {$x_{1,1}$};
\node[state] (x3) [right of=x2,label=left:{$q$}] {$x_{3,1}$};
\node[state] (xx2) [below of=x2,label=left:{$q,p_2$}] {$x_{2,2}$};
\node[state] (xx3) [below of=x3,label=left:{$q$}] {$x_{3,2}$};
\node (xx) [right of=xx3] {$\dots$};
\node[state] (xxx3) [below of=xx3,label=left:{$q,p_3$}] {$x_{3,3}$};
\path (c1) edge node {}(c12);
\path (c2) edge node {}(c22);
\path (c3) edge node {}(c32);
\path (c12) edge node {}(c13);
\path (c22) edge node {}(c23);
\path (c32) edge node {}(c33);
\path (x2) edge node {}(xx2);
\path (x3) edge node {}(xx3);
\path (xx3) edge node {}(xxx3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1104.1034 | arxiv | 2012-01-30T02:02:34 |
|
Kripke structure construction in the proof of diamond-wedge-bounded | \documentclass[a4paper,oneside]{scrartcl}
\usepackage{amsmath, amssymb}
\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,positioning}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.5cm,thick]
\node[state] (C1) {$c_1$};
\node[state] (C2) [right of=C1] {$c_2$};
\node[state] (C3) [right of=C2] {$c_3$};
\node (Cx) [right of=C3] {$\dots$};
\node[state] (x1) [below of=C1] {$s_{1,1}$};
\node[state] (tx1) [right of=x1] {$\overline{s}_{1,1}$};
\node[state] (x2) [right of=tx1] {$s_{1,2}$};
\node[state] (tx2) [right of=x2] {$\overline{s}_{1,2}$};
\node[state] (x3) [right of=tx2] {$s_{1,3}$};
\node (xx) [right of=x3] {$\dots$};
\node[state] (tt1) at (-1.5,-2) [label=225:{$r_1$}] {$\overline{t}_{1}$};
\node[state] (t1) at (-3,-1) [label=225:{$r_1,p_1$}] {$t_{1}$};
\node[state] (xx1) [below of=x1] {$s_{2,1}$};
\node (xx) at (-2.5,-3) {$\vdots$};
\node[state] (txx1) [below of=tx1] {$\overline{s}_{2,1}$};
\node[state] (xx2) [below of=x2] {$s_{2,2}$};
\node[state] (txx2) [below of=tx2] {$\overline{s}_{2,2}$};
\node[state] (xx3) [below of=x3] {$s_{2,3}$};
\node (xx) [right of=xx3] {$\dots$};
\node[state] (xxx1) [below of=xx1] {$s_{3,1}$};
\node[state] (txxx1) [below of=txx1] {$\overline{s}_{3,1}$};
\node[state] (xxx2) [below of=xx2,label=below:{$\vdots$}] {$s_{3,2}$};
\node[state] (txxx2) [below of=txx2] {$\overline{s}_{3,2}$};
\node[state] (xxx3) [below of=xx3] {$s_{3,3}$};
\node (xxx) [right of=xxx3] {$\dots$};
\path (C1) edge node {}(x1);
\path (C1) edge node {}(tx2);
\path (C2) edge node {}(x1);
\path (C2) edge node {}(x2);
\path (C2) edge node {}(x3);
\path (C3) edge node {}(tx1);
\path (C3) edge node {}(x3);
\path (x1) edge node {}(xx1);
\path (tx1) edge node {}(txx1);
\path (x2) edge node {}(xx2);
\path (tx2) edge node {}(txx2);
\path (x3) edge node {}(xx3);
\path (x1) edge node {}(t1);
\path (x2) edge [bend right=14] node {}(t1);
\path (tx2) edge [bend right=14] node {}(t1);
\path (x3) edge [bend right=14] node {}(t1);
\path (tx1) edge [bend left=10] node {}(tt1);
\path (x2) edge [bend left=10] node {}(tt1);
\path (tx2) edge [bend left=10] node {}(tt1);
\path (x3) edge [bend left=10] node {}(tt1);
\path (xx1) edge node {}(xxx1);
\path (txx1) edge node {}(txxx1);
\path (xx2) edge node {}(xxx2);
\path (txx2) edge node {}(txxx2);
\path (xx3) edge node {}(xxx3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1104.1034 | arxiv | 2012-01-30T02:02:34 |
|
A schematic view of the Yukawa coupling between left- and right-handed fermions, interpreted in a five dimensional space time. The left- and right-handed fermions live on separate four-dimensional sheets. The Higgs field couples left- to right-handed spinors via quantum tunnelling. | \documentclass[ a4paper,11pt]{revtex4}
\usepackage{subfigure, amsfonts, amsmath}
\usepackage{amssymb}
\usepackage{subfigure, amsfonts, amsmath}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tikz,pgflibraryshapes}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\draw[-,thick] (4,-2) -- (11,-7);
\draw[-,thick] (6,0) -- (13,-4.5);
\draw (13,-4.5) node[below] {$\psi_R$};
\draw(11,-7) node[below] {$\psi_L$};
\draw[<->] (7.5,-4.3) to[bend left=60] (9.7,-2.5);
\draw(8.5,-3) node[below] {$\phi$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1201.2661 | arxiv | 2012-11-29T02:00:39 |
|
A natural embedding of P into S. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
\draw [very thin] (0,1) ellipse (0.1 and 1);
\draw [very thin] (0,2) .. controls (1,2) .. (3,3);
\draw [very thin] (0,0) .. controls (1,0) .. (3,-1);
\draw [very thin] (3,3) to[out=-10,in=110] (4,2) ;
\draw [dashed] (4,2) to[out=170,in=280] (3,3) ;
\draw [very thin, dashed] (3,-1) to[out=80,in=190] (4,0) ;
\draw [very thin] (3,-1) to[out=10,in=260] (4,0) ;
\draw (4,2) to[out=250,in=120] (4,0);
\draw [dashed] (4,2) to[out=170,in=280] (3,3) ;
%EMBEDDED GRAPH
\draw [fill=black] (0.1,1) circle (0.1);
\draw [fill=black] (3.65,2.65) circle (0.1);
\draw [fill=black] (3.65,-.65) circle (0.1);
\draw [very thick] (0.1,1) to[in=180,out=0] (3.65,2.65);
\draw [very thick] (0.1,1) to[in=180,out=0] (3.65,-.65);
\draw [very thick] (3.65,-.65) to[in=200,out=150] (3.65,2.65);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
If (), () and () do not bound a pair of pants. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%fondo, figura principal
\shadedraw[inner color=white!35!black, outer color=white!90!black, very thick]
(0,-1) to[out=0,in=100] (1.5,-2.5) to[out=80,in=180]
(2.5,-1.5) to[out=150,in=270] (1,2) to[out=190,in=0]
(0,1.7) to[out=180,in=350] (-1,2) to[out=270,in=30]
(-2.5,-1.5) to[out=0,in=100] (-1.5,-2.5) to[out=80,in=180] (0,-1);
%genero
\filldraw [fill=white, very thick] (0,0) circle (.5);
%componentes de frontera de abajo
\shadedraw[top color=white!35!black, bottom color=white!90!black, very thick] (1.5,-2.5) to[out=80,in=180]
(2.5,-1.5) to[out=260,in=10] (1.5,-2.5);
\shadedraw[top color=white!35!black, bottom color=white!90!black, very thick,rotate around={90:(2,-2)},shift={(0,3.99)}] (1.5,-2.5) to[out=80,in=180]
(2.5,-1.5) to[out=260,in=10] (1.5,-2.5);
% componente de frontera de arriba
\shadedraw[top color=white!35!black, bottom color=white!90!black, very thick] (1,2) to[out=190,in=0]
(0,1.7) to[out=180,in=350] (-1,2) to[out=10,in=170] (1,2);
%lineas
\draw[very thick] (0,-1) to[out=190,in=190] (0,-.5);
\draw[very thick, dashed] (0,-1) to[out=80,in=280] (0,-.5);
\draw[very thick] (0.5,0) to[out=280,in=190] (1.5,-.5);
\draw[very thick, dashed] (0.5,0) to[out=80,in=190] (1.5,-.5);
\draw[very thick] (-0.5,0) to[out=270,in=190] (-1.4,-.5);
\draw[very thick, dashed] (-0.5,0) to[out=80,in=190] (-1.4,-.5);
\draw (0,-1.5) node{$\phi(\gamma)$} ;
\draw (-2,0) node{$\phi(\alpha)$} ;
\draw (2,0) node{$\phi(\beta)$} ;
\draw (-1.7,-1.5) node{$\delta_{3}$} ;
\draw (1.6,-1.5) node{$\delta_{2}$} ;
\draw (0,1.2) node{$\delta_{1}$} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
Catching in a S_0,4. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%fondo y contorno
\shadedraw[left color=white!35!black, right color=white!90!black,thick]
(-4,0) to[out=0,in=180] (4,0)
to[out=100,in=260] (4,3)
to[out=180,in=0] (-4,3)
to[out=260,in=100] (-4,0);
\draw[dashed] (-4,3) to[out=280,in=80] (-4,0);
\shadedraw[left color=white!35!black, right color=white!90!black,thick]
(4,0)to[out=100,in=260] (4,3)
to[out=280,in=80] (4,0);
%genero
\filldraw[fill=white, very thick] (-2,1.5) ellipse (1 and .5);
\filldraw[fill=white, very thick] (2,1.5) ellipse (1 and .5);
%lineas
\draw (-2,1) to[out=260,in=100] (-2,0);
\draw (2,1) to[out=260,in=100] (2,0);
\draw (-2,3) to[out=260,in=100] (-2,2);
\draw (2,3) to[out=260,in=100] (2,2);
\draw (0,3) to[out=260,in=100] (0,0);
\draw (-2,1.5) ellipse (1.5 and 1);
\draw (2,1.5) ellipse (1.5 and 1);
\draw (-2,-.3) node{$\gamma_{1}$};
\draw (2,-.3) node{$\gamma_{2}$};
\draw (-2,3.3) node{$\beta_{1}$};
\draw (2,3.3) node{$\beta_{2}$};
\draw (-.8,.5) node{$\delta_{1}$};
\draw (.8,.5) node{$\delta_{2}$};
\draw (0.1,1.5) node{$\alpha$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
Diagram of N. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%fondo y contorno
\shadedraw[inner color=white!35!black, outer color=white!90!black,thick]
(0,0)--(6,0)--(6,3.5)--(0,3.5)--cycle;
\filldraw [rounded corners=1mm,fill=white] (2,.5)--(4,.5)--(4,3)--(2,3)--cycle;
%lineas
%lado izquierdo
\foreach \x in{0,.2,.4}
\draw[dotted, very thick] (0,.4+\x)--(2,1+\x);
\foreach \x in{0,.2,.4,.6,.8}
\draw[dotted, very thick] (0,2+\x)--(2,1.6+\x);
\draw[very thick] (0,3.1)--(3.7,3.5);
%lado derecho
\foreach \x in{0,.2,.4,.6,.8}
\draw[dotted, very thick] (4,1+\x)--(6,2.1+\x);
\foreach \x in{0,.2,.4}
\draw[dotted, very thick] (4.8-\x,0)--(6,.5+\x);
\foreach \x in{0,.2,.4}
\draw[dotted, very thick] (4,2.2+\x)--(4.9-\x,3.5);
\draw[very thick] (3.7,0)--(6,3.2);
%etiquetas
\draw (-.2,2) node{$\alpha$};
\draw (3,3.7) node{$\gamma$};
\draw (-.2,2) node{$\alpha$};
\draw (6.3,3) node{$\gamma'$};
\draw[very thick] (6.5,3)--(6.9,3) ;
\draw (6.3,2.5) node{$\beta$};
\draw[dotted, very thick] (6.5,2.5)--(6.9,2.5) ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
Three nonseparating curves bounding a pair of pants. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%figura izquiera
\shadedraw[inner color=white!35!black, outer color=white!90!black, very thick]
(3,2) to[out=100,in=270] (2.8,3) to[out=90,in=260]
(3,4) to[out=180,in=0] (-4,4) to[out=190,in=90]
(-4.5,3) to[out=280,in=180] (-4,2) to[out=0,in=180] (3,2);
\shadedraw[left color=white!40!black, right color= white, very thick,shift={(3,1)}]
(-1+1,2-1) to[out=100,in=270] (-1.2+1,3-1) to[out=90,in=260]
(-1+1,4-1) to[out=280,in=90] (-.8+1,3-1) to[out=270,in=80] (-1+1,2-1);
%genero
\foreach \x in {0,2,4}
\filldraw[fill=white, very thick, shift={(\x,0)}]
(-3.25,2.8) to[out=340,in=180] (-2.75,2.6) to[out=0,in=200] (-2.25,2.8)
to[out=160,in=0] (-2.75,3) to[out=180,in=20] (-3.25,2.8);
\foreach \x in {0,2,4}
\draw[ very thick, shift={(\x,0)}] (-3.5,3) to[out=340,in=150](-3.25,2.8) to[out=340,in=180] (-2.75,2.6) to[out=0,in=200] (-2.25,2.8)
to[out=20,in=200] (-2,3);
%lineas
\draw[very thick] (-3.25,2.8) to[out=110,in=0]
(-3.8,3.5) node[anchor=south] {$\alpha$} to[out=180,in=70] (-4.5,3);
\foreach \x in {2,4}
\draw[very thick] (-2.75+\x,3) to[out=100,in=270] (-3+\x,3.5) to[out=90,in=190] (-2.75+\x,4);
\draw (-.65,3.3) node[anchor=south] {$\gamma$};
\foreach \x in {2,4}
\draw[very thick] (-2.75+\x,2.59) to[out=180,in=90] (-3+\x,2.2) to[out=270,in=190] (-2.75+\x,2);
\foreach \x in {0,2}
\draw[very thick] (-2.44+\x,2.9) to[out=40,in=180] (-1.8+\x,3.4) to[out=0,in=110]
(-1+\x,2.95);
\draw (-2.3,3.2) node[anchor=south] {$\beta$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
Example for K_0, K_1, and _0, _1,. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%Parte de afuera. y hueco
\shadedraw [inner color=white,outer color=white!60!black, very thick]
(-4,0) to[out=180,in=270] (-4.5,1.5) to[out=90,in=180] (-4,3) to[out=0,in=180] (6,3) to[out=180, in=90] (5.5,1.5) to[out=270,in=180] (6,0) to[out=180,in=0] (-4,0) ;
\shadedraw [left color=white!35!black, right color=white, very thick]
(6,3) to[out=180, in=90] (5.5,1.5) to[out=270,in=180] (6,0) to[out=50,in=270] (6.3,1.5) to[out=90,in=310] (6,3);
%puntitos
\foreach \x in {.5,1,1.5}
\filldraw (6.3+\x,1.5) circle (.1);
%genero
\foreach \x in {0,2,4,6,8}
\filldraw[fill=white, thick] (-3.9+\x,1.45) to[out=340,in=180] (-3.5+\x, 1.4) to [out=0,in=200] (-3.1+\x,1.45) to[out=160,in=0] (-3.5+\x,1.55) to[out=180,in=20] (-3.9+\x,1.45);
\foreach \x in {2,4,6,8}
\draw[thick] (-4+\x,1.5) to[out=340,in=160] (-3.9+\x,1.45) to[out=340,in=180] (-3.5+\x, 1.4) to [out=0,in=200] (-3.1+\x,1.45) to[out=20,in=200] (-3+\x,1.5);
%curvas
%elipses
\foreach \x in {0,2,4,6,8}
\draw (-3.5+\x,1.5) ellipse (.8
and .3);
\foreach \x in {2,4,6,8}
\draw (-3.5+\x,1.55) to[out=100,in=270] (-3.7+\x,2.3) to[out=90,in=200] (-3.5+\x,3);
%curvas horizontales
\foreach \x in {0,2,6}
\draw [thin] (-3.1+\x,1.45) to[out=70,in=180] (-2.5+\x,1.8) to[out=0,in=110](-1.9+\x,1.45);
%curvas verticales
\foreach \x in {2,4,6,8}
\draw (-3.5+\x,1.4) to[out=260,in=90] (-3.7+\x,.6) to[out=270,in=110] (-3.5+\x,0);
\foreach \x in {2}
\draw[thin] (-.2+\x,0) to[out=100,in=270] (-.6+\x,1.5) to[out=90,in=260] (-.2+\x,3);
\draw[very thick] (1.6,-.5) -- (-.8,-.5) node[anchor=east]{$K_{0}$};
\draw[very thick] (1.6,-.5) to[out=0,in=270] (1.8,-.3);
\draw[very thick] (-3.8,-.5) -- (-1.6,-.5);
\draw[very thick] (-3.8,-.5) to[out=180,in=270] (-4,-.3);
\foreach \x in {4}
\draw[very thick] (1.6+\x,-1) -- (-.8,-1) node[anchor=east]{$K_{1}$};
\foreach \x in {4}
\draw[very thick] (1.6+\x,-1) to[out=0,in=270] (1.8+\x,-.7);
\draw[very thick] (-3.8,-1) -- (-1.6,-1);
\draw[very thick] (-3.8,-1) to[out=180,in=270] (-4,-.8);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
A superinjective but not surjective simplicial map. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%fondo y contorno
%figura izquiera
\shadedraw[left color=white!35!black, right color=white!90!black, very thick]
(-5,-1) to[out=0,in=180] (-1,-1)
to[out=100,in=260] (-1,1)
to[out=180,in=0] (-5,1)
to[out=260,in=100] (-5,-1);
\draw[dashed] (-5,-1) to[out=80,in=280] (-5,1);
\shadedraw[left color=white!35!black, right color=white!90!black, very thick]
(-1,1) to[out=260,in=100] (-1,-1)
to[out=80,in=280] (-1,1);
%figura derecha
\shadedraw[left color=white!35!black, right color=white!90!black, very thick]
(1,1) to[out=0,in=180] (7,1)
to[out=260,in=100] (7,-1)
to[out=180,in=0] (1,-1)
to[out=100,in=260] (1,1);
\draw[dashed] (1,-1) to[out=80,in=280] (1,1);
\shadedraw[left color=white!35!black, right color=white!90!black, very thick]
(7,1) to[out=260,in=100] (7,-1)
to[out=80,in=280] (7,1);
%genus
% izq
\filldraw[fill=white, very thick] (-4,0) circle (.25);
\filldraw[fill=white, very thick] (-2,0) circle (.25);
%derech
\filldraw[fill=white, very thick] (2,0) circle (.25);
\filldraw[fill=white, very thick] (4,0) circle (.25);
\filldraw[fill=white, very thick] (6,0) circle (.25);
%lineas
%izquierda
\draw (-3,1) to[out=260,in=100] (-3,-1);
\draw (-2,0) ellipse (.5 and .5);
\draw (-3,0) ellipse (1.75 and .75);
%derecha
\draw (3,1) to[out=260,in=100] (3,-1);
\draw (5,1) to[out=260,in=100] (5,-1);
\draw (4,0) ellipse (.5 and .5);
\draw (6,0) ellipse (.5 and .5);
\draw (4,0) ellipse (2.75 and .9);
\draw[->] (-.5,0)--(.5,0);
%etiquetas
%izquierda
\draw(-3,-1.2) node{$\alpha$};
\draw(-3.3,0) node{$\beta$};
\draw(-1.3,0.7) node{$\beta'$};
%derecha
\draw(3,-1.2) node{$\alpha$};
\draw(3.3,0) node{$\gamma$};
\draw(5.3,0.5) node{$f(\beta)$};
\draw(6.7,1.3) node{$f(\beta')$};
\draw[dashed] (6.2,1.3) -- (5.9,0.7);
\draw(0,0.5) node{$f$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
Catching again in a S_0,4. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%fondo y contorno
\shadedraw[left color=white!35!black, right color=white!90!black,thick]
(0,0) to[out=0,in=180] (4,0)
to[out=100,in=260] (4,3)
to[out=180,in=0] (0,3)
to[out=260,in=100] (0,2)
to[out=0,in=90] (.5,1.5)
to[out=270,in=0] (0,1)
to[out=260,in=100] (0,0);
\draw[dashed] (0,1) to[out=280,in=80] (0,0);
\draw[dashed] (0,3) to[out=280,in=80] (0,2);
\shadedraw[left color=white!35!black, right color=white!90!black,thick]
(4,0)
to[out=100,in=260] (4,3)
to[out=280,in=80] (4,0);
%genero
\filldraw[fill=white] (2.5,1.5) circle (.5);
%lineas
\draw (1.5,3) to[out=260,in=100] (1.5,0);
\draw (.5,1.5) to[out=10,in=170] (2,1.5);
\draw (2.5,1) to[out=260,in=100] (2.5,0);
\draw (2.5,3) to[out=260,in=100] (2.5,2);
\draw (2.5,1.5) ellipse (1 and 1);
%etiquetas
\draw (.8,1.2) node{$\beta$};
\draw (1.2,2.5) node{$\alpha$};
\draw (3.2,2.5) node{$\gamma$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
The two options for (v)=1. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%figura izquiera
\shadedraw[inner color=white!35!black, outer color=white!90!black, very thick]
(-1+1,2-1) to[out=100,in=270] (-1.2+1,3-1) to[out=90,in=260]
(-1+1,4-1) to[out=180,in=0] (-4+1,4-1) to[out=190,in=90]
(-4.5+1,3-1) to[out=280,in=180] (-4+1,2-1) to[out=0,in=180] (-1+1,2-1);
\shadedraw[left color=white!40!black, right color= white, very thick]
(-1+1,2-1) to[out=100,in=270] (-1.2+1,3-1) to[out=90,in=260]
(-1+1,4-1) to[out=280,in=90] (-.8+1,3-1) to[out=270,in=80]
(-1+1,2-1);
%genero
\filldraw[fill=white, very thick]
(-3.25+1,2.8-1) to[out=340,in=180] (-2.75+1,2.6-1) to[out=0,in=200] (-2.25+1,2.8-1)
to[out=160,in=0] (-2.75+1,3-1) to[out=180,in=20] (-3.25+1,2.8-1);
\draw[ very thick] (-3.5+1,3-1) to[out=340,in=150](-3.25+1,2.8-1) to[out=340,in=180] (-2.75+1,2.6-1) to[out=0,in=200] (-2.25+1,2.8-1)
to[out=20,in=200] (-2+1,3-1);
%lineas
\draw[very thick] (-3.25+1,2.8-1) to[out=110,in=0]
(-3.8+1,3.5-1) node[anchor=south] {$v$} to[out=180,in=70] (-4.5+1,3-1);
\draw [dashed, thick] (-4.5+1,3-1) to[out=290,in=180] (-3.8+1,2.5-1) to[out=0,in=250] (-3.25+1,2.8-1);
%figura derecha
%interior
\shadedraw[inner color=white!35!black, outer color=white!90!black, very thick]
(2,0) to[out=90,in=270] (1,2)
to[out=290,in=180] (2.5-1,-.25+2) to[out=0,in=240] (3-1,0+2)
(2,+2) to[out=290,in=180] (2.5,-.25+2) to[out=0,in=240] (3,0+2) to[out=290,in=180] (2.5+1,-.25+2) to[out=0,in=240] (3+1,0+2)
to[out=270,in=90] (3,0) to[out=250,in=0] (2.5,-.25) to[out=180,in=290] (2,0);
\shadedraw[inner color=white!35!black, outer color=white!90!black, very thick]
(2+1,0+2) to[out=90,in=270] (1+1,2+2)
to[out=290,in=180] (2.5-1+1,-.25+2+2) to[out=0,in=240] (3-1+1,0+2+2)
(2+1,+2+2) to[out=290,in=180] (2.5+1,-.25+2+2) to[out=0,in=240] (3+1,0+2+2) to[out=290,in=180] (2.5+1+1,-.25+2+2) to[out=0,in=240] (3+1+1,0+2+2)
to[out=270,in=90] (3+1,0+2) to[out=250,in=0] (2.5+1,-.25+2) to[out=180,in=290] (2+1,0+2);
% u
\draw[very thick] (2,0) to[out=290,in=180] (2.5,-.25) to[out=0,in=240] (3,0);
\draw[thick, dashed] (2,0) to[out=70,in=180] (2.5,.25) to[out=0,in=110] (3,0) node[anchor=west]{$u$};
% frontera hasta arriba
\shadedraw[top color=white, bottom color=white!40!black, very thick, shift={(1 ,2 )}] (2-1,0+2) to[out=290,in=180] (2.5-1,-.25+2) to[out=0,in=240] (3-1,0+2)
to[out=110,in=0] (2.5-1,.25+2)
to[out=180,in=70] (2-1,0+2);
\shadedraw[top color=white, bottom color=white!40!black, very thick, shift={(3 ,2 )}] (2-1,0+2) to[out=290,in=180] (2.5-1,-.25+2) to[out=0,in=240] (3-1,0+2)
to[out=110,in=0] (2.5-1,.25+2)
to[out=180,in=70] (2-1,0+2);
\shadedraw[top color=white, bottom color=white!40!black, very thick] (2-1,0+2) to[out=290,in=180] (2.5-1,-.25+2) to[out=0,in=240] (3-1,0+2)
to[out=110,in=0] (2.5-1,.25+2)
to[out=180,in=70] (2-1,0+2);
\draw[very thick] (2,+4) to[out=290,in=180] (2.5,-.25+4) to[out=0,in=240] (3,0+4);
\draw[very thick, dashed] (2,0+4) to[out=70,in=180] (2.5,.25+4) to[out=0,in=110] (3,0+4);
%frontera middle izquierda
\shadedraw[top color=white, bottom color=white!40!black, very thick] (2-1,0+2) to[out=290,in=180] (2.5-1,-.25+2) to[out=0,in=240] (3-1,0+2)
to[out=110,in=0] (2.5-1,.25+2)
to[out=180,in=70] (2-1,0+2);
% v
\draw[very thick] (2+1,0+2) to[out=290,in=180] (2.5+1,-.25+2) to[out=0,in=240] (3+1,0+2) node[anchor=west]{$v$} ;
\draw[thick, dashed] (2+1,0+2) to[out=70,in=180] (2.5+1,.25+2) to[out=0,in=110] (3+1,0+2);
\draw [very thick](-.5,1) to[out=120,in=240] (-.5,3);
\draw [dashed](-.5,1) to[out=70,in=290] (-.5,3);
\draw (-.5,3.2) node{$u$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
Catching in an annulus. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%fondo y contorno
\shadedraw[left color=white!35!black, right color=white!90!black, very thick]
(-2*.5,-4*.5) to[out=0,in=180] (6*.5,-4*.5)
to[out=100,in=260] (6*.5,4*.5)
to[out=180,in=0] (-2*.5,4*.5)
to[out=270,in=0] (-3*.5,3*.5)
to[out=0,in=90] (-2*.5,2.5*.5)
to[out=270,in=0] (-3*.5,2*.5)
to[out=280,in=80] (-3*.5,1*.5)
to[out=0,in=90] (-2*.5,0)
to[out=270,in=0] (-3*.5,-1*.5)
to[out=280,in=80] (-3*.5,-2*.5)
to[out=0,in=90] (-2*.5,-2.5*.5)
to[out=270,in=0] (-3*.5,-3*.5)
to[out=0,in=90] (-2*.5,-4*.5);
\shadedraw[left color=white!35!black, right color=white!90!black]
(6*.5,-4*.5)
to[out=100,in=260] (6*.5,4*.5)
to[out=280,in=80] (6*.5,-4*.5);
\shadedraw[right color=white!35!black, left color=white!90!black]
(-2*.5,4*.5)
to[out=270,in=0] (-3*.5,3*.5)
to[out=90,in=180] (-2*.5,4*.5);
\shadedraw[right color=white!35!black, left color=white!90!black]
(-3*.5,2*.5)
to[out=280,in=80] (-3*.5,1*.5)
to[out=120,in=240] (-3*.5,2*.5);
\shadedraw[right color=white!35!black, left color=white!90!black]
(-3*.5,-1*.5)
to[out=280,in=80] (-3*.5,-2*.5)
to[out=120,in=240] (-3*.5,-1*.5);
\shadedraw[right color=white!35!black, left color=white!90!black]
(-3*.5,-3*.5)
to[out=0,in=90] (-2*.5,-4*.5)
to[out=180,in=270] (-3*.5,-3*.5);
%genero
\filldraw[fill=white,very thick] (1.5,0) circle (.25);
%lineas
\draw (-.5,2) to[out=270,in=45] (-1.03,.1);
\draw (-.5,-2) to[out=90,in=315] (-1.03,-.1);
\draw (-1,1.25) to[out=315,in=45] (-1,-1.25);
\draw (.5,2) to[out=260,in=100] (.5,-2);
\draw (1.5,2) to[out=260,in=100] (1.5,.25);
\draw (1.5,-.25) to[out=260,in=100] (1.5,-2);
\draw (1.5,0) ellipse (.5 and 1);
\draw(1*.5,0) node{$\alpha$};
\draw(2.2,0) node{$\gamma$};
\draw(1.8,1.5) node{$\delta_{1}$};
\draw(1.8,-1.5) node{$\delta_{2}$};
\draw(-.2,1.5) node{$\beta_{1}$};
\draw(-.25,0) node{$\beta_{2}$};
\draw(-.2,-1.5) node{$\beta_{3}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
Examples of and in S_ | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
\shadedraw[inner color=white!35!black, outer color=white!90!black, very thick]
%contorno
(-2,-1) to[out=350,in=190] (2,-1)
to[out=80,in=270] (3,3)
to[out=180,in=0] (2,2.8)
to[out=180,in=0] (1,3)
to[out=270,in=0] (0,2)
to[out=180,in=270] (-1,3)
to[out=190,in=10] (-1.5,2.8)
to[out=180,in=350] (-2.5,3)
to[out=260,in=100] (-2,-1);
%contorno frontera
\shadedraw[bottom color=white!35!black, top color=white!90!black, very thick]
(3,3)
to[out=180,in=0] (2,2.8)
to[out=180,in=0] (1,3)
to[out=0,in=180] (2,3.2)
to[out=0,in=180] (3,3);
\shadedraw[bottom color=white!35!black, top color=white!90!black, very thick]
(-1,3)
to[out=190,in=10] (-1.5,2.8)
to[out=180,in=350] (-2.5,3)
to[out=0,in=180] (-1.5,3.2)
to[out=0,in=180] (-1,3);
%GENERO
\filldraw [fill=white, very thick] (-1.75,1.5) ellipse (.3 and .2);
\filldraw [fill=white, very thick] (1.25,2) ellipse (.3 and .2);
%LINEAS
%beta lado izquiedo
\draw (-1.5,2.8) to[out=200,in=160] (-1.75,1.7);
\draw[dashed] (-1.5,3.2) to[out=310,in=0] (-1.75,1.7);
%beta lado derecho
\draw (0,2) to[out=270,in=180] (1,1)
to[out=8,in=270] (2.5,2.9);
\draw [dashed] (0,2) to[out=350,in=150] (1,1.2)
to[out=10,in=270] (2,3.2)
;
%gamma
\draw (-1,3) to[out=270,in=180] (1,0);
\draw (1,0) to[out=0,in=270] (2.5,1.5);
\draw (2.5,1.5) to[out=90,in=0] (2,2.8)
;
%frontera abajo
\draw[dashed,very thick] (-2,-1) to[out=10,in=170] (2,-1);
%etiquetas
\draw (-2.2,2) node{$\beta$};
\draw (1,.3) node{$\gamma$};
\draw (-.2,1.7) node{$\beta$};
% figura de la derecha
\begin{scope}[xshift=8cm]
\shadedraw[inner color=white!35!black, outer color=white!90!black, very thick]
%contorno
(-2,-1) to[out=350,in=190] (2,-1)
to[out=80,in=270] (3,3)
to[out=180,in=0] (2,2.8)
to[out=180,in=0] (1,3)
to[out=270,in=0] (0,2)
to[out=180,in=270] (-1,3)
to[out=190,in=10] (-1.5,2.8)
to[out=180,in=350] (-2.5,3)
to[out=260,in=100] (-2,-1);
%contorno frontera
\shadedraw[bottom color=white!35!black, top color=white!90!black, very thick]
(3,3)
to[out=180,in=0] (2,2.8)
to[out=180,in=0] (1,3)
to[out=0,in=180] (2,3.2)
to[out=0,in=180] (3,3);
\shadedraw[bottom color=white!35!black, top color=white!90!black, very thick]
(-1,3)
to[out=190,in=10] (-1.5,2.8)
to[out=180,in=350] (-2.5,3)
to[out=0,in=180] (-1.5,3.2)
to[out=0,in=180] (-1,3);
%GENERO
\filldraw [fill=white, very thick] (-1.75,1.5) ellipse (.3 and .2);
\filldraw [fill=white, very thick] (1.25,2) ellipse (.3 and .2);
%LINEAS
%beta lado izquiedo
\draw (-1.5,2.8) to[out=200,in=160] (-1.75,1.7);
\draw[dashed] (-1.5,3.2) to[out=310,in=0] (-1.75,1.7);
%beta lado derecho
\draw (1.55,2) to[out=0,in=270] (2.5,2.9);
\draw [dashed] (1.55,2) to[out=80,in=200] (2,3.2);
%gamma
\draw (-1,3) to[out=270,in=180] (1,0);
\draw (1,0) to[out=0,in=270] (2.5,1.5);
\draw (2.5,1.5) to[out=90,in=0] (2,2.8)
;
%frontera abajo
\draw[dashed,very thick] (-2,-1) to[out=10,in=170] (2,-1);
%etiquetas
\draw (-2.2,2) node{$\beta$};
\draw (1,.3) node{$\gamma$};
\draw (1.9,1.8) node{$\beta$};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
Example of a convenient pants decomposition. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%contorno
\shadedraw[inner color=white!35!black, outer color=white!90!black, very thick]
(-1,0) to[out=90,in=0] (-1.5,.5) to[out=45,in=335] (-1.5,1)
to[out=0,in=270] (-1,1.25) to[out=90,in=0] (-1.5,1.5)
to[out=0,in=270] (-1,2) to[out=0,in=180] (0,2) to[out=0,in=160] (1.5,1.5)
to[out=0,in=180] (4,1.5) to[out=220,in=140] (4,.5)
to[out=180,in=0] (1.5,.5) to[out=190,in=90] (1,0)
to[out=270,in=170] (1.5,-.5) to[out=0,in=180] (4,-.5)
to[out=220,in=140] (4,-1.5) to[out=180,in=0] (1.5,-1.5)
to[out=200,in=0] (0,-2) to[out=180,in=0] (-1,-2)
to[out=90,in=0] (-1.5,-1.5) to[out=0,in=270] (-1,-1.25)
to[out=90,in=0] (-1.5,-1) to[out=45,in=335] (-1.5,-.5)
to[out=0,in=270] (-1,0);
%genero
\draw[fill=white, very thick] (1.5,1) ellipse (.4 and .2);
\draw[fill=white, very thick] (3,1) ellipse (.4 and .2);
\draw[fill=white, very thick] (1.5,-1) ellipse (.4 and .2);
\draw[fill=white, very thick] (3,-1) ellipse (.4 and .2);
%lineas
\draw (-1,0) to[out=10,in=170] (-.5,0);
\draw (-1,1.25) to[out=330,in=170] (-.25,.25);
\draw (0,.5) to[out=70,in=290] (0,2);
\draw (-1,-1.25) to[out=30,in=210] (-.25,-.25);
\draw (0,-.5) to[out=290,in=70] (0,-2);
\draw (.25,.25) to[out=45,in=180] (1.1,1);
\draw (.25,-.25) to[out=45,in=180] (1.1,-1);
\foreach \x in {0,1.5}
\foreach \y in {0,.7}
\draw (1.5+\x,1.2-\y) to[out=45,in=325] (1.5+\x,1.5-\y);
\foreach \x in {0,1.5}
\foreach \y in {0,.7}
\draw (1.5+\x,-1.2+\y) to[out=45,in=325] (1.5+\x,-1.5+\y);
\draw (0.5,0) to (.95,0);
\shadedraw[left color=white!35!black, right color=white!90!black, very thick] (4,1.5) to[out=220,in=140] (4,.5) to[out=50,in=320] (4,1.5);
\shadedraw[left color=white!35!black, right color=white!90!black, very thick] (4,1.5-2) to[out=220,in=140] (4,.5-2) to[out=50,in=320] (4,1.5-2);
\shadedraw[right color=white!35!black, left color=white!90!black, very thick] (-1.5,.5) to[out=45,in=335] (-1.5,1) to[out=205,in=135] (-1.5,.5);
\shadedraw[right color=white!35!black, left color=white!90!black, very thick] (-1.5,.5-1.5) to[out=45,in=335] (-1.5,1-1.5) to[out=205,in=135] (-1.5,.5-1.5);
\shadedraw[right color=white!35!black, left color=white!90!black, very thick] (-1.5,1.5)
to[out=0,in=270] (-1,2) to[out=220,in=90] (-1.5,1.5) ;
\shadedraw[right color=white!35!black, left color=white!90!black, very thick] (-1,-2)
to[out=90,in=0] (-1.5,-1.5) to[out=270,in=130] (-1,-2) ;
\draw [fill=white,very thick] (0,0) circle (0.5);
\draw (-.5,1) node{$\beta$};
\draw (.33,1.5) node{$\alpha$};
\foreach \x in {.2,.5,.8}
\filldraw[fill=black] (4.3+\x,1) circle (0.05);
\foreach \x in {.2,.5,.8}
\filldraw[fill=black] (4.3+\x,1-2) circle (0.05);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
A superinjecive map between two nonhomeomorphic surfaces. | \documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\begin{document}
\begin{tikzpicture}
%fondo y contorno
%figura izquiera
\shadedraw[left color=white!35!black, right color=white!90!black, very thick]
(-6,-1) to[out=0,in=180] (-1,-1)
to[out=100,in=260] (-1,1)
to[out=180,in=0] (-6,1)
to[out=260,in=100] (-6,-1);
\draw[dashed] (-6,-1) to[out=80,in=280] (-6,1);
\shadedraw[left color=white!35!black, right color=white!90!black, very thick]
(-1,1) to[out=260,in=100] (-1,-1)
to[out=80,in=280] (-1,1);
%figura derecha
\shadedraw[left color=white!35!black, right color=white!90!black, very thick]
(1,1) to[out=0,in=180] (2.5,1)
to[out=0,in=270] (3,2)
to[out=350,in=190] (5,2)
to[out=270,in=180] (6,1)
to[out=0,in=180] (9,1)
to[out=260,in=100] (9,-1)
to[out=180,in=0] (1,-1)
to[out=100,in=260] (1,1);
\draw[dashed] (1,1) to[out=80,in=280] (1,-1);
\shadedraw[left color=white!35!black, right color=white!90!black, very thick]
(9,1) to[out=260,in=100] (9,-1)
to[out=80,in=280] (9,1);
\shadedraw[bottom color=white!35!black, top color=white!90!black, very thick]
(3,2) to[out=10,in=170] (5,2)
to[out=190,in=350] (3,2);
%GENUS
%izquierda
\filldraw[fill=white, very thick] (-5,0) circle (.25);
\filldraw[fill=white, very thick] (-3.5,0) circle (.25);
\filldraw[fill=white, very thick] (-2.5,0) circle (.25);
%derecha
\filldraw[fill=white, very thick] (1.75,0) circle (.25);
\filldraw[fill=white, very thick] (3,0) circle (.25);
\filldraw[fill=white, very thick] (4,0) circle (.25);
\filldraw[fill=white, very thick] (5,0) circle (.25);
\filldraw[fill=white, very thick] (4,.75) circle (.25);
\filldraw[fill=white, very thick] (4,1.5) circle (.25);
\filldraw[fill=white, very thick] (7,0) circle (.25);
\filldraw[fill=white, very thick] (8.25,0) circle (.25);
%lineas
%izquierda
\draw (-4.5,1) to[out=260,in=100] (-4.5,-1);
\draw (-3.5,0) ellipse (.5 and .5);
\draw (-3.5,0) ellipse (2 and .75);
%derecha
\draw (2.5,1) to[out=260,in=100] (2.5,-1);
\draw (6,1) to[out=260,in=100] (6,-1);
\draw (7,0) ellipse (.5 and .5);
\draw (5,0) ellipse (3.75 and .75);
%etiquetas
%izquierda
\draw (-4.5, -1.2) node{$\alpha$};
\draw (-4.2, 0) node{$\beta$};
\draw (-1.4, .5) node{$\beta'$};
%derecha
\draw (2.5, -1.2) node{$\alpha$};
\draw (8.3, .7) node{$f(\beta')$};
\draw[dashed] (7,.6)--(7.5,1.5);
\draw (8, 1.5) node{$f(\beta)$};
\draw(0,0.5) node{$f$};
\draw[->] (-.5,0)--(.5,0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1402.3275 | arxiv | 2014-02-14T02:09:23 |
|
Piecewise syndetic sets always consist of eventually growing intervals that have bounded gaps. The space between these intervals may be arbitrary, however. | \documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[yscale=0.5,xscale=0.66,scale=0.5]
\def\block#1#2{\draw (#1,-1) rectangle +(#2,2)}
\def\number#1[#2]{\node[#2] at (#1+0.5,0) {$#1$}}
\node[left] at (0.5,0) {$A = \Big\{$};
\block{1}{3};
\number{1}[black];
\number{2}[black!70];
\number{3}[black!60];
\node at (5.6,0) {$…$};
% interval
\block{7}{4};
\block{13}{3};
\def\gapsize#1#2{
\draw (#1,-2) -- +(0,-0.5) -- node[midway,below,style={font=\footnotesize}] {gap size $\leq d$} (#2,-2.5) -- +(0,0.5)}
\gapsize{11}{13};
\def\intervals#1#2#3{
\draw (#1,-5) -- +(0,-0.5) -- node[midway,below,style={font=\footnotesize}] {#3} (#2,-5.5) -- +(0,0.5)}
\intervals{7}{16}{large interval};
% small block
\node at (17.6,0) {$…$};
\block{19}{1};
% interval
\node at (21.6,0) {$…$};
\block{23}{6};
\block{30}{5};
\gapsize{29}{30};
\intervals{23}{35}{larger interval};
\path (37.6,0) node {$\dots\dots$} +(2.5,0) node {$\Big\}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1206.0967 | arxiv | 2012-06-06T02:04:38 |
|
In a compact space Y, every sequence will have one or more limit points. An ultrafilter limit picks one of them. | \documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}
\draw (0,0) ellipse (2.3 and 2);
\path (90:2.1) node[above] {$Y$};
\def\mypoint{\fill circle (0.05)}
\def\y#1{\mypoint node[above=1pt] {$y_{#1}$}}
\def\yl#1{\mypoint node[left] {$y_{#1}$}}
\def\yr#1{\mypoint node[right] {$y_{#1}$}}
\def\yend{\mypoint node[above] (yend) {$y$}}
\begin{scope}[decoration={markings
,mark=at position 0.00 with \y1;
,mark=at position 0.36 with \yl3;
,mark=at position 0.62 with \yl5;
,mark=at position 0.70 with \mypoint;
,mark=at position 0.80 with \mypoint;
,mark=at position 0.88 with \mypoint;
,mark=at position 0.93 with \mypoint;
,mark=at position 0.96 with \mypoint;
,mark=at position 0.99 with \mypoint;
}]
\draw decorate{ (0,-1.5) .. controls (0,-0.8) and (130:1.6) .. (140:1.7) };
\end{scope}
\begin{scope}[decoration={markings
,mark=at position 0.30 with \yr2;
,mark=at position 0.5 with \yr4;
,mark=at position 0.70 with \mypoint;
,mark=at position 0.80 with \mypoint;
,mark=at position 0.88 with \mypoint;
,mark=at position 0.93 with \mypoint;
,mark=at position 0.96 with \mypoint;
,mark=at position 0.99 with \mypoint;
}]
\draw decorate{ (0,-1.5) .. controls (0,-1) and (50:1.5) .. (40:1.6) };
\draw (40:1.7) -- (30:2.6) node[right] {pick this limit point};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1206.0967 | arxiv | 2012-06-06T02:04:38 |
|
A set A is not piecewise syndetic if and only if a gap of length at least d can be found in each interval that has size at least l(d). | \documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[yscale=0.5,xscale=0.66,scale=0.6]
\def\block#1#2{\draw (#1,-1) rectangle +(#2,2)}
\def\number#1[#2]{\node[#2] at (#1+0.5,0) {$#1$}}
\node[left] at (0.5,0) {$A = \Big\{$};
\block{1}{3};
\number{1}[black];
\number{2}[black!70];
\number{3}[black!60];
\node at (5.6,0) {$…$};
% interval
\block{7}{4};
\block{12}{5};
\block{20}{3};
\block{24}{4};
\def\gapsize#1#2{
\draw (#1,-2) -- +(0,-0.5) -- node[midway,below,style={font=\footnotesize}] {some gap has size $\geq d$} (#2,-2.5) -- +(0,0.5)}
\gapsize{17}{20};
\def\intervals#1#2#3{
\draw (#1,-4.7) -- +(0,-0.5) -- node[midway,below,style={font=\footnotesize}] {#3} (#2,-4.7-0.5) -- +(0,0.5)}
\intervals{9}{30}{when looking at any interval of size $\geq l(d)$};
\path (30.6,0) node {$\dots\dots$} +(2.5,0) node {$\Big\}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1206.0967 | arxiv | 2012-06-06T02:04:38 |
|
Illustration of a syndetic set. The rectangular blocks indicate natural numbers that are contained in the set, while empty space indicates numbers that are absent from the set. Being syndetic means that no gap may exceed a fixed size d. | \documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[yscale=0.5,xscale=0.7,scale=0.6]
\def\block#1#2{\draw (#1,-1) rectangle +(#2,2)}
\def\number#1[#2]{\node[#2] at (#1+0.5,0) {$#1$}}
\node[left] at (0.5,0) {$A = \Bigg\{$};
\block{1}{4};
\number{1}[black];
\number{2}[black!70];
\number{3}[black!60];
\number{4}[black!50];
\block{7}{3};
\number{7}[black!40];
\number{8}[black!20];
\number{9}[black!10];
\block{11}{1};
\block{15}{6};
\draw (12,-2) -- +(0,-0.5) -- node[midway,below,style={font=\footnotesize}] {all gap sizes $\leq d$} (15,-2.5) -- (15,-2);
\node at (25,0) {$\dots\dots \quad \Bigg\}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1206.0967 | arxiv | 2012-06-06T02:04:38 |
|
A Complete (and Undecomposable) Function. | \documentclass[11pt]{article}
\usepackage{amssymb,amsfonts}
\usepackage{amsmath}
\usepackage[usenames,dvipsnames]{color}
\usepackage[pdftex,bookmarks=true,pdfstartview=FitH,colorlinks,linkcolor=blue,filecolor=blue,citecolor=blue,urlcolor=blue,pagebackref=true]{hyperref}
\usepackage{tikz}
\usetikzlibrary{fit, matrix, positioning, calc}
\begin{document}
\begin{tikzpicture}
\tikzset{sim/.style={rounded corners, rectangle, draw, thick, dotted, inner sep = 0}}
\pgfsetmatrixcolumnsep{8pt}
\pgfsetmatrixrowsep{8pt}
\matrix at (0,0) [left delimiter = (, right delimiter = )]
{
\node (n00) {0}; & \node (n01) {1}; \\
\node (n10) {1}; & \node (n11) {1}; \\
};
\node [sim, fit = (n01) (n11)] {};
\node [sim, fit = (n10) (n11)] {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1205.3554 | arxiv | 2012-05-17T02:01:45 |
|
Decomposition of a Decomposable Function | \documentclass[11pt]{article}
\usepackage{amssymb,amsfonts}
\usepackage{amsmath}
\usepackage[usenames,dvipsnames]{color}
\usepackage[pdftex,bookmarks=true,pdfstartview=FitH,colorlinks,linkcolor=blue,filecolor=blue,citecolor=blue,urlcolor=blue,pagebackref=true]{hyperref}
\usepackage{tikz}
\usetikzlibrary{fit, matrix, positioning, calc}
\begin{document}
\begin{tikzpicture}
\coordinate (o) at (0,0);
\coordinate (x) at (1,0);
\coordinate (y) at (0,-1);
\coordinate (dy) at ($0.2*(y)$);
\draw (o) node {}
++(x) node (y1) {$0$}
++(x) node (y2) {$2$}
++(x) node (y3) {$4$}
(o)
++(y) node (x1) {$1$}
++(x) node (m11) {$1$}
++(x) node (m12) {$2$}
++(x) node (m13) {$4$}
(o)
++($2*(y)$) node (x2) {$3$}
++(x) node (m21) {$3$}
++(x) node (m22) {$3$}
++(x) node (m23) {$4$}
(o)
++($3*(y)$) node (x3) {$5$}
++(x) node (m31) {$5$}
++(x) node (m32) {$5$}
++(x) node (m33) {$5$};
\node [rectangle, rounded corners, draw, fit = (m11) (m33)] {};
\draw ($(m21)!.5!(m31)$) -- ($(m23)!.5!(m33)$);
\draw ($(m13)!.5!(m12) - (dy)$) -- ($(m23)!.5!(m22) + (dy)$);
\draw ($(m11)!.5!(m21)$) -- ($(m12)!.5!(m22)$);
\draw ($(m11)!.5!(m12) - (dy)$) -- ++($0.4*(y)$);
\coordinate (p) at ($(o) + 6*(x)$);
\coordinate (s) at ($(x) + (y)$);
\coordinate (t) at ($(y) - (x)$);
\draw (p) node (r) [circle, draw] {A}
++(s) node (r1) [circle, draw] {B}
++(s) node (r11) [circle, draw] {A}
++(s) node (r111) [circle, draw] {B}
++(s) node (r1111) [rectangle, draw] {$2$}
(r111)
++(t) node (r1110) [rectangle, draw] {$1$}
(r11)
++(t) node (r110) [rectangle, draw] {$3$}
(r1)
++(t) node (r10) [rectangle, draw] {$4$}
(r)
++(t) node (r0) [rectangle, draw] {$5$};
\draw (r) -- (r0)
(r) -- (r1)
(r1) -- (r10)
(r1) -- (r11)
(r11) -- (r110)
(r11) -- (r111)
(r111) -- (r1110)
(r111) -- (r1111);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1205.3554 | arxiv | 2012-05-17T02:01:45 |
|
An Incomplete but Undecomposable Function (Minimum ||+||). | \documentclass[11pt]{article}
\usepackage{amssymb,amsfonts}
\usepackage{amsmath}
\usepackage[usenames,dvipsnames]{color}
\usepackage[pdftex,bookmarks=true,pdfstartview=FitH,colorlinks,linkcolor=blue,filecolor=blue,citecolor=blue,urlcolor=blue,pagebackref=true]{hyperref}
\usepackage{tikz}
\usetikzlibrary{fit, matrix, positioning, calc}
\begin{document}
\begin{tikzpicture}
\tikzset{sim/.style={rounded corners, rectangle, draw, thick, dotted, inner sep = 0}}
\pgfsetmatrixcolumnsep{8pt}
\pgfsetmatrixrowsep{8pt}
\matrix at (0,0) [left delimiter = (, right delimiter = )]
{
\node (n11) {1}; & \node (n12) {1}; & \node (n13) {2}; \\
\node (n21) {4}; & \node (n22) {0}; & \node (n23) {2}; \\
\node (n31) {4}; & \node (n32) {3}; & \node (n33) {3}; \\
};
\node [sim, fit = (n11) (n12)] {};
\node [sim, fit = (n13) (n23)] {};
\node [sim, fit = (n32) (n33)] {};
\node [sim, fit = (n21) (n31)] {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1205.3554 | arxiv | 2012-05-17T02:01:45 |
|
An Incomplete but Undecomposable Function (Minimum ||). | \documentclass[11pt]{article}
\usepackage{amssymb,amsfonts}
\usepackage{amsmath}
\usepackage[usenames,dvipsnames]{color}
\usepackage[pdftex,bookmarks=true,pdfstartview=FitH,colorlinks,linkcolor=blue,filecolor=blue,citecolor=blue,urlcolor=blue,pagebackref=true]{hyperref}
\usepackage{tikz}
\usetikzlibrary{fit, matrix, positioning, calc}
\begin{document}
\begin{tikzpicture}
\tikzset{sim/.style={rounded corners, rectangle, draw, thick, dotted, inner sep = 0}}
\pgfsetmatrixcolumnsep{8pt}
\pgfsetmatrixrowsep{8pt}
\matrix at (0,0) [left delimiter = (, right delimiter = )]
{
\node (n11) {1}; & \node (n12) {1}; & \node (n13) {3}; & \node (n14) {4}; \\
\node (n21) {3}; & \node (n22) {2}; & \node (n23) {2}; & \node (n24) {4}; \\
\node (n31) {3}; & \node (n32) {4}; & \node (n33) {1}; & \node (n34) {1}; \\
\node (n41) {2}; & \node (n42) {4}; & \node (n43) {3}; & \node (n44) {2}; \\
};
\node [sim, fit = (n11) (n12)] {};
\node [sim, fit = (n22) (n23)] {};
\node [sim, fit = (n33) (n34)] {};
\node [sim, fit = (n13) ] (open13) {}; \draw [color=white, line width=5pt] (open13.north west) -- (open13.north east);
\node [sim, fit = (n43) ] (open43) {}; \draw [color=white, line width=5pt] (open43.south west) -- (open43.south east);
\node [sim, fit = (n21) (n31)] {};
\node [sim, fit = (n32) (n42)] {};
\node [sim, fit = (n14) (n24)] {};
\node [sim, fit = (n41) ] (open41) {}; \draw [color=white, line width=5pt] (open41.north west) -- (open41.south west);
\node [sim, fit = (n44) ] (open44) {}; \draw [color=white, line width=5pt] (open44.south east) -- (open44.north east);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1205.3554 | arxiv | 2012-05-17T02:01:45 |
|
The tree H_n,k. | \documentclass[10pt,bezier]{article}
\usepackage{amsmath,amssymb,amsfonts,xspace}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=.8]
\filldraw [black]
(-1,0) circle (3.5 pt)
(1,0) circle (3.5 pt)
(-2,1) circle (3.5 pt)
(-2,0.5) circle (3.5 pt)
(-2,-1) circle (3.5 pt)
(-2,0.1) circle (1 pt)
(-2,-0.3) circle (1 pt)
(-2,-0.7) circle (1 pt)
(2,0.1) circle (1 pt)
(2,-0.3) circle (1 pt)
(2,-0.7) circle (1 pt)
(2,1) circle (3.5 pt)
(2,0.5) circle (3.5 pt)
(2,-1) circle (3.5 pt);
\node [label=below:$H_{n,k}$] (H_{n,k}) at (0,-0.75) {};
\node [label=left:$1$] (1) at (-2,1) {};
\node [label=left:$2$] (2) at (-2,0.5) {};
\node [label=left:$k-1$] (k-1) at (-2,-1) {};
\node [label=right:$1$] (1) at (2,1) {};
\node [label=right:$2$] (2) at (2,0.5) {};
\node [label=right:$n-k-1$] (n-k-1) at (2,-1) {};
\draw[thick] (-1,0) -- (1,0);
\draw[thick] (-1,0) -- (-2,1);
\draw[thick] (-1,0) -- (-2,0.5);
\draw[thick] (-1,0) -- (-2,-1);
\draw[thick] (1,0) -- (2,1);
\draw[thick] (1,0) -- (2,0.5);
\draw[thick] (1,0) -- (2,-1);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1303.3222 | arxiv | 2013-03-14T01:02:55 |
|
I(G_n,x)=I(C_n,x). | \documentclass[10pt,bezier]{article}
\usepackage{amsmath,amssymb,amsfonts,xspace}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=1]
\filldraw [black]
(-3,0) circle (3.5 pt)
(-2,0) circle (3.5 pt)
(-1.5,0) circle (1 pt)
(-1,0) circle (1 pt)
(-0.5,0) circle (1 pt)
(0,0) circle (3.5 pt)
(1,0.5) circle (3.5 pt)
(1,-0.5) circle (3.5 pt);
\node [label=below:$G_n$] (G_n) at (-0.65,-0.75) {};
\node [label=above:$1$] (1) at (-3,0) {};
\node [label=above:$2$] (2) at (-2,0) {};
\node [label=above:$n-2$] (n-2) at (0,0) {};
\node [label=right:$n-1$] (n-1) at (1,0.5) {};
\node [label=right:$n$] (n) at (1,-0.5) {};
\draw[thick] (-3,0) --(-2,0);
\draw[thick] (-2,0) -- (-1.6,0);
\draw[thick] (-0.4,0) -- (0,0);
\draw[thick] (0,0) -- (1,0.5);
\draw[thick] (0,0) -- (1,-0.5);
\draw[thick] (1,0.5) -- (1,-0.5);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1303.3222 | arxiv | 2013-03-14T01:02:55 |
|
the tree T. | \documentclass[10pt,bezier]{article}
\usepackage{amsmath,amssymb,amsfonts,xspace}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.7]
\filldraw [black]
(0,0) circle (3.5 pt)
(0,-2) circle (3.5 pt)
(2,-2) circle (3.5 pt)
(-2,-2) circle (3.5 pt)
(.075,-2) circle (1 pt)
(1,-2) circle (1 pt)
(1.25,-2) circle (1 pt);
\node [label=below:$T$] (T) at (0,-5.5) {};
\node [label=left:$v$] (v) at (0.25,0.25) {};
\node [label=left:$v_k$] (v_k) at (2.75,-1.75) {};
\node [label=above:$v_2$] (v_2) at (-.25,-2.1) {};
\node [label=left:$v_1$] (v_1) at (-2,-2) {};
\draw[thick] (0,0) -- (-2,-2);
\draw[thick] (0,0) -- (0,-2);
\draw[thick] (0,0) -- (2,-2);
\draw (-1.95,-3.35) ellipse (20pt and 40pt);
\node [label=below:$H_1$] (H_1) at (-2,-2.75) {};
\draw (0,-3.35) ellipse (20pt and 40pt);
\node [label=below:$H_2$] (H_2) at (0,-2.75) {};
\draw (2.05,-3.35) ellipse (20pt and 40pt);
\node [label=below:$H_k$] (H_k) at (2,-2.75) {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1303.3222 | arxiv | 2013-03-14T01:02:55 |
|
A graphing and one of its refinements | \documentclass[a4paper]{article}
\usepackage[applemac]{inputenc}
\usepackage{amsmath,amsthm,amssymb,bussproofs,tikz,stmaryrd,mathtools}
\begin{document}
\begin{tikzpicture}[x=0.7cm,y=0.7cm]
\draw[-] (0,0) -- (2,0) node [below,very near start] {\scriptsize{$[0,2]$}};
\draw[-] (3,0) -- (5,0) node [below,very near end] {\scriptsize{$[3,5]$}};
\node (1) at (1,0) {};
\node (4) at (4,0) {};
\draw[->,red] (1) .. controls (1,1.5) and (4,1.5) .. (4) node [midway,above] {\scriptsize{$x\mapsto 5-x$}};
\draw[-] (7.5,0) -- (8.5,0) node [below,very near start] {\scriptsize{$[0,1]$}};
\draw[-] (9,0) -- (10,0) node [below,very near start] {\scriptsize{$[1,2]$}};
\draw[-] (10.5,0) -- (11.5,0) node [below,very near end] {\scriptsize{$[3,4]$}};
\draw[-] (12,0) -- (13,0) node [below,very near end] {\scriptsize{$[4,5]$}};
\node (8) at (8,0) {};
\node (95) at (9.5,0) {};
\node (11) at (11,0) {};
\node (125) at (12.5,0) {};
\draw[->,red] (8) .. controls (8,2) and (12.5,2) .. (125) node [midway,above] {\scriptsize{$x\mapsto 5-x$}};
\draw[->,red] (95) .. controls (9.5,1) and (11,1) .. (11) node [midway,above] {\scriptsize{$x\mapsto 5-x$}};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1312.1094 | arxiv | 2014-07-09T02:08:35 |
|
Plugging of the thick graphs G and H | \documentclass[a4paper]{article}
\usepackage[applemac]{inputenc}
\usepackage{amsmath,amsthm,amssymb,bussproofs,tikz,stmaryrd,mathtools}
\begin{document}
\begin{tikzpicture}
\node (G111) at (0,0,0) {$1_{1,1}$};
\node (G211) at (2,0,0) {$2_{1,1}$};
\node (G121) at (0,2,0) {$1_{2,1}$};
\node (G221) at (2,2,0) {$2_{2,1}$};
\node[opacity=0.6] (G112) at (0,0,-4) {$1_{1,2}$};
\node[opacity=0.6] (G212) at (2,0,-4) {$2_{1,2}$};
\node[opacity=0.6] (G122) at (0,2,-4) {$1_{2,2}$};
\node[opacity=0.6] (G222) at (2,2,-4) {$2_{2,2}$};
\draw[<->,blue] (G111) .. controls (-1,0.5,0) and (-1,1.5,0) .. (G121) {};
\draw[<->,blue] (G121) .. controls (0.5,3,0) and (1.5,3,0) .. (G221) {};
\draw[<->,blue] (G111) .. controls (0.5,-1,0) and (1.5,-1,0) .. (G211) {};
\draw[<->,blue,dashed] (G112) .. controls (-1,0.5,-4) and (-1,1.5,-4) .. (G122) {};
\draw[<->,blue,dashed] (G122) .. controls (0.5,3,-4) and (1.5,3,-4) .. (G222) {};
\draw[<->,blue,dashed] (G112) .. controls (0.5,-1,-4) and (1.5,-1,-4) .. (G212) {};
\draw[->,dotted] (0,0,0) -- (7,0,0) {};
\draw[->,dotted] (0,0,0) -- (0,5,0) {};
\draw[->,dotted] (0,0,0) -- (0,0,-12) {};
\draw[fill=blue,draw=red,opacity=.2,very thin,line join=round]
(0,0,0) --
(2,0,0) --
(2,2,0) --
(0,2,0) --
(0,0,0) {} ;
\draw[fill=blue,draw=red,opacity=.2,very thin,line join=round]
(0,0,-4) --
(2,0,-4) --
(2,2,-4) --
(0,2,-4) --
(0,0,-4) {} ;
\node (H211) at (4,0,0) {$3_{1,1}$};
\node[opacity=0.6] (H212) at (4,0,-4) {$3_{1,2}$};
\node (H221) at (4,2,0) {$3_{2,1}$};
\node[opacity=0.6] (H222) at (4,2,-4) {$3_{2,2}$};
\draw[<-,red] (H211) -- (3,0,-2) {};
\draw[->,red,densely dashed] (3,0,-2) -- (G212) {};
\draw[->,red,dashed] (H212) .. controls (3.5,0,-6) and (4.5,0,-6) .. (H212) {};
\draw[->,red] (G211) .. controls (1.5,0,-2) and (2.5,0,-2) .. (G211) {};
\draw[<-,red] (H221) -- (3,2,-2) {};
\draw[->,red,densely dashed] (3,2,-2) -- (G222) {};
\draw[->,red,dashed] (H222) .. controls (3.5,2,-6) and (4.5,2,-6) .. (H222) {};
\draw[->,red] (G221) .. controls (1.5,2,-2) and (2.5,2,-2) .. (G221) {};
\draw[fill=red,draw=red,opacity=.2,very thin,line join=round]
(2,0,0) --
(4,0,0) --
(4,0,-4) --
(2,0,-4) --
(2,0,0) {} ;
\draw[fill=red,draw=red,opacity=.2,very thin,line join=round]
(2,2,0) --
(4,2,0) --
(4,2,-4) --
(2,2,-4) --
(2,2,0) {} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1312.1094 | arxiv | 2014-07-09T02:08:35 |
|
Two thick graphs G and H, both with dialect \{1,2\} | \documentclass[a4paper]{article}
\usepackage[applemac]{inputenc}
\usepackage{amsmath,amsthm,amssymb,bussproofs,tikz,stmaryrd,mathtools}
\begin{document}
\begin{tikzpicture}[node distance=2cm]
\node (G11) at (0,0) {$1_{1}$};
\node (G21) at (2,0) {$2_{1}$};
\node (G12) at (0,2) {$1_{2}$};
\node (G22) at (2,2) {$2_{2}$};
\node (H11) at (6,0) {$2_{1}$};
\node (H21) at (8,0) {$3_{1}$};
\node (H12) at (6,2) {$2_{2}$};
\node (H22) at (8,2) {$3_{2}$};
\draw[<->,blue] (G11) .. controls (-1,0.5) and (-1,1.5) .. (G12) {};
\draw[<->,blue] (G12) .. controls (0.5,3) and (1.5,3) .. (G22) {};
\draw[<->,blue] (G11) .. controls (0.5,-1) and (1.5,-1) .. (G21) {};
\draw[dashed,blue] (-1.3,-1) -- (-1.3,3) node [sloped,above,near end] {slice $2$} node [sloped,above,near start] {slice $1$};
\draw[dashed,blue] (-1.3,-1) -- (3,-1) {};
\draw[dashed,blue] (-1.3,3) -- (3,3) {};
\draw[dashed,blue] (3,-1) -- (3,3) {};
\draw[dotted,blue] (-1.3,1) -- (3,1) {};
\node (G) at (-1.1,2.8) {\textcolor{blue}{G}};
\draw[<->,red] (H12) -- (H21) {};
\draw[->,red] (H22) .. controls (7.5,3) and (8.5,3) .. (H22) {};
\draw[->,red] (H11) .. controls (5.5,-1) and (6.5,-1) .. (H11) {};
\draw[-,dashed,red] (4.85,-1) -- (4.85,3) node [sloped,above,near end] {slice $2$} node [sloped,above,near start] {slice $1$};
\draw[dashed,red] (4.85,-1) -- (9.15,-1) {};
\draw[dashed,red] (4.85,3) -- (9.15,3) {};
\draw[dashed,red] (9.15,-1) -- (9.15,3) {};
\draw[dotted,red] (4.85,1) -- (9.15,1) {};
\node (G) at (8.8,2.8) {\textcolor{red}{H}};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1312.1094 | arxiv | 2014-07-09T02:08:35 |
|
Result of the execution of the thick graphs G and H | \documentclass[a4paper]{article}
\usepackage[applemac]{inputenc}
\usepackage{amsmath,amsthm,amssymb,bussproofs,tikz,stmaryrd,mathtools}
\begin{document}
\begin{tikzpicture}
\node (G111) at (0,0,0) {$1_{1,1}$};
\node (G121) at (0,2,0) {$1_{2,1}$};
\node[opacity=0.6] (G112) at (0,0,-4) {$1_{1,2}$};
\node[opacity=0.6] (G122) at (0,2,-4) {$1_{2,2}$};
\node (H211) at (4,0,0) {$3_{1,1}$};
\node[opacity=0.6] (H212) at (4,0,-4) {$3_{1,2}$};
\node (H221) at (4,2,0) {$3_{2,1}$};
\node[opacity=0.6] (H222) at (4,2,-4) {$3_{2,2}$};
\draw[<->,violet] (G111) .. controls (-1,0.5,0) and (-1,1.5,0) .. (G121) {};
\draw[<->,violet] (G121) .. controls (-0.5,3,0) and (0.5,3,0) .. (G121) {};
\draw[<->,violet] (G111) .. controls (-0.5,-1,0) and (0.5,-1,0) .. (G111) {};
\draw[<->,violet,dashed] (G112) .. controls (-1,0.5,-4) and (-1,1.5,-4) .. (G122) {};
\draw[<-,violet,densely dashed] (G122) -- (2,2,-2) {};
\draw[<-,violet,densely dashed] (G112) -- (2,0,-2) {};
\draw[->,violet] (2,2,-2) -- (H221) {};
\draw[->,violet] (2,0,-2) -- (H211) {};
\draw[->,violet,dashed] (H212) .. controls (3.5,0,-6) and (4.5,0,-6) .. (H212) {};
\draw[->,violet,dashed] (H222) .. controls (3.5,2,-6) and (4.5,2,-6) .. (H222) {};
\draw[->,dotted] (0,0,0) -- (7,0,0) {};
\draw[->,dotted] (0,0,0) -- (0,5,0) {};
\draw[->,dotted] (0,0,0) -- (0,0,-12) {};
\draw[fill=blue,draw=red,opacity=.2,very thin,line join=round]
(0,0,0) --
(4,0,0) --
(4,2,0) --
(0,2,0) --
(0,0,0) {} ;
\draw[violet,opacity=0.6] (0,0,0) -- (4,0,0) node [sloped, above, midway, opacity=0.5] {\scriptsize{slice $(1,1)$}};
\draw[violet,opacity=0.6] (0,2,0) -- (4,2,0) node [sloped, above, midway, opacity=0.5] {\scriptsize{slice $(2,1)$}};
\draw[violet,opacity=0.6] (0,0,-4) -- (4,0,-4) node [sloped, below, midway, opacity=0.5] {\scriptsize{slice $(1,2)$}};
\draw[violet,opacity=0.6] (0,2,-4) -- (4,2,-4) node [sloped, below, midway, opacity=0.5] {\scriptsize{slice $(2,2)$}};
\draw[fill=blue,draw=red,opacity=.2,very thin,line join=round]
(0,0,-4) --
(4,0,-4) --
(4,2,-4) --
(0,2,-4) --
(0,0,-4) {} ;
\draw[fill=red,draw=red,opacity=.2,very thin,line join=round]
(0,0,0) --
(4,0,0) --
(4,0,-4) --
(0,0,-4) --
(0,0,0) {} ;
\draw[fill=red,draw=red,opacity=.2,very thin,line join=round]
(0,2,0) --
(4,2,0) --
(4,2,-4) --
(0,2,-4) --
(0,2,0) {} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1312.1094 | arxiv | 2014-07-09T02:08:35 |
|
Alternating paths in the plugging of thick graphs G and H | \documentclass[a4paper]{article}
\usepackage[applemac]{inputenc}
\usepackage{amsmath,amsthm,amssymb,bussproofs,tikz,stmaryrd,mathtools}
\begin{document}
\begin{tikzpicture}
\node (G111) at (0,0,0) {$1_{1,1}$};
\node (G121) at (0,2,0) {$1_{2,1}$};
\node[opacity=0.6] (G112) at (0,0,-4) {$1_{1,2}$};
\node[opacity=0.6] (G122) at (0,2,-4) {$1_{2,2}$};
\draw[<->,blue] (G111) .. controls (-1,0.5,0) and (-1,1.5,0) .. (G121) {};
\draw[->,blue] (G121) .. controls (0.5,3,0) and (1.5,3,0) .. (1.8,2,0) {};
\draw[->,blue] (G111) .. controls (0.5,-1,0) and (1.5,-1,0) .. (1.8,0,0) {};
\draw[<-,blue] (G121) .. controls (0.5,3,0) and (1.5,3,0) .. (2.2,2,0) {};
\draw[<-,blue] (G111) .. controls (0.5,-1,0) and (1.5,-1,0) .. (2.2,0,0) {};
\draw[<->,blue,dashed] (G112) .. controls (-1,0.5,-4) and (-1,1.5,-4) .. (G122) {};
\draw[->,blue,dashed] (G122) .. controls (0.5,3,-4) and (1.5,3,-4) .. (1.8,2,-4) {};
\draw[->,blue,dashed] (G112) .. controls (0.5,-1,-4) and (1.5,-1,-4) .. (1.8,0,-4) {};
\draw[<-,blue,dashed] (G122) .. controls (0.5,3,-4) and (1.5,3,-4) .. (2.2,2,-4) {};
\draw[<-,blue,dashed] (G112) .. controls (0.5,-1,-4) and (1.5,-1,-4) .. (2.2,0,-4) {};
\draw[->,dotted] (0,0,0) -- (7,0,0) {};
\draw[->,dotted] (0,0,0) -- (0,5,0) {};
\draw[->,dotted] (0,0,0) -- (0,0,-12) {};
\draw[fill=blue,draw=red,opacity=.2,very thin,line join=round]
(0,0,0) --
(2,0,0) --
(2,2,0) --
(0,2,0) --
(0,0,0) {} ;
\draw[fill=blue,draw=red,opacity=.2,very thin,line join=round]
(0,0,-4) --
(2,0,-4) --
(2,2,-4) --
(0,2,-4) --
(0,0,-4) {} ;
\node (H211) at (4,0,0) {$3_{1,1}$};
\node[opacity=0.6] (H212) at (4,0,-4) {$3_{1,2}$};
\node (H221) at (4,2,0) {$3_{2,1}$};
\node[opacity=0.6] (H222) at (4,2,-4) {$3_{2,2}$};
\draw[-,red] (H211) -- (3.1,0,-2) {};
\draw[-,red,densely dashed] (1.8,0,-4) -- (2.9,0,-2) {};
\draw[->,red,densely dashed] (3.1,0,-2) -- (2.2,0,-4) {};
\draw[->,red] (2.9,0,-2) -- (H211) {};
\draw[->,red,dashed] (H212) .. controls (3.5,0,-6) and (4.5,0,-6) .. (H212) {};
\draw[->,red] (1.8,0,0) .. controls (1.5,0,-2) and (2.5,0,-2) .. (2.2,0,0) {};
\draw[-,red] (H221) -- (3.1,2,-2) {};
\draw[-,red,densely dashed] (1.8,2,-4) -- (2.9,2,-2) {};
\draw[->,red,densely dashed] (3.1,2,-2) -- (2.2,2,-4) {};
\draw[->,red] (2.9,2,-2) -- (H221) {};
\draw[->,red,dashed] (H222) .. controls (3.5,2,-6) and (4.5,2,-6) .. (H222) {};
\draw[->,red] (1.8,2,0) .. controls (1.5,2,-2) and (2.5,2,-2) .. (2.2,2,0) {};
\draw[fill=red,draw=red,opacity=.2,very thin,line join=round]
(4,0,-4) --
(2,0,-4) --
(2,0,0) --
(4,0,0) --
(4,0,-4) {} ;
\draw[fill=red,draw=red,opacity=.2,very thin,line join=round]
(2,2,0) --
(4,2,0) --
(4,2,-4) --
(2,2,-4) --
(2,2,0) {} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1312.1094 | arxiv | 2014-07-09T02:08:35 |
|
The graphs G^_D^H and H^_D^G | \documentclass[a4paper]{article}
\usepackage[applemac]{inputenc}
\usepackage{amsmath,amsthm,amssymb,bussproofs,tikz,stmaryrd,mathtools}
\begin{document}
\begin{tikzpicture}[scale=0.9]
\node (G111) at (0,0,0) {$1_{1,1}$};
\node (G211) at (2,0,0) {$2_{1,1}$};
\node (G121) at (0,2,0) {$1_{2,1}$};
\node (G221) at (2,2,0) {$2_{2,1}$};
\node[opacity=0.6] (G112) at (0,0,-4) {$1_{1,2}$};
\node[opacity=0.6] (G212) at (2,0,-4) {$2_{1,2}$};
\node[opacity=0.6] (G122) at (0,2,-4) {$1_{2,2}$};
\node[opacity=0.6] (G222) at (2,2,-4) {$2_{2,2}$};
\draw[<->,blue] (G111) .. controls (-1,0.5,0) and (-1,1.5,0) .. (G121) {};
\draw[<->,blue] (G121) .. controls (0.5,3,0) and (1.5,3,0) .. (G221) {};
\draw[<->,blue] (G111) .. controls (0.5,-1,0) and (1.5,-1,0) .. (G211) {};
\draw[<->,blue,dashed] (G112) .. controls (-1,0.5,-4) and (-1,1.5,-4) .. (G122) {};
\draw[<->,blue,dashed] (G122) .. controls (0.5,3,-4) and (1.5,3,-4) .. (G222) {};
\draw[<->,blue,dashed] (G112) .. controls (0.5,-1,-4) and (1.5,-1,-4) .. (G212) {};
\draw[->,dotted] (0,0,0) -- (5,0,0) {};
\draw[->,dotted] (0,0,0) -- (0,5,0) {};
\draw[->,dotted] (0,0,0) -- (0,0,-12) {};
\draw[fill=blue,draw=red,opacity=.2,very thin,line join=round]
(3,3,-0) --
(-1,3,0) --
(-1,-1,0) --
(3,-1,0) --
(3,3,0) node [sloped,above,midway,opacity=0.5] {slices $(\cdot,1)$} ;
\draw[fill=blue,draw=red,opacity=.2,very thin,line join=round]
(3,3,-4) --
(-1,3,-4) --
(-1,-1,-4) --
(3,-1,-4) --
(3,3,-4) node [sloped,above,midway,opacity=0.5] {slices $(\cdot,2)$} ;
\node (H111) at (7,0,0) {$2_{1,1}$};
\node (H211) at (9,0,0) {$3_{1,1}$};
\node[opacity=0.6] (H112) at (7,0,-4) {$2_{1,2}$};
\node[opacity=0.6] (H212) at (9,0,-4) {$3_{1,2}$};
\node (H121) at (7,2,0) {$2_{2,1}$};
\node (H221) at (9,2,0) {$3_{2,1}$};
\node[opacity=0.6] (H122) at (7,2,-4) {$2_{2,2}$};
\node[opacity=0.6] (H222) at (9,2,-4) {$3_{2,2}$};
\draw[<-,red] (H211) -- (8,0,-2) {};
\draw[->,red,densely dashed] (8,0,-2) -- (H112) {};
\draw[->,red,dashed] (H212) .. controls (8.5,0,-6) and (9.5,0,-6) .. (H212) {};
\draw[->,red] (H111) .. controls (6.5,0,-2) and (7.5,0,-2) .. (H111) {};
\draw[<-,red] (H221) -- (8,2,-2) {};
\draw[->,red,densely dashed] (8,2,-2) -- (H122) {};
\draw[->,red,dashed] (H222) .. controls (8.5,2,-6) and (9.5,2,-6) .. (H222) {};
\draw[->,red] (H121) .. controls (6.5,2,-2) and (7.5,2,-2) .. (H121) {};
\draw[->,dotted] (7,0,0) -- (12,0,0) {};
\draw[->,dotted] (7,0,0) -- (7,5,0) {};
\draw[->,dotted] (7,0,0) -- (7,0,-12) {};
\draw[fill=red,draw=red,opacity=.2,very thin,line join=round]
(10,0,-6) --
(6,0,-6) --
(6,0,2) --
(10,0,2) --
(10,0,-6) node [sloped,above,near start,opacity=0.5] {slices $(1,\cdot )$} ;
\draw[fill=red,draw=red,opacity=.2,very thin,line join=round]
(10,2,-6) --
(6,2,-6) --
(6,2,2) --
(10,2,2) --
(10,2,-6) node [sloped,above,near start,opacity=0.5] {slices $(2,\cdot )$} ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1312.1094 | arxiv | 2014-07-09T02:08:35 |
|
Les graphes G_1 et G_2 | \documentclass[a4paper]{article}
\usepackage[applemac]{inputenc}
\usepackage{amsmath,amsthm,amssymb,bussproofs,tikz,stmaryrd,mathtools}
\begin{document}
\begin{tikzpicture}
\node (A1a) at (1,1) {$1_{a}$};
\node (A2a) at (3,1) {$2_{a}$};
\node (A1b) at (1,3) {$1_{b}$};
\node (A2b) at (3,3) {$2_{b}$};
\draw[->,blue] (A1a) .. controls (1.5,2) and (2.5,2) .. (A2a) {};
\draw[->,blue] (A2a) .. controls (2.5,0) and (3.5,0) .. (A2a) {};
\draw[->,blue] (A1b) .. controls (1.5,4) and (2.5,4) .. (A2b) {};
\draw[->,blue] (A1b) .. controls (0.5,2) and (1.5,2) .. (A1b) {};
\draw[dashed,blue] (0,0) -- (0,4) {};
\draw[dashed,blue] (0,4) -- (4,4) {};
\draw[dashed,blue] (4,4) -- (4,0) {};
\draw[dashed,blue] (4,0) -- (0,0) {};
\draw[dotted,blue] (0,2) -- (4,2) {};
\node (G1) at (3.7,3.7) {\textcolor{blue}{$F_{c}$}};
\node (1a) at (7,1) {$1_{a}$};
\node (2a) at (9,1) {$2_{a}$};
\node (1b) at (7,3) {$1_{b}$};
\node (2b) at (9,3) {$2_{b}$};
\draw[->,red] (1a) .. controls (7.5,2) and (8.5,2) .. (2a) {};
\draw[->,red] (2a) .. controls (8.5,0) and (9.5,0) .. (2a) {};
\draw[->,red] (1b) .. controls (7.5,4) and (8.5,4) .. (2b) {};
\draw[->,red] (1b) .. controls (6.5,2) and (7.5,2) .. (1b) {};
\draw[dashed,red] (6,0) -- (6,4) {};
\draw[dashed,red] (6,4) -- (10,4) {};
\draw[dashed,red] (10,4) -- (10,0) {};
\draw[dashed,red] (10,0) -- (6,0) {};
\draw[dashed,red] (6,2) -- (10,2) {};
\node (Fa) at (9.6,1.6) {\textcolor{red}{$\frac{1}{2}F_{a}$}};
\node (Fb) at (9.6,3.6) {\textcolor{red}{$\frac{1}{2}F_{b}$}};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1312.1094 | arxiv | 2014-07-09T02:08:35 |
|
Examples of sliced thick graphs: 12 F + 3 G and F_a+F_b | \documentclass[a4paper]{article}
\usepackage[applemac]{inputenc}
\usepackage{amsmath,amsthm,amssymb,bussproofs,tikz,stmaryrd,mathtools}
\begin{document}
\begin{tikzpicture}
\node (A1) at (0,0) {$1_{1}$};
\node (B1) at (0,2) {$1_{2}$};
\node (C1) at (0,4) {$1_{3}$};
\node (A2) at (2,0) {$2_{1}$};
\node (B2) at (2,2) {$2_{2}$};
\node (C2) at (2,4) {$2_{3}$};
\node (A3) at (4,0) {$3_{1}$};
\node (B3) at (4,2) {$3_{2}$};
\node (C3) at (4,4) {$3_{3}$};
\draw[->,blue] (A1) -- (B2) {};
\draw[->,blue] (B2) .. controls (1.5,3) and (2.5,3) .. (B2) {};
\draw[->,blue] (A2) .. controls (2.5,-1) and (3.5,-1) .. (A3) {};
\draw[->,blue] (B3) -- (A2) {};
\draw[->,blue] (C1) .. controls (1,5) and (3,5) .. (C3) {};
\draw[->,blue] (C3) .. controls (3.5,3) and (2.5,3) .. (C2) {};
\draw[-,dashed,blue] (-1,-1) -- (-1,5) {};
\draw[-,dashed,blue] (-1,-1) -- (5,-1) {};
\draw[-,dashed,blue] (5,-1) -- (5,5) {};
\draw[-,dashed,blue] (5,5) -- (-1,5) {};
\node (F) at (4.6,4.6) {\textcolor{blue}{$\frac{1}{2}F$}};
\node (F) at (4.6,2.7) {\textcolor{blue}{$3G$}};
\draw[-,dashed,blue] (-1,3) -- (5,3) {};
\draw[-,dotted,blue] (-1,1) -- (5,1) {};
\node (1a) at (7,1) {$1_{a}$};
\node (2a) at (9,1) {$2_{a}$};
\node (1b) at (7,3) {$1_{b}$};
\node (2b) at (9,3) {$2_{b}$};
\draw[->,red] (1a) .. controls (7.5,2) and (8.5,2) .. (2a) {};
\draw[->,red] (2a) .. controls (8.5,0) and (9.5,0) .. (2a) {};
\draw[->,red] (1b) .. controls (7.5,4) and (8.5,4) .. (2b) {};
\draw[->,red] (1b) .. controls (6.5,2) and (7.5,2) .. (1b) {};
\draw[dashed,red] (6,0) -- (6,4) {};
\draw[dashed,red] (6,4) -- (10,4) {};
\draw[dashed,red] (10,4) -- (10,0) {};
\draw[dashed,red] (10,0) -- (6,0) {};
\draw[dashed,red] (6,2) -- (10,2) {};
\node (Fa) at (9.7,1.7) {\textcolor{red}{$F_{a}$}};
\node (Fb) at (9.7,3.7) {\textcolor{red}{$F_{b}$}};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1312.1094 | arxiv | 2014-07-09T02:08:35 |
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