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Worst possible unannounced absences after two completed rounds. | \documentclass[12pt]{article}
\usepackage[ansinew]{inputenc}%ß als Eingabe statt "s u.s.w.
\usepackage[T1]{fontenc}%this is needed for correct output of umlauts in pdf
\usepackage{tikz}
\usepackage{tkz-graph}
\usepackage{color}
\usepackage{colortbl}
\usepackage{amsmath}
\usepackage{amssymb}%
\begin{document}
\begin{tikzpicture}
[transform canvas={scale=1.35}, every node/.style={circle, scale=0.5}]
\node[draw,fill=green!25,scale=1.1] (a) at (0,1) {\(\!\bf3\!\)};
\node[scale=1.3] (a+) at (-0.32,1.07) {\(\bf A\)};
\node[draw,fill=brown!45,scale=1.1] (b) at (-0.868,-0.5) {\(\!\bf4\!\)};
\node[scale=1.3] (b+) at (-1.186,-0.57) {\(\bf B\)};
\node[draw,fill=gray!10, scale=1.1] (c) at (0.868,-0.5) {\(\!\phantom{\bf4}\!\)};
\node[scale=1.3] (c+) at (1.186,-0.57) {\(\bf C\)};
\SetUpEdge[lw = 1.8pt,
labelcolor = white,
labeltext = red,
labelstyle = {font=\sffamily\small,scale=0.8,font=\bf,sloped}]
\Edge[color=red!80, labeltext=red, label=Round\,1](a)(c)
\Edge[color=blue!90, labeltext=blue, label=Round\,2](b)(c)
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1509.00488 | arxiv | 2016-05-23T02:12:02 |
|
A simple example of argumentation framework | \documentclass[oribibl]{llncs}
\usepackage{amssymb}
\usepackage{amsmath,bm}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows,automata}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.4cm, semithick]
\tikzstyle{vBlue}=[draw=blue!50,fill=blue!5,circle,text width=5.5mm,inner sep=1pt,minimum height=6pt, align=center]
\tikzstyle{every edge}=[draw=black!60]
\node[vBlue](x4){$x_4$};
\node[vBlue, above left of=x4, yshift=-4mm, xshift=-4mm](x1){$x_1$};
\node[vBlue, below left of=x4, yshift=4mm, xshift=-4mm](x3){$x_3$};
\node[vBlue, above right of=x4, yshift=-4mm, xshift=4mm](x2){$x_2$};
\node[vBlue, below right of=x4, yshift=4mm, xshift=4mm](x5){$x_5$};
\path (x4) edge (x1)
(x3) edge (x4)
(x4) edge (x2)
(x5) edge (x4)
(x5) edge [bend left=12] (x2)
(x2) edge [bend left=12] (x5)
(x5) edge [loop right] (x5)
(x2) edge [loop right] (x2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1406.3877 | arxiv | 2014-07-17T02:08:51 |
|
Optimal control problem: The dynamical system states are represented by \{x_i\}, and the control by nodes \{u_i\}. | \documentclass[]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage[latin1]{inputenc}
\usepackage{tikz}
\usetikzlibrary{trees, arrows, matrix, positioning}
\begin{document}
\begin{tikzpicture}[shorten >=1pt,->]
\tikzstyle{vertex}=[circle, minimum size=0pt,inner sep=0pt]
\foreach \name/\x in {0/0, 1/1, 2/2, 3/3, n-1/6}
\node[vertex] (U-\name) at (\x,0) {$u_{\name}$};
\foreach \name/\x in {1/1, 2/2, 3/3, n-1/6, n/7}
\node[vertex] (X-\name) at (\x, 25pt) {$x_{\name}$};
\foreach \from/\to in {1/2, 2/3, n-1/n}
{ \draw (X-\from) edge (X-\to); }
\draw[->, dotted] (X-3) -- (4, 25pt);
\draw[->, dotted] (X-3) -- (4, 25pt);
\draw[->, dotted] (5, 25pt) -- (X-n-1);
\foreach \from/\to in {0/1, 1/2, 2/3, n-1/n}
{ \draw[->] (U-\from) -- (X-\to); }
\draw[-, dotted] (U-3) -- (4, 25pt);
\draw[-, dotted] (4, 0) -- (5, 0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1508.00952 | arxiv | 2016-04-26T02:19:33 |
|
In this figure we show transceivers number of the set l^t=\{l_1,l_2,,l_r\} with the closed circular shape. The complimentary transceivers out of this circular shape can be modeled by the set \{1,,K\}-l^t. Also there is a connection between all transmitters and receivers but to avoid being so crowded we show a few of them. | \documentclass[10pt,onecolumn]{IEEEtran}
\usepackage{amssymb}
\usepackage[cmex10]{amsmath}
\usepackage{tikz}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw (-12,4) ellipse (0.8cm and 1.5cm);
\draw (-9,4) ellipse (0.8cm and 1.5cm);
\draw (-12,6) circle (0.05cm);
\node (a) at (-12.25,6){$1$};
\draw (-12,5) circle (0.05cm);
\node (b) at (-12.25,5){$l_1$};
\draw (-12,4.5) circle (0.05cm);
\node (c) at (-12.25,4.5){$q_1$};
\node (c) at (-12.25,4){$q_2$};
\draw (-12,4) circle (0.05cm);
\node (d) at (-12,3.75){$\vdots$};
\draw (-12,3) circle (0.05cm);
\node (e) at (-12.25,3){$l_r$};
\draw (-12,2) circle (0.05cm);
\node (f) at (-12.25,2){$q_4$};
\draw (-12,1) circle (0.05cm);
\node (f) at (-12.25,1){$K$};
\draw (-9,6) circle (0.05cm);
\node (g) at (-8.75,6){$1$};
\draw (-9,5) circle (0.05cm);
\node (h) at (-8.75,5){$l_1$};
\draw (-9,4.5) circle (0.05cm);
\node (i) at (-8.75,4.5){$q_3$};
\draw (-9,4) circle (0.05cm);
\node (j) at (-9,3.75){$\vdots$};
\draw (-9,3) circle (0.05cm);
\node (k) at (-8.75,3){$l_r$};
\draw (-9,2) circle (0.05cm);
\node (l) at (-8.75,2){$q_4$};
\draw (-9,1) circle (0.05cm);
\node (l) at (-8.75,1){$K$};
\node (m) at (-7,4){$l^{t}$ RX set};
\node (n) at (-14,4){$l^{t}$ TX set};
\node (o) at (-12.25,0){\begin{LARGE}
TX
\end{LARGE}};
\node (p) at (-9,0){\begin{LARGE}
RX
\end{LARGE}};
\node (tk) at (-11.75,1){};
\node (rk) at (-9.25,1){};
\node (t1) at (-11.75,2){};
\node (tlq) at (-11.75,4){};
\node (tq4) at (-11.75,6){};
\node (r1) at (-9.25,2){};
\node (rlq) at (-9.25,4){};
\node (rq4) at (-9.25,6){};
\draw[->] (t1) edge (r1);
\draw[->] (t1) edge (rlq);
\draw[->] (t1) edge (rq4);
\draw[->] (tlq) edge (r1);
\draw[->] (tlq) edge (rlq);
\draw[->] (tlq) edge (rq4);
\draw[->] (tq4) edge (r1);
\draw[->] (tq4) edge (rlq);
\draw[->] (tq4) edge (rq4);
\draw[->] (t1) edge (rk);
\draw[->] (tk) edge (r1);
\draw[->] (tk) edge (rk);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1602.03328 | arxiv | 2016-02-11T02:06:42 |
|
Automaton Generating the Cantor Sequence. | \documentclass{amsart}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{pgf}
\usepackage{tikz}
\usetikzlibrary{arrows,automata}
\begin{document}
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,auto]
\node[initial,state] (q_0) {$a/1$};
\node[state] (q_1) [right of=q_0] {$b/0$};
\path[->] (q_0) edge [loop above] node {0,2} ()
edge node {1} (q_1)
(q_1) edge [loop above] node {0,1,2} ();
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1407.3578 | arxiv | 2014-10-27T01:10:52 |
|
The pair in the node are the identifier of the node and the color of the node. The pair outside the node are the minimum color in conflict (or if none) and the maximum color used. Node D is a relay for node C and E because c_D=1, the color of C and V. Similarly, Node C is a relay for nodes B and D. | \documentclass[11pt,letter]{article}
\usepackage[latin1,utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage[colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=red]{hyperref}
\usepackage{tikz}
\usepackage{tkz-graph}
\usetikzlibrary{plotmarks,trees,arrows}
\usetikzlibrary{calc}
\usetikzlibrary{graphs}
\usetikzlibrary{shapes.geometric}
\usepackage{pgf}
\begin{document}
\begin{tikzpicture}
\tikzstyle{VertexStyle}=[shape = circle,
fill = green!90!white,
minimum size = 18pt,
draw]
\Vertex[x=4, y=0,L={\tiny $C,1$}]{C}
\node at (4.4,0.5) {\tiny $2,2$};
\Vertex[x=8, y=0,L={\tiny $E,1$}]{E}
\node at (8.4,0.5) {\tiny $\bot,2$};
\tikzset{VertexStyle/.append style={fill = blue!80!white}}
\Vertex[x=0, y=0,L={\tiny $A,3$}]{A}
\node at (0.4,0.5) {\tiny $\bot,3$};
\tikzset{VertexStyle/.append style={fill = red!80!white}}
\Vertex[x=2, y=0,L={\tiny $B,2$}]{B}
\node at (2.4,0.5) {\tiny $\bot,3$};
\Vertex[x=6, y=0,L={\tiny $D,2$}]{D}
\node at (6.4,0.5) {\tiny $1,2$};
\Edge(A)(B)
\Edge(B)(C)
\Edge(C)(D)
\Edge(D)(E)
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.07605 | arxiv | 2017-02-27T02:05:40 |
|
Reliability and latency performance of 4G/5G radio interface solutions relative to different WAMS/SCADA SE services. | \documentclass[journal]{IEEEtran}
\usepackage{amsmath}
\usepackage[cmyk]{xcolor}
\usepackage{pgfplots}
\pgfplotsset{compat=1.5}
\pgfplotsset{legend image with text/.style={legend image code/.code={%
\node[anchor=center] at (0.3cm,0cm) {#1};}},}
\begin{document}
\begin{tikzpicture}
\begin{axis}[width=9cm,height=9cm,
every axis x label/.style={
at={(ticklabel* cs:0.86,7.0)},
anchor=west}, every axis y label/.style={
at={(ticklabel* cs:0.94,10)},
anchor=south},
xlabel={Latency},
grid=major, grid style={dashed, gray!20},
ylabel={PLR},
label style={font=\footnotesize},
xtick={1, 2, 3, 4, 5},
xticklabels={$1\,\mathrm{ms}$, $10\,\mathrm{ms}$, $100\,\mathrm{ms}$,
$1\,\mathrm{s}$, $10\,\mathrm{s}$},
ytick={ 1, 2, 3, 4, 5, 6},
yticklabels={$10^{-5}$, $10^{-4}$, $10^{-3}$, $10^{-2}$, $10^{-1}$},
tick label style={font=\footnotesize},
ymin = 0, ymax = 6,
xmin = 0, xmax = 6.5]
\draw [black, dashed, thin, fill=orange!20, fill opacity=0.2]
(axis cs:0.1,0.1) rectangle (axis cs:4.5,5.5)
node[pos=.5, text width=2.3cm, text=black,
font=\scriptsize, align=center, fill opacity=1, yshift=15ex, xshift=7ex]
{WAMS/SCADA \\ Quasi Real-Time \\ SE};
\draw[black, dashed, thin, fill=yellow!40, fill opacity=0.2] (axis cs:0.1,0.1) --
(axis cs:0.1,5.5) -- (axis cs:2.2,2.3) -- (axis cs:2.2,0.1) -- cycle
node[pos=.5, text width=2cm, text=black,
font=\scriptsize, align=center, fill opacity=1, yshift=15ex, xshift=0ex]
{WAMS \\ Real-Time SE};
\draw [black, dashed, thin, fill=yellow!20, fill opacity=0.2]
(axis cs:4.5,0.1) rectangle (axis cs:6.5,5.7)
node[pos=.5, text width=2cm, text=black,
font=\scriptsize, align=center, fill opacity=1, yshift=0ex, xshift=0ex]
{SCADA \\ Snap-Shot Real-Time SE};
\draw [black, thin, fill=green!20, fill opacity=0.2]
(axis cs:0.3,0.3) rectangle (axis cs:1.5,1.0)
node[pos=.5, text width=1cm, align=center, text=black,
font=\scriptsize, fill opacity=1]
{5G URLLC};
\draw [black, thin, fill=green!20, fill opacity=0.2]
(axis cs:1.7,2.8) rectangle (axis cs:3.1,4)
node[pos=.5, text width=1.7cm, text=black,
font=\scriptsize,align=center, fill opacity=1]
{LTE-PHY HARQ \\ no RLC ARQ};
\draw [black, thin, fill=green!20, fill opacity=0.2]
(axis cs:4.2,4.1) rectangle (axis cs:6.5,5.0)
node[pos=.5, text width=1.5cm, text=black,
font=\scriptsize,align=center, fill opacity=1]
{NB-IoT \\ 5G mMTC};
\draw [black, thin, fill=green!20, fill opacity=0.2]
(axis cs:1.1,4.1) rectangle (axis cs:2.3,5.3)
node[pos=.5, text width=1.1cm, text=black,
font=\scriptsize,align=center, fill opacity=1]
{LTE-PHY no HARQ};
\draw [black, thin, fill=green!20, fill opacity=0.2]
(axis cs:2.4,1.1) rectangle (axis cs:3.6,2.3)
node[pos=.5, text width=1.1cm, text=black,
font=\scriptsize,align=center, fill opacity=1]
{LTE-PHY HARQ \\ RLC ARQ};
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.00178 | arxiv | 2017-05-23T02:05:30 |
|
The block construction | \documentclass[10pt,reqno]{amsart}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{calc,positioning}
\begin{document}
\begin{tikzpicture}[dot/.style={circle,inner sep=0pt,fill,minimum size=5pt},
extended line/.style={shorten >=-#1,shorten <=-#1},
extended line/.default=10cm,
scale=0.8]
\clip (-5,-5) rectangle (5,5);
\node[dot,label={$X_5$}] (5) at (-2,4) {};
\node[dot,label={$X_6$}] (6) at (3,3) {};
\node[dot,label={$X_1$}] (1) at (-1,0) {};
\node[dot,label={$X_2$}] (2) at (1,0) {};
\node[dot,label={$X_3$}] (3) at (-3,-3) {};
\node[dot,label={$X_4$}] (4) at (4,-4) {};
\node[dot,label={$Y$}] (Y) at (intersection of 5--1 and 3--4) {};
\node[dot,label={$Z$}] (Z) at (intersection of 6--2 and 3--4) {};
\node[dot,label={$X'_5$}] (5p) at (intersection of Y--2 and 5--6) {};
\node[dot,label={$X'_6$}] (6p) at (intersection of Z--1 and 5--6) {};
\draw[thick, extended line] (5)--(6);
\draw[thick, extended line] (3)--(4);
\draw[thin, dotted, extended line] (5)--(Y);
\draw[thin, dotted, extended line] (6)--(Z);
\draw[thin, dotted, extended line] (Y)--(5p);
\draw[thin, dotted, extended line] (Z)--(6p);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1705.06801 | arxiv | 2017-05-22T02:01:36 |
|
The global strategy g_A | \documentclass[10pt,letterpaper,conference]{IEEEtran}
\usepackage{amsmath, amsthm, amssymb, latexsym}
\usepackage[svgnames,hyperref]{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,shapes,snakes,automata,backgrounds,fit,positioning,shapes.multipart}
\begin{document}
\begin{tikzpicture}
\node (G1) [] {$G_1$};
\node (g1) [below = .5cm of G1, align = center] {play $g_1$ \\ for $A \cdot c_1$ steps};
\node (G2) [right = 3cm of G1] {$G_2$};
\node (g2) [below = .5cm of G2, align = center] {play $g_2$ \\ for $A \cdot c_2$ steps};
\node (G3) [right = 3cm of G2] {$G_3$};
\node (g3) [below = .5cm of G3, align = center] {play $g_3$ \\ for $A \cdot c_3$ steps};
\path[->] (g1) edge [bend left = 30] node [above = 1ex] {play $h_2$} (g2);
\path[->] (g2) edge [bend left = 30] node [above = 1ex] {play $h_3$} (g3);
\path[->] (g3) edge [bend left = 15] node [below = 1ex] {play $h_1$} (g1);
\begin{pgfonlayer}{background}
\node [fill=blue!20, rectangle, rounded corners = 12pt, fit=(G1) (g1)] {};
\node [fill=blue!20, rectangle, rounded corners = 12pt, fit=(G2) (g2)] {};
\node [fill=blue!20, rectangle, rounded corners = 12pt, fit=(G3) (g3)] {};
\end{pgfonlayer}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1504.08211 | arxiv | 2015-05-01T02:09:01 |
|
The original Picaria board and a Tic-tac-toe board | \documentclass[oneside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.10,baseline=10]
\draw[fill] (0,0) circle [radius=.6];
\draw[fill] (10,0) circle [radius=.6];
\draw[fill] (20,0) circle [radius=.6];
\draw[fill] (0,10) circle [radius=.6];
\draw[fill] (10,10) circle [radius=.6];
\draw[fill] (20,10) circle [radius=.6];
\draw[fill] (0,20) circle [radius=.6];
\draw[fill] (10,20) circle [radius=.6];
\draw[fill] (20,20) circle [radius=.6];
\draw (0,0) -- (20,0);
\draw (0,10) -- (20,10);
\draw (0,20) -- (20,20);
\draw (0,0) -- (0,20);
\draw (10,0) -- (10,20);
\draw (20,0) -- (20,20);
\draw (0,0) -- (20,20);
\draw (0,20) -- (20,0);
\draw (0,10) -- (10,0);
\draw (10,20) -- (20,10);
\draw (0,10) -- (10,20);
\draw (10,0) -- (20,10);
\draw (40,6.5) -- (60,6.5);
\draw (40,13.5) -- (60,13.5);
\draw (46.5,0) -- (46.5,20);
\draw (53.5,0) -- (53.5,20);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1607.04236 | arxiv | 2016-07-19T02:07:28 |
|
Graphical model for sticky HDP-SLDS. It should be noted that _0 only affects s_1. Similarly _i and _i are only connected to x_1^n. | \documentclass[journal]{IEEEtran}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{fit,positioning}
\usetikzlibrary{shapes.geometric,positioning}
\begin{document}
\begin{tikzpicture}
\tikzstyle{main}=[circle, minimum size = 6mm, thick, draw =black!80, node distance = 6mm]
\tikzstyle{connect}=[-latex, thick]
\tikzstyle{main2}=[circle, minimum size = 6mm, thick, draw =black!80, node distance = 25mm]
\tikzstyle{connect}=[-latex, thick]
\tikzstyle{main3}=[circle, minimum size = 6mm, thick, node distance = 3mm]
\tikzstyle{connect}=[-latex, thick]
\tikzstyle{hyper}=[rectangle, minimum size = 6mm, thick, node distance = 6mm]
\tikzstyle{connect}=[-latex, thick]
\tikzstyle{hyper2}=[rectangle, minimum size = 6mm, thick, node distance = 3mm]
\tikzstyle{connect}=[-latex, thick]
\tikzstyle{box}=[rectangle, draw=black!100]
\node[main, fill = white!100] (beta) [label=center:$\beta$] { };
\node[main] (ci) [below=of beta,label=center:$c_{i}$] { };
\node[main] (pi) [below=of ci,label=center:$\pi_{i}$] { };
\node[main] (pi_zero) [below=of pi,label=center:$\pi_{0}$] { };
\node[main] (mu) [below=of pi_zero, label=center:$\mu_{i}$] { };
\node[main] (Sigma) [below=of mu, label=center:$\Sigma_{i}$] { };
\node[main] (F) [below=of Sigma, label=center:$F_{i}$] { };
\node[main] (H) [below=of F, label=center:$H_{i}$] { };
\node[main] (R) [below=of H, label=center:$R_{i}$] { };
\node[hyper] (gamma) [left=of beta,label=center:$\gamma$] { };
\node[hyper] (kappa) [left=of ci,label=center:$\kappa$] { };
\node[hyper] (alpha) [left=of pi,label=center:$\alpha$] { };
\node[hyper] (alpha_zero) [left=of pi_zero,label=center:$\alpha_{0}$] { };
\node[hyper] (b_mu) [left=of mu,label=center:$(b_{\mu})_{i}$] { };
\node[hyper2] (a_sigma) [below=of b_mu,label=center:$(a_{\Sigma})_{i}$] { };
\node[hyper2] (b_sigma) [below=of a_sigma,label=center:$(b_{\Sigma})_{i}$] {};
\node[hyper] (zeta) [left=of F,label=center:$\zeta_{i}$] { };
\node[hyper] (eta) [left=of H,label=center:$\eta_{i}$] { };
\node[hyper2] (a) [below=of eta,label=center:$a_{i}$] { };
\node[hyper2] (b) [below=of a,label=center:$b_{i}$] { };
\draw [->] (gamma) -- (beta) ;
\draw [->] (kappa) -- (ci) ;
\draw [->] (kappa) -- (pi) ;
\draw [->] (alpha) -- (ci) ;
\draw [->] (beta) -- (ci) ;
\draw [->] (ci) -- (pi) ;
\draw [->] (alpha) -- (pi) ;
\draw [->] (alpha_zero) -- (pi_zero) ;
\draw [->] (b_mu) -- (mu) ;
\draw [->] (a_sigma) -- (Sigma) ;
\draw [->] (b_sigma) -- (Sigma) ;
\draw [->] (zeta) -- (F) ;
\draw [->] (eta) -- (H) ;
\draw [->] (a) -- (R) ;
\draw [->] (b) -- (R) ;
\draw [->] (R) -- (H) ;
\node[main2] (s) [right=of pi,label=center:$s_{t}$] { };
\node[main2] (x) [right=of Sigma,label=center:$x_{t}^{n}$] { };
\node[main3] (s_next) [right=of s] { };
\node[main3] (x_next) [right=of x] { };
\node[main2,fill = black!10 ] (z) [right=of H,label=center:$z_{t}^{n}$] { };
\draw [->] (pi) -- (s) ;
\draw [->] (pi_zero) -- (s) ;
\draw [->] (mu) -- (x) ;
\draw [->] (Sigma) -- (x) ;
\draw [->] (F) -- (x) ;
\draw [->] (H) -- (z) ;
\draw [->] (R) -- (z) ;
\draw [->] (s) -- (x) ;
\draw [->] (x) -- (z) ;
\draw [->] (s) -- (s_next) ;
\draw [->] (x) -- (x_next) ;
\draw [bend left,->] (s) to (z) ;
\node[rectangle, inner sep=0mm, fit= (ci) (pi),label=south east:$\infty$] {};
\node[rectangle, inner sep=4.5mm,draw=black!100, fit= (ci) (pi),xshift=1mm] {};
\node[rectangle, inner sep=1mm, fit= (b_mu) (b) (mu) (R),label=south east:$\infty$] {};
\node[rectangle, inner sep=6mm,draw=black!100, fit= (b_mu) (b) (mu) (R),yshift=-3mm,xshift=2mm] {};
\node[rectangle, inner sep=3mm,fit= (s) (x) (z),label=south east:T] {};
\node[rectangle, inner sep=8mm,draw=black!100,dashed, fit= (s) (x) (z)] {};
\node[rectangle, inner sep=10mm,fit= (x) (z),label=south east:N] {};
\node[rectangle, inner sep=15mm,draw=black!100, fit= (x) (z)] {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1510.05477 | arxiv | 2015-10-20T02:18:33 |
|
MonteCarlo simulations for K=128, N=2^32. We compare the SAFFRON scheme with the proposed regular-SAFFRON scheme for a left degree =12. We fix the number of bins and vary the rate of the error control code used. The plots in blue indicate the SAFFRON schemelee2015saffron and the plots in red indicate the regular-SAFFRON scheme based on left-and-right-regular bipartite graphs. | \documentclass[conference,twocolumn]{IEEEtran}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{fontenc,enumerate}
\usepackage{blindtext,color}
\usepackage{tikz,pgfplots}
\usetikzlibrary{arrows,shapes,chains,matrix,positioning,scopes,patterns,fit}
\usetikzlibrary{decorations.markings,decorations.pathmorphing,backgrounds}
\usetikzlibrary{external}
\usepgflibrary{shapes}
\pgfplotsset{compat=newest}
\pgfplotsset{plot coordinates/math parser=false}
\begin{document}
\begin{tikzpicture}
\def\fsize{\normalsize}
\pgfplotsset{every y tick label/.append style={font=\footnotesize}}
\pgfplotsset{every y tick label/.append style={font=\small}}
\begin{axis}[%
width=0.85\columnwidth,
height=0.8\columnwidth,
scale only axis,
xmin=1,
xmax=12,
xmajorgrids,
xtick = {4,6,8,10,12},
ymode=log,
ymin=1e-07,
ymax=1,
yminorticks=true,
ymajorgrids,
yminorgrids,
xlabel={\fsize{Number of tests ($\times 10^5$)}},
ylabel={\fsize{Fraction of unidentified defectives}},
legend style={at={(0,0)},anchor=south west,draw=black,fill=white,legend cell align=left, font=\tiny}
]
\addplot [color=blue,dashed,mark=square,mark options={solid}]
table[row sep=crcr]{4.1877504 0.12\\
5.5836672 0.011\\
6.979584 0.0009\\
8.3755008 8e-05\\
9.7714176 1.9e-05\\
11.1673344 8e-06\\
};
\addlegendentry{q=0.03};
% pattern=on 1pt off 3pt on 3pt off 3pt
\addplot [color=blue,dashed,mark=triangle,mark options={solid}]
table[row sep=crcr]{4.1877504 0.5\\
5.5836672 0.16\\
6.979584 0.035\\
8.3755008 0.008\\
9.7714176 0.0016\\
11.1673344 0.00035\\
};
\addlegendentry{q=0.04};
\addplot [color=blue,dashed,line width=1.0pt,mark=o,mark options={solid}]
table[row sep=crcr]{4.1877504 0.8\\
5.5836672 0.5\\
6.979584 0.3\\
8.3755008 0.12\\
9.7714176 0.05\\
11.1673344 0.02\\
};
\addlegendentry{q=0.05};
\addplot [color=red,solid,line width=1.0pt,mark=square,mark options={solid}]
table[row sep=crcr]{
1.63 0.1797 \\
2.44 6.363e-3\\
3.26 2.948e-4\\
4.07 3.700e-5\\
4.89 1.16e-5\\
5.70 2.00e-6\\
};
\addlegendentry{q=0.03, regular};
\addplot [color=red,solid,line width=1.0pt,mark=triangle,mark options={solid}]
table[row sep=crcr]{
2.44 5.469e-2\\
3.26 6.168e-3\\
4.89 1.250e-4\\
6.52 8.000e-6\\
};
\addlegendentry{q=0.04, regular};
\addplot [color=red,solid,line width=1.0pt,mark=o,mark options={solid}]
table[row sep=crcr]{
2.44 1.302e-1 \\
3.26 3.348e-2\\
4.89 3.005e-3\\
6.52 4.340e-4\\
8.15 1.5625e-5 \\
};
\addlegendentry{q=0.05, regular};
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.07477 | arxiv | 2017-01-27T02:00:42 |
|
MonteCarlo simulations for K=100, N=2^16. We compare the SAFFRON scheme lee2015saffron with the proposed regular SAFFRON scheme for various left degrees \{3,5,7\}. The plots in blue indicate the SAFFRON scheme and the plots in red indicate our regular SAFFRON scheme based on left-and-right-regular bipartite graphs. | \documentclass[conference,twocolumn]{IEEEtran}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{fontenc,enumerate}
\usepackage{blindtext,color}
\usepackage{tikz,pgfplots}
\usetikzlibrary{arrows,shapes,chains,matrix,positioning,scopes,patterns,fit}
\usetikzlibrary{decorations.markings,decorations.pathmorphing,backgrounds}
\usetikzlibrary{external}
\usepgflibrary{shapes}
\pgfplotsset{compat=newest}
\pgfplotsset{plot coordinates/math parser=false}
\begin{document}
\begin{tikzpicture}
\def\fsize{\normalsize}
\pgfplotsset{every y tick label/.append style={font=\footnotesize}}
\pgfplotsset{every y tick label/.append style={font=\small}}
\begin{axis}[%
width=0.85\columnwidth,
height=0.8\columnwidth,
scale only axis,
xmin=20,
xmax=700,
xtick = {100,200,...,700},
xmajorgrids,
ymode=log,
ymin=1e-06,
ymax=1,
yminorticks=true,
ymajorgrids,
yminorgrids,
xlabel={\fsize{Number of tests per defective item ($m/K$)}},
ylabel={\fsize{Fraction of unidentified defectives}},
legend style={at={(0,0)},anchor=south west,draw=black,fill=white,legend cell align=left,font=\fsize}
]
\addplot [color=blue,dashed, mark=square,mark options={solid},line width=1pt]
table[row sep=crcr]{96 0.8\\
144 0.4\\
192 0.16\\
240 0.055\\
288 0.025\\
336 0.013\\
384 0.006\\
432 0.0035\\
480 0.0023\\
528 0.0014\\
576 0.0009\\
624 0.00055\\
672 0.0003\\
};
\addlegendentry{$\ell=3$};
\addplot [color=blue,dashed,line width=1pt,mark=triangle,mark options={solid}]
table[row sep=crcr]{96 0.94\\
144 0.68\\
192 0.32\\
240 0.11\\
288 0.036\\
336 0.015\\
384 0.005\\
432 0.0024\\
480 0.0011\\
528 0.00055\\
576 0.0004\\
624 0.00025\\
672 0.0001\\
};
\addlegendentry{$\ell=5$};
\addplot [color=blue,dashed,mark=o,mark options={solid},line width=1pt]
table[row sep=crcr]{96 0.98\\
144 0.88\\
192 0.62\\
240 0.25\\
288 0.082\\
336 0.029\\
384 0.011\\
432 0.0045\\
480 0.0017\\
528 0.00065\\
576 0.00032\\
624 0.00017\\
672 6e-05\\
};
\addlegendentry{$\ell=7$};
\addplot [color=red,solid, line width=1pt, mark=square,mark options={solid}]
table[row sep=crcr]{
36 0.99261\\
50.40 8.22e-1 \\
99.00 3.43e-1\\
150.00 6.01e-2 \\
204.00 1.61e-2\\
251.10 3.84e-3 \\
299.70 1.72e-3 \\
351.00 8.28e-4 \\
405.00 4.67e-4\\
450.24 2.08e-4\\
501.60 1.26e-4 \\
576.00 1.09e-4\\
672.00 5.50e-5\\
};
\addlegendentry{$\ell=3$, regular};
\addplot [color=red, solid, line width=1pt, mark=triangle,mark options={solid}]
table[row sep=crcr]{
39.000 0.970769\\
50.700 9.16e-1 \\
100.800 7.33e-1 \\
148.500 1.93e-1 \\
201.000 2.07e-2 \\
249.000 5.22e-3 \\
300.000 1.450e-3\\
351.000 2.51e-4\\
450.900 4.90e-5\\
500.580 1.90e-5 \\
550.800 1.20e-5\\
675.000 6.00e-6\\
};
\addlegendentry{$\ell=5$, regular};
\addplot [color=red, solid, line width=1.0pt,mark=o]
table[row sep=crcr]{
42.00 0.99 \\
58.50 0.9995 \\
78.00 0.9937 \\
108.00 0.9142 \\
151.20 0.5487 \\
198.00 8.92e-2 \\
282.00 5.0e-3 \\
360.00 5.4e-4 \\
462.00 6.42e-5 \\
499.50 9.00e-6 \\
540.00 4.00e-6 \\
594.00 1.25e-6 \\
};
\addlegendentry{$\ell=7$,regular};
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.07477 | arxiv | 2017-01-27T02:00:42 |
|
Rules for Boolean algebra with two elements | \documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[pdftex]{xcolor}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{chains,positioning,backgrounds,mindmap,shadows,trees,decorations,arrows,matrix,fit,shapes.geometric,shapes.symbols,lindenmayersystems}
\begin{document}
\begin{tikzpicture}
\tikzstyle{dark} = [draw=blue!80, fill=blue!20, minimum width=18pt, minimum height=18pt, font=\bfseries]
\tikzstyle{light} = [draw=black!80, fill=black!20, minimum width=18pt, minimum height=18pt]
\matrix[column sep=1pt, row sep=1pt] (and) {
\node[dark] {$\land$}; & \node[dark] {$0$}; & \node[dark] {$1$}; \\
\node[dark] {$0$}; & \node[light] {$0$}; & \node[light] {$0$}; \\
\node[dark] {$1$}; & \node[light] {$0$}; & \node[light] {$1$}; \\
};
\matrix[column sep=1pt, row sep=1pt, right=8pt of and] (or) {
\node[dark] {$\lor$}; & \node[dark] {$0$}; & \node[dark] {$1$}; \\
\node[dark] {$0$}; & \node[light] {$0$}; & \node[light] {$1$}; \\
\node[dark] {$1$}; & \node[light] {$1$}; & \node[light] {$1$}; \\
};
\matrix[column sep=1pt, row sep=1pt, right=8pt of or] (not) {
\node[dark] {$a$}; & \node[dark] {$0$}; & \node[dark] {$1$}; \\
\node[dark] {$\lnot a$}; & \node[light] {$1$}; & \node[light] {$0$}; \\
};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.03734 | arxiv | 2016-09-14T02:03:33 |
|
Truth tables of and | \documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[pdftex]{xcolor}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{chains,positioning,backgrounds,mindmap,shadows,trees,decorations,arrows,matrix,fit,shapes.geometric,shapes.symbols,lindenmayersystems}
\begin{document}
\begin{tikzpicture}
\tikzstyle{dark} = [draw=blue!80, fill=blue!20, minimum width=18pt, minimum height=18pt, font=\bfseries]
\tikzstyle{light} = [draw=black!80, fill=black!20, minimum width=18pt, minimum height=18pt]
\matrix[column sep=1pt, row sep=1pt] (and) {
\node[dark] {$\bullet$}; & \node[dark] {$0$}; & \node[dark] {$1$}; \\
\node[dark] {$0$}; & \node[light] {$0$}; & \node[light] {$0$}; \\
\node[dark] {$1$}; & \node[light] {$0$}; & \node[light] {$1$}; \\
};
\matrix[column sep=1pt, row sep=1pt, right=8pt of and] (or) {
\node[dark] {$\oplus$}; & \node[dark] {$0$}; & \node[dark] {$1$}; \\
\node[dark] {$0$}; & \node[light] {$0$}; & \node[light] {$1$}; \\
\node[dark] {$1$}; & \node[light] {$1$}; & \node[light] {$0$}; \\
};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.03734 | arxiv | 2016-09-14T02:03:33 |
|
Intervals I_c, I_d covering S^1 and I_k, I_k with N = 36. | \documentclass[12pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amsthm,amsfonts,amscd,amssymb,bbm,mathrsfs,enumerate,url}
\usepackage{graphicx,tikz}
\usetikzlibrary{arrows}
\usepackage[utf8x]{inputenc}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm, scale = 0.8]
\clip(-5,-5) rectangle (5,5);
\draw [line width=3pt] (0,0) circle (2.5cm);
\draw (0.694592711,3.939231012) arc (80:300:4) ;
\draw (-0.392200842,-4.482876141) arc (265:480:4.5) ;
\draw (0.278898377,3.187823034) arc (85:95:3.2) ;
\draw (0,3.6) arc (90:100:3.6) ;
\draw (-2.9,4.23) node[anchor=north west] {$I_d$};
\draw (0.86,4.1) node[anchor=north west] {$I_c$};
\draw (0.33,3.35) node[anchor=north west] {$ I_k $};
\draw (0,3.94) node[anchor=north west] {$\tilde I_k$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.02196 | arxiv | 2016-09-09T02:01:03 |
|
Localization of the factors of C_r. The indicated intervals I_, I_ correspond to thick segments. The operators _l=k^j+1 X_l,\,_l=k^j Y_l,\,_l=k+1^j X_l are localized in the arcs, from the inside, respectively. The corresponding factors in D_r are localized in the complements of these arcs, respectively. | \documentclass[12pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amsthm,amsfonts,amscd,amssymb,bbm,mathrsfs,enumerate,url}
\usepackage{graphicx,tikz}
\usetikzlibrary{arrows}
\usepackage[utf8x]{inputenc}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm, scale = 0.6]
\clip(-7,-7) rectangle (7,7);
\draw [line width=4pt] (0,0) circle (2.5cm);
\draw (1.128713155,6.401250395) arc (80:300:6.5) ;
\draw (-1.041889066,-5.908846518) arc (260:480:6) ;
\draw [line width=3pt] (0.278898377,3.187823034) arc (85:95:3.2) ;
\draw [line width=1pt] (0.278898377,3.187823034) arc (85:275:3.2) ;
\draw [line width=3pt] (0.278898377,-3.187823034) arc (275:285:3.2) ;
\draw [line width=3pt] (0,4) arc (90:100:4) ;
\draw [line width=1pt] (0,4) arc (90:270:4) ;
\draw [line width=3pt] (0,-4) arc (270:280:4) ;
\draw [line width=3pt] (-0.435778714,4.98097349) arc (95:105:5) ;
\draw [line width=1pt] (-0.435778714,4.98097349) arc (95:265:5) ;
\draw [line width=3pt] (-0.435778714,-4.98097349) arc (265:275:5) ;
\draw (1.3,6.7) node[anchor=north west] {$I_c$};
\draw (-3.6,5.4) node[anchor=north west] {$I_d$};
\draw (0.33,3.35) node[anchor=north west] {$ I_k $};
\draw (0.18,4.5) node[anchor=north west] {$\tilde I_k$};
\draw (-0.2,5.4) node[anchor=north west] {$ I_{k+1} $};
\draw (1,-2.65) node[anchor=north west] {$ I_{j+1} $};
\draw (0.88,-3.5) node[anchor=north west] {$\tilde I_j$};
\draw (0.7,-4.6) node[anchor=north west] {$ I_j $};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.02196 | arxiv | 2016-09-09T02:01:03 |
|
Intervals I_c, I_d, K_1,c, K_1,d, K_2,c, K_2,d. | \documentclass[12pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amsthm,amsfonts,amscd,amssymb,bbm,mathrsfs,enumerate,url}
\usepackage{graphicx,tikz}
\usetikzlibrary{arrows}
\usepackage[utf8x]{inputenc}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(0,-6.07) rectangle (13.77,5.03);
\draw [line width=2pt] (5.66,-0.5) circle (2.8cm);
\draw [shift={(5.66,-0.5)}] plot[domain=1.34:5.13,variable=\t]({1*3.76*cos(\t r)+0*3.76*sin(\t r)},{0*3.76*cos(\t r)+1*3.76*sin(\t r)});
\draw [shift={(5.66,-0.5)}] plot[domain=-1.86:1.96,variable=\t]({1*3.28*cos(\t r)+0*3.28*sin(\t r)},{0*3.28*cos(\t r)+1*3.28*sin(\t r)});
\draw [shift={(5.66,-0.5)},dotted] plot[domain=1.64:4.84,variable=\t]({1*5.04*cos(\t r)+0*5.04*sin(\t r)},{0*5.04*cos(\t r)+1*5.04*sin(\t r)});
\draw [shift={(5.66,-0.5)},dotted] plot[domain=-1.53:1.82,variable=\t]({1*5.28*cos(\t r)+0*5.28*sin(\t r)},{0*5.28*cos(\t r)+1*5.28*sin(\t r)});
\draw [shift={(5.66,-0.5)},dash pattern=on 4pt off 4pt] plot[domain=1.45:5.01,variable=\t]({1*4.26*cos(\t r)+0*4.26*sin(\t r)},{0*4.26*cos(\t r)+1*4.26*sin(\t r)});
\draw [shift={(5.66,-0.5)},dash pattern=on 4pt off 4pt] plot[domain=-1.38:1.51,variable=\t]({1*4.52*cos(\t r)+0*4.52*sin(\t r)},{0*4.52*cos(\t r)+1*4.52*sin(\t r)});
\draw (4.01,2.71) node[anchor=north west] {$I_d$};
\draw (6.8,3.34) node[anchor=north west] {$I_c$};
\draw (6.29,3.88) node[anchor=north west] {$K_{1,c}$};
\draw (4.8,4.4) node[anchor=north west] {$K_{1,d}$};
\draw (5.38,4.75) node[anchor=north west] {$K_{2,c}$};
\draw (3.35,5.06) node[anchor=north west] {$K_{2,d}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.02196 | arxiv | 2016-09-09T02:01:03 |
|
A triangular array of Fock-Goncharov coordinates for (4,3)(i.e. 3 affine flags in 4-space). The directed edges will serve as a fragment of a quiver. The three ``corners'' of the triangle are not included in the array, as they correspond to (a,b,c) with two entries equal to 0. | \documentclass[12pt]{amsart}
\usepackage{amsfonts,amsmath,amsthm,amssymb,tikz}
\begin{document}
\begin{tikzpicture}[scale = 1]
\coordinate (AAAC) at (-.75,3);
\coordinate (AAAB) at (.75,3);
\coordinate (AACC) at (-1.5,2);
\coordinate (AABC) at (0,2);
\coordinate (AABB) at (1.5,2);
\coordinate (ACCC) at (-2.25,1);
\coordinate (ABCC) at (-.585,1);
\coordinate (ABBC) at (.585,1);
\coordinate (ABBB) at (2.25,1);
\coordinate (BCCC) at (-1.5,0);
\coordinate (BBCC) at (0,0);
\coordinate (BBBC) at (1.5,0);
\node at (AAAC) {$\Delta_{301}$};
\node at (AAAB) {$\Delta_{310}$};
\node at (AACC) {$\Delta_{202}$};
\node at (AABC) {$\Delta_{211}$};
\node at (AABB) {$\Delta_{220}$};
\node at (ACCC) {$\Delta_{103}$};
\node at (ABCC) {$\Delta_{112}$};
\node at (ABBC) {$\Delta_{121}$};
\node at (ABBB) {$\Delta_{130}$};
\node at (BCCC) {$\Delta_{013}$};
\node at (BBCC) {$\Delta_{022}$};
\node at (BBBC) {$\Delta_{031}$};
\draw [shorten >=0.5cm,shorten <=0.5cm,->] (AAAB)--(AAAC);
\draw [shorten >=0.45cm,shorten <=0.45cm,->] (AABB)--(AABC);
\draw [shorten >=0.45cm,shorten <=0.45cm,->] (AABC)--(AACC);
\draw [shorten >=0.45cm,shorten <=0.45cm,->] (ABBB)--(ABBC);
\draw [shorten >=0.45cm,shorten <=0.45cm,->] (ABBC)--(ABCC);
\draw [shorten >=0.45cm,shorten <=0.45cm,->] (ABCC)--(ACCC);
\draw [shorten >=0.45cm,shorten <=0.45cm,->] (BBBC)--(BBCC);
\draw [shorten >=0.45cm,shorten <=0.45cm,->] (BBCC)--(BCCC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (AAAC)--(AABC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (AABC)--(AAAB);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (AACC)--(ABCC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (ABCC)--(AABC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (AABC)--(ABBC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (ABBC)--(AABB);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (ACCC)--(BCCC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (BCCC)--(ABCC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (ABCC)--(BBCC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (BBCC)--(ABBC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (ABBC)--(BBBC);
\draw [shorten >=0.35cm,shorten <=0.35cm,->] (BBBC)--(ABBB);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.00385 | arxiv | 2017-02-02T02:08:03 |
|
An arborization step indicated schematically. The tensor diagram T has two copies, T' and T'', of the same binary tree, connecting to the boundary in the same way. These trees are joined by a path of length~4. The dashed lines indicate how T' and T'' are connected to the rest of T. The arborization step removes the path of length 4 and connects T' and T'' to the rest of the diagram as indicated on the right-hand side. A similar arborization step holds with all of the colors reversed. | \documentclass[12pt]{amsart}
\usepackage{amsfonts,amsmath,amsthm,amssymb,tikz}
\begin{document}
\begin{tikzpicture}[scale = .5]
\coordinate (A) at (0,0);
\coordinate (B) at (1,-1);
\coordinate (C) at (-1,-1);
\coordinate (D) at (1,-2);
\coordinate (E) at (-1,-2);
\draw (E)--(C)--(A)--(B)--(D);
\draw (-1.5,-2.5)--(E)--(-.5,-2.5);
\draw (1.5,-2.5)--(D)--(.5,-2.5);
\node at (-1,-3) {$T'$};
\node at (1,-3) {$T''$};
\draw [dashed] (A)--(0,1.3);
\draw [dashed] (C)--(-2.2,-.5);
\draw [dashed] (B)--(2.2,-.5);
\draw [fill= black] (A) circle [radius = .12];
\draw [fill= black] (D) circle [radius = .12];
\draw [fill= black] (E) circle [radius = .12];
\draw [fill= white] (B) circle [radius = .12];
\draw [fill= white] (C) circle [radius = .12];
\node at (4,-1) {$\xrightarrow{\text{arborization}}$};
%%%%%%
\begin{scope}[xshift = 8.5cm]
\coordinate (DD) at (1,-2);
\coordinate (EE) at (-1,-2);
\coordinate (BB) at (1,-1);
\draw (-1.5,-2.5)--(EE)--(-.5,-2.5);
\draw (1.5,-2.5)--(DD)--(.5,-2.5);
\draw [dashed] (EE)--(0,1.3);
\draw (DD)--(BB);
\draw [dashed] (BB)--(-2.2,-.5);
\draw [dashed] (BB)--(2.2,-.5);
\node at (-1,-3) {$T'$};
\node at (1,-3) {$T''$};
\draw [fill= black] (DD) circle [radius = .12];
\draw [fill= black] (EE) circle [radius = .12];
\draw [fill= white] (BB) circle [radius = .12];
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.00385 | arxiv | 2017-02-02T02:08:03 |
|
A tensor diagram for (3,9). | \documentclass[12pt]{amsart}
\usepackage{amsfonts,amsmath,amsthm,amssymb,tikz}
\begin{document}
\begin{tikzpicture}[scale = 1.75]
\def \nnn{9};
\def \tic{360/9};
\draw [black] (1,0) arc [radius = 1, start angle = 0, end angle = 360];
\foreach \s in {1,...,\nnn}
{
\node at ({\tic* (-\s+4)}:1.3 cm) {$v_{\s}$};
\draw [fill= black] ({\tic * (\s - 1)}:1 cm) circle [radius = .04];
}
\coordinate (A) at (1.5*\tic:.5);
\coordinate (B) at (3*\tic:.5);
\coordinate (C) at (4.5*\tic:.5);
\coordinate (D) at (6*\tic:.5);
\coordinate (E) at (7.5*\tic:.5);
\coordinate (F) at (9*\tic:.5);
\coordinate (G) at (1.5*\tic:.8);
\coordinate (H) at (4.5*\tic:.8);
\coordinate (I) at (7.5*\tic:.8);
\draw (A)--(B)--(C)--(D)--(E)--(F)--(A);
\draw (A)--(G);
\draw (C)--(H);
\draw (E)--(I);
\draw (B)--(3*\tic:1);
\draw (D)--(6*\tic:1);
\draw (F)--(9*\tic:1);
\draw (1*\tic:1)--(G)--(2*\tic:1);
\draw (4*\tic:1)--(H)--(5*\tic:1);
\draw (7*\tic:1)--(I)--(8*\tic:1);
\draw [fill= white] (G) circle [radius = .04];
\draw [fill= white] (H) circle [radius = .04];
\draw [fill= white] (I) circle [radius = .04];
\draw [fill= white] (B) circle [radius = .04];
\draw [fill= white] (D) circle [radius = .04];
\draw [fill= white] (F) circle [radius = .04];
\draw [fill= black] (A) circle [radius = .04];
\draw [fill= black] (C) circle [radius = .04];
\draw [fill= black] (E) circle [radius = .04];
\begin{scope}
\draw [black] (1,0) arc [radius = 1, start angle = 0, end angle = 360];
\foreach \s in {1,...,\nnn}
{
\draw [fill= black] ({\tic * (\s - 1)}:1 cm) circle [radius = .04];
}
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.00385 | arxiv | 2017-02-02T02:08:03 |
|
The first diagram shows how to compute ^* ^* ^*(x) by plugging a tensor diagram x C(3,6) via the connections to the boundary as indidcated. The second diagram does the same for ^* (^2)^* ^*(x). | \documentclass[12pt]{amsart}
\usepackage{amsfonts,amsmath,amsthm,amssymb,tikz}
\begin{document}
\begin{tikzpicture}[scale = 2.5]
\draw [black] (1,0) arc [radius = 1, start angle = 0, end angle = 360];
\foreach \s in {1,...,6}
{
\node at ({360/6 * (-\s+6)-180}:1.3 cm) {$\s$};
\draw [fill= black] ({360/6 * (\s - 1)}:1 cm) circle [radius = .04];
}
\draw (0:1cm)--(30:.6cm);
\draw (60:1cm)--(30:.6cm);
\draw (120:1cm)--(150:.6cm);
\draw (180:1cm)--(150:.6cm);
\draw (240:1cm)--(270:.6cm);
\draw (300:1cm)--(270:.6cm);
\draw (65:1cm)--(90:.6cm);
\draw (115:1cm)--(90:.6cm);
\draw (185:1cm)--(210:.6cm);
\draw (235:1cm)--(210:.6cm);
\draw (305:1cm)--(330:.6cm);
\draw (355:1cm)--(330:.6cm);
\draw (30:.6cm)--(30:.4cm);
\node at (45:.5cm) {\tiny $F_{22}$};
\draw (150:.6cm)--(150:.4cm);
\node at (165:.5cm) {\tiny $F_{62}$};
\draw (270:.6cm)--(270:.4cm);
\node at (285:.5cm) {\tiny $F_{42}$};
\draw (90:.6cm)--(90:.4cm);
\node at (105:.5cm) {\tiny $F_{11}$};
\draw (210:.6cm)--(210:.4cm);
\node at (225:.5cm) {\tiny $F_{51}$};
\draw (330:.6cm)--(330:.4cm);
\node at (345:.5cm) {\tiny $F_{31}$};
\draw (120:1cm)--(140:.5cm);
\node at (140:.45cm) {\tiny $F_{61}$};
\draw (240:1cm)--(260:.5cm);
\node at (260:.45cm) {\tiny $F_{41}$};
\draw (0:1cm)--(20:.5cm);
\node at (20:.45cm) {\tiny $F_{21}$};
\node at (75:.45cm) {\tiny $F_{12}$};
\draw (65:1cm)--(75:.55cm);
\node at (-45:.45cm) {\tiny $F_{32}$};
\draw (-55:1cm)--(-45:.5cm);
\node at (195:.45cm) {\tiny $F_{52}$};
\draw (185:1cm)--(195:.5cm);
\draw [fill= white] (115:1 cm) circle [radius = .04];
\draw [fill= white] (65:1 cm) circle [radius = .04];
\draw [fill= white] (355:1 cm) circle [radius = .04];
\draw [fill= white] (-55:1 cm) circle [radius = .04];
\draw [fill= white] (185:1cm) circle [radius = .04];
\draw [fill= white] (235:1cm) circle [radius = .04];
\draw [fill= black] (90:.6 cm) circle [radius = .04];
\draw [fill= black] (210:.6 cm) circle [radius = .04];
\draw [fill= black] (-30:.6 cm) circle [radius = .04];
\draw [fill= white] (30:.6 cm) circle [radius = .04];
\draw [fill= white] (150:.6 cm) circle [radius = .04];
\draw [fill= white] (-90:.6 cm) circle [radius = .04];
\begin{scope}[xshift = 3.5cm]
\draw [black] (1,0) arc [radius = 1, start angle = 0, end angle = 360];
\foreach \s in {1,...,6}
{
\node at ({360/6 * (-\s+6)-180}:1.3 cm) {$\s$};
\draw [fill= black] ({360/6 * (\s - 1)}:1 cm) circle [radius = .04];
}
\draw (0:1cm)--(30:.6cm);
\draw (60:1cm)--(30:.6cm);
\draw (120:1cm)--(150:.6cm);
\draw (180:1cm)--(150:.6cm);
\draw (240:1cm)--(270:.6cm);
\draw (300:1cm)--(270:.6cm);
\draw (65:1cm)--(90:.6cm);
\draw (115:1cm)--(90:.6cm);
\draw (185:1cm)--(210:.6cm);
\draw (235:1cm)--(210:.6cm);
\draw (305:1cm)--(330:.6cm);
\draw (355:1cm)--(330:.6cm);
\draw (30:.6cm)--(30:.4cm);
\node at (17:.43cm) {\tiny $F_{12}$};
\draw (150:.6cm)--(150:.4cm);
\node at (137:.5cm) {\tiny $F_{52}$};
\draw (270:.6cm)--(270:.4cm);
\node at (257:.5cm) {\tiny $F_{32}$};
\draw (90:.6cm)--(90:.4cm);
\node at (80:.35cm) {\tiny $F_{61}$};
\draw (210:.6cm)--(210:.4cm);
\node at (200:.35cm) {\tiny $F_{41}$};
\draw (330:.6cm)--(330:.4cm);
\node at (320:.45cm) {\tiny $F_{21}$};
\draw (60:1cm)--(45:.5cm);
\node at (45:.45cm) {\tiny $F_{11}$};
\draw (180:1cm)--(165:.5cm);
\node at (165:.5cm) {\tiny $F_{51}$};
\draw (300:1cm)--(285:.5cm);
\node at (285:.45cm) {\tiny $F_{31}$};
\node at (110:.43cm) {\tiny $F_{62}$};
\draw (115:1cm)--(105:.55cm);
\node at (350:.43cm) {\tiny $F_{22}$};
\draw (-5:1cm)--(345:.53cm);
\node at (230:.45cm) {\tiny $F_{42}$};
\draw (235:1cm)--(220:.5cm);
\draw [fill= white] (115:1 cm) circle [radius = .04];
\draw [fill= white] (65:1 cm) circle [radius = .04];
\draw [fill= white] (355:1 cm) circle [radius = .04];
\draw [fill= white] (-55:1 cm) circle [radius = .04];
\draw [fill= white] (185:1cm) circle [radius = .04];
\draw [fill= white] (235:1cm) circle [radius = .04];
\draw [fill= black] (90:.6 cm) circle [radius = .04];
\draw [fill= black] (210:.6 cm) circle [radius = .04];
\draw [fill= black] (-30:.6 cm) circle [radius = .04];
\draw [fill= white] (30:.6 cm) circle [radius = .04];
\draw [fill= white] (150:.6 cm) circle [radius = .04];
\draw [fill= white] (-90:.6 cm) circle [radius = .04];
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.00385 | arxiv | 2017-02-02T02:08:03 |
|
A Fock-Goncharov seed (T) inside C((3,6), i.e. for 6 affine flags in 3-space. T is the triangulation of the hexagon indicated in dashed lines. The extended quiver _3(T) is indicated by the directed edges drawn inside the hexagon. The 12 frozen variables lie on the boundary of the hexagon. There are 10 cluster variables. %listed at the left of the figure. | \documentclass[12pt]{amsart}
\usepackage{amsfonts,amsmath,amsthm,amssymb,tikz}
\begin{document}
\begin{tikzpicture}
\coordinate (A) at (0,3);
\node at (0,3.5) {$1$};
\coordinate (D) at (0,-3);
\node at (0,-3.5) {$4$};
\coordinate (B) at (3.5,2);
\node at (3.7,2.5) {$2$};
\coordinate (F) at (-3.5,2);
\node at (-3.7,2.5) {$6$};
\coordinate (C) at (3,0);
\node at (3.5,0) {$3$};
\coordinate (E) at (-3,0);
\node at (-3.5,-.2) {$5$};
\draw [dashed] (A)--(B)--(C)--(D)--(E)--(F)--(A);
\draw [dashed] (A)--(C)--(E)--(A);
\coordinate (AAB) at (.66*0+.33*3.5,.66*3+.33*2);
\node at (AAB) {$\boxed{}$};
\coordinate (ABB) at (.33*0+.66*3.5,.33*3+.66*2);
\node at (ABB) {$\boxed{}$};
\coordinate (BBC) at (.666*3.5+.333*3,.66*2+.33*0);
\node at (BBC) {$\boxed{}$};
\coordinate (BCC) at (.333*3.5+.666*3,.33*2+.66*0);
\node at (BCC) {$\boxed{}$};
\coordinate (CCD) at (.666*3+.333*0,.66*0-.333*3);
\node at (CCD) {$\boxed{}$};
\coordinate (CDD) at (.333*3+.666*0,.33*0-.666*3);
\node at (CDD) {$\boxed{}$};
\coordinate (DDE) at (.666*0-.333*3,-.66*3+.333*0);
\node at (DDE) {$\boxed{}$};
\coordinate (DEE) at (.333*0-.666*3,-.33*3+.666*0);
\node at (DEE) {$\boxed{}$};
\coordinate (EEF) at (-.66*3-.33*3.5,.666*0+.333*2);
\node at (EEF) {$\boxed{}$};
\coordinate (EFF) at (-.333*3-.666*3.5,.333*0+.666*2);
\node at (EFF) {$\boxed{}$};
\coordinate (AFF) at (-.666*3.5+.333*0,.666*2+.333*3);
\node at (AFF) {$\boxed{}$};
\coordinate (AAF) at (-.333*3.5,.333*2+.666*3);
\node at (AAF) {$\boxed{}$};
\coordinate (AAC) at (.66*0+.33*3,.66*3+.33*0);
\node at (AAC) {$\bullet$};
\coordinate (ACC) at (.33*0+.66*3,.33*3+.66*0);
\node at (ACC) {$\bullet$};
\coordinate (AAE) at (.66*0-.33*3,.66*3+.33*0);
\node at (AAE) {$\bullet$};
\coordinate (AEE) at (.33*0-.66*3,.33*3+.66*0);
\node at (AEE) {$\bullet$};
\coordinate (CCE) at (1,0);
\node at (CCE) {$\bullet$};
\coordinate (CEE) at (-1,0);
\node at (CEE) {$\bullet$};
\coordinate (ACE) at (0,1);
\node at (ACE) {$\bullet$};
\coordinate (CDE) at (0,-1);
\node at (CDE) {$\bullet$};
\coordinate (ABC) at (2,1.66);
\node at (ABC) {$\bullet$};
\coordinate (AEF) at (-2,1.66);
\node at (AEF) {$\bullet$};
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AAC) -- (AAE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AAE) -- (ACE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (ACE) -- (AAC);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (ACC) -- (ACE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (ACE) -- (CCE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (CCE) -- (ACC);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (ACE) -- (AEE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AEE) -- (CEE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (CEE) -- (ACE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AAB) -- (AAC);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AAC) -- (ABC);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (ABC) -- (AAB);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (ABB) -- (ABC);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (ABC) -- (BBC);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (BBC) -- (ABB);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (ABC) -- (ACC);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (ACC) -- (BCC);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (BCC) -- (ABC);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AAE) -- (AAF);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AAF) -- (AEF);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AEF) -- (AAE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AEE) -- (AEF);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AEF) -- (EEF);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (EEF) -- (AEE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AEF) -- (AFF);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (AFF) -- (EFF);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (EFF) -- (AEF);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (CDE) -- (DDE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (DDE) -- (CDD);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (CDD) -- (CDE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (CDE) -- (CEE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (CEE) -- (DEE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (DEE) -- (CDE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (CDE) -- (CCD);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (CCD) -- (CCE);
\draw [shorten >=0.2cm,shorten <=.2cm,->] (CCE) -- (CDE);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.00385 | arxiv | 2017-02-02T02:08:03 |
|
Graphical depiction of the proof of Theorem~L:2nd. | \documentclass[11pt]{article}
\usepackage{amsthm,amsfonts,amssymb,amsmath,latexsym, amscd, mathabx,oldgerm,float}
\usepackage{color}
\usepackage[dvipsnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{patterns,calc}
\usepackage[colorlinks]{hyperref}
\begin{document}
\begin{tikzpicture}
\newcommand{\crad}{0.7ex} % circle radius
\newcommand{\lht}{-.4} % label height
\newcommand{\xone}{-1.2}
\newcommand{\yone}{0.6}
\newcommand{\xtwo}{1.8}
\newcommand{\ytwo}{4.4}
% gridlines
\draw [very thick, <->] (-2.5,0) -- (5.5,0);
\draw [very thick, ->] (0,0) -- (0,2.5);
% curves
\draw[very thick, ProcessBlue] (\xtwo,0) arc (0:180:\xtwo/2-\xone/2);
\draw[very thick, Red] (\ytwo,0) arc (0:180:\ytwo/2-\yone/2);
% points
\draw[thick, fill=Cyan] (\xone,0) circle (\crad);
\draw[thick, fill=Red] (\yone,0) circle (\crad);
\draw[thick, fill=Cyan] (\xtwo,0) circle (\crad);
\draw[thick, fill=Red] (\ytwo,0) circle (\crad);
% labels
\node at (\xone,\lht) {$x_1^+$};
\node at (\yone,\lht) {$x_1^-$};
\node at (\xtwo,\lht) {$x_2^+$};
\node at (\ytwo,\lht) {$x_2^-$};
\node at (-.7,1.4) {$\gamma^+$};
\node at (4.4,1.4) {$\gamma^-$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.02189 | arxiv | 2016-12-07T02:08:30 |
|
Optimized green bands for the Brunswick scenario. Time and state of the signals is shown on the vertical axis. Signals are labelled with intersection numbers and signal groups, e.g., signal 3A and 3B must not be green at the same time. Distances on the horizontal axis are chosen with respect to transit time, the slope of the parallelograms is chosen with respect to free speed. Note that the purple commodity is travelling from right to left and the cyclic overflow is visualized by a negative slope. | \documentclass[1p,number,sort&compress]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amssymb, amsthm}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale=0.02,
vertex/.style={circle,draw,thick,inner sep=0pt,minimum size=4mm,color=black,fill=white},
source/.style={circle,draw,thick,inner sep=0pt,minimum size=6mm},
sink/.style={rectangle,draw,thick,inner sep=0pt,minimum size=6mm,color=red,fill=white},
vor/.style={-stealth',shorten >=1pt,semithick},
comm1/.style={-stealth',shorten >=1pt,line width=3pt,color=orange},
comm2/.style={-stealth',shorten >=1pt,line width=3pt,color=blue},
comm3/.style={-stealth',shorten >=1pt,line width=3pt,color=purple}
]
\small
\node at (-20,0) {};
%axis
\begin{scope}[xshift=-15cm]
\draw (0,0) -- (0,84);
\draw[gray,opacity=0.5] (0,0) -- (480,0) -- (480,84) -- (0,84);
\foreach \x in {6,12,18,24,30,36,42,48,54,60,66,72,78}
\draw[gray,opacity=0.25] (0,\x) -- (480,\x);
\draw (-2,0) -- (2,0);
\draw (-2,84) -- (2,84);
\node[left] at (-2,0) {0};
\node[left] at (-2,84) {84};
\end{scope}
\begin{scope}[xshift=-15cm,yshift=110cm]
\draw (0,0) -- (0,84);
\draw[gray,opacity=0.5] (0,0) -- (480,0) -- (480,84) -- (0,84);
\foreach \x in {6,12,18,24,30,36,42,48,54,60,66,72,78}
\draw[gray,opacity=0.25] (0,\x) -- (480,\x);
\draw (-2,0) -- (2,0);
\draw (-2,84) -- (2,84);
\node[left] at (-2,0) {0};
\node[left] at (-2,84) {84};
\end{scope}
\begin{scope}[xshift=-15cm,yshift=220cm]
\draw (0,0) -- (0,84);
\draw[gray,opacity=0.5] (0,0) -- (480,0) -- (480,84) -- (0,84);
\foreach \x in {6,12,18,24,30,36,42,48,54,60,66,72,78}
\draw[gray,opacity=0.25] (0,\x) -- (480,\x);
\draw (-2,0) -- (2,0);
\draw (-2,84) -- (2,84);
\node[left] at (-2,0) {0};
\node[left] at (-2,84) {84};
\end{scope}
%Ampel1
\begin{scope}[xshift=0,yshift=0]
\draw[color=green,fill=green] (0,0) rectangle (5,24);
\draw[color=red,fill=red] (0,24) rectangle (5,84);
\coordinate (v1a3) at (5,0);
\coordinate (v1a4) at (5,24);
\node at (2,-10) {1};
\end{scope}
%Ampel2
\begin{scope}[xshift=80cm,yshift=0]
\draw[color=green,fill=green] (0,8) rectangle (5,74);
\draw[color=red,fill=red] (0,74) rectangle (5,84);
\draw[color=red,fill=red] (0,0) rectangle (5,8);
\coordinate (v2e3) at (0,8);
\coordinate (v2e4) at (0,32);
\coordinate (v2a3) at (5,8);
\coordinate (v2a4) at (5,32);
\node at (2,-10) {2};
\end{scope}
%Ampel3a
\begin{scope}[xshift=230cm,yshift=0]
\draw[color=red,fill=red] (0,0) rectangle (5,23);
\draw[color=green,fill=green] (0,23) rectangle (5,47);
\draw[color=red,fill=red] (0,47) rectangle (5,84);
\coordinate (v3e1) at (0,23);
\coordinate (v3e2) at (0,47);
\coordinate (v3a1) at (5,23);
\coordinate (v3a2) at (5,47);
\node at (3,-10) {3A};
\end{scope}
%Ampel6
\begin{scope}[xshift=330cm,yshift=0]
\draw[color=red,fill=red] (0,13) rectangle (5,33);
\draw[color=green,fill=green] (0,33) rectangle (5,63);
\draw[color=red,fill=red] (0,63) rectangle (5,84);
\draw[color=green,fill=green] (0,0) rectangle (5,12);
\draw[color=red,fill=red] (0,12) rectangle (5,13);
\coordinate (v4e1) at (0,33);
\coordinate (v4e2) at (0,57);
\coordinate (v4a1) at (5,33);
\coordinate (v4a2) at (5,57);
\node at (2,-10) {6};
\end{scope}
%Ampel7
\begin{scope}[xshift=380cm,yshift=0]
\draw[color=red,fill=red] (0,17) rectangle (5,38);
\draw[color=green,fill=green] (0,38) rectangle (5,68);
\draw[color=red,fill=red] (0,68) rectangle (5,84);
\draw[color=red,fill=red] (0,0) rectangle (5,5);
\draw[color=green,fill=green] (0,5) rectangle (5,17);
\coordinate (v5e1) at (0,38);
\coordinate (v5e2) at (0,62);
\coordinate (v5a1) at (5,38);
\coordinate (v5a2) at (5,62);
\node at (2,-10) {7};
\end{scope}
%Ampel4
\begin{scope}[xshift=440cm,yshift=0]
\draw[color=green,fill=green] (0,0) rectangle (5,23);
\draw[color=red,fill=red] (0,23) rectangle (5,44);
\draw[color=green,fill=green] (0,44) rectangle (5,84);
\coordinate (v6e1) at (0,44);
\coordinate (v6e2) at (0,68);
\node at (2,-10) {4A};
\end{scope}
%Ampel3b
\begin{scope}[xshift=230cm,yshift=110cm]
\draw[color=green,fill=green] (0,0) rectangle (5,21);
\draw[color=red,fill=red] (0,21) rectangle (5,49);
\draw[color=green,fill=green] (0,49) rectangle (5,84);
\coordinate (v3e3) at (0,47);
\coordinate (v3e4) at (0,84);
\coordinate (v3e5) at (0,0);
\coordinate (v3e6) at (0,2);
\coordinate (v3a3) at (5,49);
\coordinate (v3a4) at (5,74);
\coordinate (v3a5) at (5,84);
\coordinate (v3a6) at (5,0);
\coordinate (v3a7) at (5,2);
\node at (2,-10) {3B};
\end{scope}
%Ampel6 lvl2
\begin{scope}[xshift=330cm,yshift=110cm]
\draw[color=red,fill=red] (0,13) rectangle (5,33);
\draw[color=green,fill=green] (0,33) rectangle (5,63);
\draw[color=red,fill=red] (0,63) rectangle (5,84);
\draw[color=green,fill=green] (0,0) rectangle (5,12);
\draw[color=red,fill=red] (0,12) rectangle (5,13);
\coordinate (v4e3) at (0,57);
\coordinate (v4e4) at (0,84);
\coordinate (v4e5) at (0,0);
\coordinate (v4e6) at (0,10);
\coordinate (v4e7) at (0,12);
\coordinate (v4a3) at (5,59);
\coordinate (v4a4) at (5,63);
\coordinate (v4a5) at (5,0);
\coordinate (v4a8) at (5,12);
\node at (2,-10) {6};
\end{scope}
%Ampel7 lvl2
\begin{scope}[xshift=380cm,yshift=110cm]
\draw[color=red,fill=red] (0,17) rectangle (5,38);
\draw[color=green,fill=green] (0,38) rectangle (5,68);
\draw[color=red,fill=red] (0,68) rectangle (5,84);
\draw[color=red,fill=red] (0,0) rectangle (5,5);
\draw[color=green,fill=green] (0,5) rectangle (5,17);
\coordinate (v5e3) at (0,64);
\coordinate (v5e4) at (0,68);
\coordinate (v5e5) at (0,5);
\coordinate (v5e8) at (0,17);
\coordinate (v5a3) at (5,64);
\coordinate (v5a4) at (5,68);
\coordinate (v5a5) at (5,5);
\coordinate (v5a10) at (5,17);
\node at (2,-10) {7};
\end{scope}
%Ampel4 lvl2
\begin{scope}[xshift=440cm,yshift=110cm]
\draw[color=green,fill=green] (0,0) rectangle (5,23);
\draw[color=red,fill=red] (0,23) rectangle (5,44);
\draw[color=green,fill=green] (0,44) rectangle (5,84);
\coordinate (v6e3) at (0,70);
\coordinate (v6e4) at (0,74);
\coordinate (v6e5) at (0,11);
\coordinate (v6e10) at (0,23);
\node at (2,-10) {4A};
\end{scope}
%Ampel4b
\begin{scope}[xshift=440cm,yshift=220cm]
\draw[color=green,fill=green] (0,0) rectangle (5,7);
\draw[color=green,fill=green] (0,44) rectangle (5,84);
\draw[color=red,fill=red] (0,7) rectangle (5,44);
\coordinate (v6a1) at (0,44);
\coordinate (v6a2) at (0,49);
\coordinate (v6a3) at (0,84);
\coordinate (v6a4) at (0,0);
\coordinate (v6a5) at (0,7);
\node at (2,-10) {4B};
\end{scope}
%Ampel5a
\begin{scope}[xshift=120cm,yshift=110cm]
\draw[color=red,fill=red] (0,0) rectangle (5,36);
\draw[color=green,fill=green] (0,36) rectangle (5,75);
\draw[color=red,fill=red] (0,75) rectangle (5,84);
\coordinate (v8a1) at (5,36);
\coordinate (v8a2) at (5,73);
\coordinate (v8a3) at (5,75);
\node at (2,-10) {5A};
\end{scope}
%Ampel5b
\begin{scope}[xshift=120cm,yshift=220cm]
\draw[color=green,fill=green] (0,0) rectangle (5,33);
\draw[color=red,fill=red] (0,33) rectangle (5,78);
\draw[color=green,fill=green] (0,78) rectangle (5,84);
\coordinate (v8e1) at (5,79);
\coordinate (v8e2) at (5,84);
\coordinate (v8e3) at (5,0);
\coordinate (v8e4) at (5,34);
\coordinate (v8e5) at (5,41);
\node at (2,-10) {5B};
\end{scope}
%comm1
\fill[fill=orange,opacity=0.5] (v1a3) -- (v2e3) -- (v2e4) -- (v1a4);
\fill[fill=orange,opacity=0.5] (v2a3) -- (v3e1) -- (v3e2) -- (v2a4);
\fill[fill=orange,opacity=0.5] (v3a1) -- (v4e1) -- (v4e2) -- (v3a2);
\fill[fill=orange,opacity=0.5] (v4a1) -- (v5e1) -- (v5e2) -- (v4a2);
\fill[fill=orange,opacity=0.5] (v5a1) -- (v6e1) -- (v6e2) -- (v5a2);
%comm2
\fill[fill=blue,opacity=0.5] (v8a1) -- (v3e3) -- (v3e4) -- (v8a2);
\fill[fill=blue,opacity=0.5] (v8a2) -- (v3e5) -- (v3e6) -- (v8a3);
\fill[fill=blue,opacity=0.5] (v3a3) -- (v4e3) -- (v4e4) -- (v3a4);
\fill[fill=blue,opacity=0.5] (v3a4) -- (v4e5) -- (v4e6) -- (v3a5);
\fill[fill=blue,opacity=0.5] (v3a6) -- (v4e6) -- (v4e7) -- (v3a7);
\fill[fill=blue,opacity=0.5] (v4a3) -- (v5e3) -- (v5e4) -- (v4a4);
\fill[fill=blue,opacity=0.5] (v5a3) -- (v6e3) -- (v6e4) -- (v5a4);
\fill[fill=blue,opacity=0.5] (v4a5) -- (v5e5) -- (v5e8) -- (v4a8);
\fill[fill=blue,opacity=0.5] (v5a5) -- (v6e5) -- (v6e10) -- (v5a10);
%comm3
\fill[fill=purple,opacity=0.5] (v6a2) -- (v8e3) -- (v8e4) -- (v6a3);
\fill[fill=purple,opacity=0.5] (v6a1) -- (v8e1) -- (v8e2) -- (v6a2);
\fill[fill=purple,opacity=0.5] (v6a4) -- (v8e4) -- (v8e5) -- (v6a5);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1509.08709 | arxiv | 2015-09-30T02:12:01 |
|
Linear Chain MDP with 50 states. State 0 is the start state and state 49 is the goal state. | \documentclass{article}
\usepackage{tikz}
\usetikzlibrary{automata,chains,arrows}
\usetikzlibrary{positioning}
\tikzset{
%Define standard arrow tip
>=stealth',
%Define style for boxes
punkt/.style={
rectangle,
rounded corners,
draw=black, very thick,
text width=6.5em,
minimum height=2em,
text centered},
% Define arrow style
pil/.style={
->,
thick,
shorten <=2pt,
shorten >=2pt,}
}
\usepackage{color}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{colortbl}
\begin{document}
\begin{tikzpicture}[start chain=double]
\node[state, on chain] (1) {0};
\node[state, on chain] (2) {2};
\node[on chain] (2-g) {$\dots$};
\node[state, on chain] (48) {48};
\node[state, on chain] (49) {49};
\draw[latex'-latex',double]
(1) edge node {} (2)
(2) edge node {} (2-g)
(2-g) edge node {} (48)
(48) edge node{} (49);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1507.00436 | arxiv | 2015-07-16T02:03:00 |
|
The four-point interaction from the cubic interaction. As before solid lines represent the field while dashed lines are . | \documentclass[11pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz,xcolor}
\usepackage{pgf}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{arrows,shapes}
\begin{document}
\begin{tikzpicture}
\draw[thick, dashed] (0,0) -- (-.5,0.5);
\draw[thick, dashed] (0,0) -- (-.5,-0.5);
\draw[thick, dashed] (0,0) -- (1,0);
\draw[thick, dashed] (1,0) -- (1.5,0.5);
\draw[thick, dashed] (1,0) -- (1.5,-0.5);
\draw[thick] (1.5,0.5) -- (2,1);
\draw[thick] (1.5,-0.5) -- (2,-1);
\draw[thick] (-0.5,0.5) -- (-1,1);
\draw[thick] (-0.5,-0.5) -- (-1,-1);
\draw (-1.2,1.2) node{$k_1$};
\draw (-1.2,-1.2) node{$k_2$};
\draw (2.2,1.2) node{$k_3$};
\draw (2.2,-1.2) node{$k_4$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1512.05365 | arxiv | 2016-04-18T02:12:52 |
|
The four-point interaction vertex. As before solid lines represent the field while dashed lines are . | \documentclass[11pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz,xcolor}
\usepackage{pgf}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{arrows,shapes}
\begin{document}
\begin{tikzpicture}
\draw[thick, dashed] (0,0) -- (-.5,0.5);
\draw[thick, dashed] (0,0) -- (-.5,-0.5);
\draw[thick, dashed] (0,0) -- (.5,0.5);
\draw[thick, dashed] (0,0) -- (.5,-0.5);
\draw[thick] (0.5,0.5) -- (1,1);
\draw[thick] (0.5,-0.5) -- (1,-1);
\draw[thick] (-0.5,0.5) -- (-1,1);
\draw[thick] (-0.5,-0.5) -- (-1,-1);
\draw (-1.2,1.2) node{$k_1$};
\draw (-1.2,-1.2) node{$k_2$};
\draw (1.2,1.2) node{$k_3$};
\draw (1.2,-1.2) node{$k_4$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1512.05365 | arxiv | 2016-04-18T02:12:52 |
|
The vertex showing the correction to the power spectrum due to a long mode. The long mode, in grey, is outside the horizon and classical. | \documentclass[11pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz,xcolor}
\usepackage{pgf}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{arrows,shapes}
\begin{document}
\begin{tikzpicture}[scale=1]
\draw [thick] (0,0) -- (1,0);
\draw [thick, dashed] (1,0) -- (3,0);
\draw [thick] (3,0) -- (4,0);
\draw [thick, dashed, gray] (2.05,0) -- (2.875,0.5);
\draw [thick,gray] (2.875,0.5) -- (3.745,1);
\draw [gray] (4.1,1.2) node{$k_L$};
\draw (-0.3,0) node{$k_2$};
\draw (4.3,0) node{$k_3$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1512.05365 | arxiv | 2016-04-18T02:12:52 |
|
A plane covering problem using "bush-shape" sets | \documentclass[12pt]{amsart}
\usepackage{amsmath}
\usepackage{tikz}
\usepgflibrary{arrows}
\begin{document}
\begin{tikzpicture}[yscale=0.4,xscale=0.6]
\node (A) at (12,0) {};
\coordinate (B) at (13,0);
\draw[->] (0,0) -- (23,0);
\draw (0,8) -- (22,8);
\draw (0,16) -- (22,16);
\draw[->] (0,0) -- (0,19);
\node at (23,-0.5) {$a$};
\node at (23,8) {$b=1$};
\node at (23,16) {$b=2$};
\node at (-0.8,19) {$b$};
\draw (10,0) to (1.5,17);
\draw (11,0) to (2.5,17);
\fill[gray] (10,0) -- (11,0) -- (2.5,17) -- (1.5,17);
\draw (10,0) to (5,17);
\draw (11,0) to (6,17);
\fill[gray] (10,0) -- (11,0) -- (6,17) -- (5,17);
\draw (10,0) to (9,17);
\draw (11,0) to (10,17);
\fill[gray] (10,0) -- (11,0) -- (10,17) -- (9,17);
\draw (10,0) to (14,17);
\draw (11,0) to (15,17);
\fill[gray] (10,0) -- (11,0) -- (15,17) -- (14,17);
\draw (10,0) to (17,17);
\draw (11,0) to (18,17);
\fill[gray] (10,0) -- (11,0) -- (18,17) -- (17,17);
\draw [line width=10pt] (10,0)--(11,0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1512.05607 | arxiv | 2015-12-18T02:11:39 |
|
Tetrahedron subdivided by barycenters of its 2-faces | \documentclass[a4paper]{amsart}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{positioning}
\newcommand{\ee}{\mathbf{e}}
\begin{document}
\begin{tikzpicture}[z=.3,y=24]
\coordinate [label=left:$\ee_i$] (i) at (-4,-2.828,-2.828) ;
\coordinate [label=right:$\ee_j$] (j) at (4,-2.828,-1.414) ;
\coordinate [label=left:$\ee_k$] (k) at (0,4,2.828) ;
\coordinate [label=below:$\ee_l$] (l) at (-1.414,-4,2.828) ;
\coordinate [label={[xshift=2pt,yshift=2pt]below right:$\ee_{ijl}$}] (ijl) at (-0.471, -3.219, -0.471) ;
\coordinate [label=right:$\ee_{ijk}$] (ijk) at (0, -0.552, -0.471);
\coordinate [label=left:$\ee_{ikl}$] (ikl) at (-1.805, -0.943, 0.943);
\coordinate [label=right:$\ee_{jkl}$] (jkl) at (0.862, -0.943, 1.414);
\draw [black!40](ijk)-- (jkl)--(ikl)--(ijl)--(jkl) (ijl)--(ijk)--(ikl);
\draw (j)--(jkl)--(k) (jkl)--(l)--(ikl)--(k)--(jkl) (i)--(ikl);
\draw [dashed](k)--(ijk)--(i)--(ijl)--(l) (ijl)--(j);
\draw [loosely dashed](j)--(ijk);
\draw [thick,dashed](i)--(j);
\draw [thick] (k)--(l)--(j)--(k)--(i)--(l) ;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.6149 | arxiv | 2014-12-16T02:18:43 |
|
K_6 mnemonic for 16-vertex R P^4 | \documentclass[a4paper]{amsart}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}[auto]
\node (A) at (120:4){A};
\node (B) at (60:4) {B} edge node[above,sloped]{$0123$}(A);
\node (C) at (360:4){C} edge node[below right,sloped]{$0456$}(A)
edge node[above,sloped]{$0789$}(B);
\node (D) at (300:4){D} edge node[pos=.6, above,sloped]{$1489$}(A)
edge node[above left,sloped]{$1567$}(B)
edge node[below,sloped]{$2347$}(C);
\node (E) at (240:4){E} edge node[below right,sloped]{$2579$}(A)
edge node[pos=.4, above ,sloped]{$2468$}(B)
edge node[above left,sloped]{$1358$}(C)
edge node[below,sloped]{$0369$}(D);
\node (F) at (180:4){F} edge node[above,sloped]{$3678$}(A)
edge node[below right,sloped]{$3459$}(B)
edge node[pos=.6, above ,sloped]{$1269$}(C)
edge node[above left,sloped]{$0258$}(D)
edge node[below,sloped]{$0147$}(E);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.6149 | arxiv | 2014-12-16T02:18:43 |
|
Neighbourhood of _ie_i in a 3-ball before quotienting. | \documentclass[a4paper]{amsart}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{positioning}
\newcommand{\ee}{\mathbf{e}}
\begin{document}
\begin{tikzpicture}[scale=1.2,vx/.style={circle,inner sep=0pt,minimum size=1mm,draw}]
\node (0) at (0,0.2,1) [vx] [fill,label=below left:\small $\mathbf{0}$]{};
\node (1) at (2,0,1) [vx] [fill,label=right:\small $\ \ee_j$]{};
\node (-1) at (-2,0,1) [vx] [fill,label=left:\small$-\ee_j$]{} ;
\node (2) at (0,2,1) [vx] [fill,label=left:\small${\ee_k\ }$]{} ;
\node (-2) at (0,-2,1) [vx] [fill,label=below:\small$-\ee_k$]{} ;
\node (3) at (0,0,0) [vx] [fill,label=right:\small $\ \varepsilon_i\ee_i$]{} ;
\node (+++) at (2,2,1) [vx] [fill=black!50,label=right:\small $q_{\varepsilon_i++}$]{};
\node (-++) at (-2,2) [vx] [fill=black!50,label=left:\small $q_{\varepsilon_i-+}$]{};
\node (+-+) at (2,-2) [vx] [fill=black!50,label=right:\small $q_{\varepsilon_i+-}$]{};
\node (--+) at (-2,-2) [vx] [fill=black!50,label=left:\small $q_{\varepsilon_i--}$]{};
\draw[dotted] (1)--(0)--(-1) (2)--(0)--(-2);
\draw[densely dotted] (0)--(3);
\draw[dashed] (-2)--(3)--(1)--(2)--(3)--(-1)--(-2)--(1) (-1)--(2);
\draw (1)--(+++)--(2)--(-++)--(-1)--(--+)--(-2)--(+-+)--(1) (+++)--(3)--(+-+) (-++)--(3)--(--+) ;
\draw[thick] (+++)--(+-+)--(--+)--(-++)--(+++);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.6149 | arxiv | 2014-12-16T02:18:43 |
|
K_6 and K_6^* | \documentclass[a4paper]{amsart}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}
\node (A) at (120:2.8){A};
\node (B) at (60:2.8) {B} edge node[above,sloped]{\scriptsize $0123$}(A);
\node (C) at (360:2.8){C} edge node[below right,sloped]{\scriptsize $0456$}(A)
edge node[above,sloped]{\scriptsize $0789$}(B);
\node (D) at (300:2.8){D} edge node[pos=.6, above,sloped]{\scriptsize $1489$}(A)
edge node[above left,sloped]{\scriptsize $1567$}(B)
edge node[below,sloped]{\scriptsize $2347$}(C);
\node (E) at (240:2.8){E} edge node[below right,sloped]{\scriptsize $2579$}(A)
edge node[pos=.4, above ,sloped]{\scriptsize $2468$}(B)
edge node[above left,sloped]{\scriptsize $1358$}(C)
edge node[below,sloped]{\scriptsize $0369$}(D);
\node (F) at (180:2.8){F} edge node[above,sloped]{\scriptsize $3678$}(A)
edge node[below right,sloped]{\scriptsize $3459$}(B)
edge node[pos=.6, above ,sloped]{\scriptsize $1269$}(C)
edge node[above left,sloped]{\scriptsize $0258$}(D)
edge node[below,sloped]{\scriptsize $0147$}(E);
\node [xshift=6cm](U) at (120:2.8){U};
\node [xshift=6cm](V) at (60:2.8) {V} edge node[above,sloped]{\scriptsize $5689$}(U);
\node [xshift=6cm](W) at (360:2.8){W} edge node[below right,sloped]{\scriptsize $1379$}(U)
edge node[above,sloped]{\scriptsize $0249$}(V);
\node [xshift=6cm](X) at (300:2.8){X} edge node[pos=.6, above,sloped]{\scriptsize $1245$}(U)
edge node[above left,sloped]{\scriptsize $0357$}(V)
edge node[below,sloped]{\scriptsize $0168$}(W);
\node [xshift=6cm](Y) at (240:2.8){Y} edge node[below right,sloped]{\scriptsize $0348$}(U)
edge node[pos=.4, above ,sloped]{\scriptsize $1278$}(V)
edge node[above left,sloped]{\scriptsize $2356$}(W)
edge node[below,sloped]{\scriptsize $4679$}(X);
\node [xshift=6cm](Z) at (180:2.8){Z} edge node[above,sloped]{\scriptsize $0267$}(U)
edge node[below right,sloped]{\scriptsize $1346$}(V)
edge node[pos=.6, above ,sloped]{\scriptsize $4578$}(W)
edge node[above left,sloped]{\scriptsize $2389$}(X)
edge node[below,sloped]{\scriptsize $0159$}(Y);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.6149 | arxiv | 2014-12-16T02:18:43 |
|
R P^2 triangulated with squares | \documentclass[a4paper]{amsart}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{positioning}
\newcommand{\ee}{\mathbf{e}}
\begin{document}
\begin{tikzpicture}[>=stealth,vx/.style={circle,inner sep=0pt,minimum size=1mm,draw}]
\node (1) at (1,0) [vx] [fill,label=right:\small $\ee_1$]{};
\node (-1) at (-1,0) [vx] [fill,label=left:\small$-\ee_1$]{} ;
\node (2) at (0,1) [vx] [fill,label=below:\small$\ee_2$]{} ;
\node (-2) at (0,-1) [vx] [fill,label=above:\small$-\ee_2$]{} ;
\node (++) at (2,2) [vx] [fill=black!50,label=right:\small$\ee_1+\ee_2$]{};
\node (-+) at (-2,2) [vx] [fill=black!50,label=left:\small$-\ee_1+\ee_2$]{};
\node (+-) at (2,-2) [vx] [fill=black!50,label=right:\small$\ee_1-\ee_2$]{};
\node (--) at (-2,-2) [vx] [fill=black!50,label=left:\small$-\ee_1-\ee_2$]{};
\node (down) at (0,-2) [vx] [label=below:\small$\ee_2$]{} ;
\draw (1)--(-1)--(2)--(1)--(-2)--(-1);
\draw (+-)--(1)--(++)--(2)--(-+)--(-1)--(--)--(-2)--(+-);
\draw [decoration={markings, mark=at position .5 with {\arrow{>>}},mark=at position .53 with {\arrow{>}}},
postaction={decorate}](++)--(+-);
\draw [decoration={markings, mark=at position .5 with {\arrow{>>}},mark=at position .53 with {\arrow{>}}},
postaction={decorate}](--)--(-+);
\draw [decoration={markings, mark=at position .75 with {\arrow{>>}}, mark=at position .25 with {\arrow{>}}},
postaction={decorate},dashed] (+-)--(down)--(--);
\draw [decoration={markings, mark=at position .25 with {\arrow{>}}, mark=at position .75 with {\arrow{>>}}},
postaction={decorate}] (-+)--(2)--(++);
\draw [dashed] (-2)--(down);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.6149 | arxiv | 2014-12-16T02:18:43 |
|
Antiprism in the link of [_ie_i,_je_j] in X^(2) | \documentclass[a4paper]{amsart}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{positioning}
\newcommand{\ee}{\mathbf{e}}
\begin{document}
\begin{tikzpicture}[vx/.style={circle,inner sep=0pt,minimum size=1mm,draw}]
\node (1) at (1,0) [vx] [fill,label=right:\small $\ee_l$]{};
\node (-1) at (-1,0) [vx] [fill,label=left:\small$-\ee_l$]{} ;
\node (2) at (0,1) [vx] [fill,label=above:\small$\ee_k$]{} ;
\node (-2) at (0,-1) [vx] [fill,label=below:\small$-\ee_k$]{} ;
\node (++) at (2,2) [vx] [fill=black!50,label=above:\small$\varepsilon_i\ee_i+\varepsilon_j\ee_j+\ee_k+\ee_l$]{};
\node (-+) at (-2,2) [vx] [fill=black!50,label=above:\small$\varepsilon_i\ee_i+\varepsilon_j\ee_j+\ee_k-\ee_l$]{};
\node (+-) at (2,-2) [vx] [fill=black!50,label=below:\small$\varepsilon_i\ee_i+\varepsilon_j\ee_j-\ee_k+\ee_l$]{};
\node (--) at (-2,-2) [vx] [fill=black!50,label=below:\small$\varepsilon_i\ee_i+\varepsilon_j\ee_j-\ee_k-\ee_l$]{};
\draw (-1)--(2)--(1)--(-2)--(-1);
\draw (+-)--(1)--(++)--(2)--(-+)--(-1)--(--)--(-2)--(+-);
\draw [thick] (++)--(+-)--(--)--(-+)--(++);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.6149 | arxiv | 2014-12-16T02:18:43 |
|
Cube Q^3 and octahedral prism D | \documentclass[a4paper]{amsart}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}[z=2cm,y=1cm,xslant=-1,
vx/.style={xshift=4cm,yshift=-4cm,circle,inner sep=0pt, minimum size=1mm,draw,fill=black!50},
vxx/.style={yshift=-5cm,circle,inner sep=0pt,minimum size=1mm,draw,fill=black!50},
v/.style={xshift=1.5cm, z=1cm, y=.5cm, circle,inner sep=0pt,minimum size=1mm,draw}]
\node (1) at (1,0,0) [vx] [label=right:{\scriptsize $(3,0,0,3)$}]{};
\node (-1) at (-1,0,0) [vx] [label={[xshift=2pt,yshift=3pt]left:{\scriptsize $(-3,0,0,3)$}}]{} ;
\node (2) at (0,1,0) [vx] [label={[xshift=2pt,yshift=3pt]left:{\scriptsize $(0,3,0,3)$}}]{} ;
\node (-2) at (0,-1,0) [vx] [label=right:{\scriptsize $(0,-3,0,3)$}]{} ;
\node (3) at (0,0,1) [vx] [label=right:{\scriptsize $(0,0,3,3)$}]{} ;
\node (-3) at (0,0,-1) [vx] [label=right:{\scriptsize $(0,0,-3,3)$}]{} ;
\node (1') at (1,0,0) [vxx] [label= {[xshift=-2pt,yshift=-3pt]right:{\scriptsize $(3,0,0,-3)$}}]{};
\node (-1') at (-1,0,0) [vxx] [label=left:{\scriptsize $(-3,0,0,-3)$}]{} ;
\node (2') at (0,1,0) [vxx] [label=left:{\scriptsize $(0,3,0,-3)$}]{} ;
\node (-2') at (0,-1,0) [vxx] [label={[xshift=-2pt,yshift=-3pt]right:{\scriptsize $(0,-3,0,-3)$}}]{} ;
\node (3') at (0,0,1) [vxx] [label=left:{\scriptsize $(0,0,3,-3)$}]{} ;
\node (-3') at (0,0,-1) [vxx] [label=left:{\scriptsize $(0,0,-3,-3)$}]{} ;
\draw [thick] (-1)--(2)(1)--(-2)--(-1)--(3)--(1) (2)--(3)--(-2)--(-3)--(-1);
\draw [thick,dashed] (1)--(-3)--(2)--(1) (1')--(-3')--(2')--(1');
\draw [thick] (-1')--(2')(1')--(-2')--(-1')--(3')--(1') (2')--(3')--(-2')--(-3')--(-1');
\draw (-1)--(-1') (-2)--(-2') (3)--(3') (-3)--(-3');
\draw [dashed] (1)--(1') (2)--(2');
\node (+++) at (1,1,1) [v] [fill,label=right:{\tiny $(1,1,1,0)$}]{};
\node (++-) at (1,1,-1) [v] [fill,label={[xshift=-3pt]right:{\tiny $(1,1,-1,0)$}}]{};
\node (+-+) at (1,-1,1) [v] [fill,label=right:{\tiny $(1,-1,1,0)$}]{};
\node (+--) at (1,-1,-1) [v] [fill,label=right:{\tiny $(1,-1,-1,0)$}]{};
\node (-++) at (-1,1,1) [v] [fill,label=left:{\tiny $(-1,1,1,0)$}]{};
\node (-+-) at (-1,1,-1) [v] [fill,label=left:{\tiny $(-1,1,-1,0)$}]{};
\node (--+) at (-1,-1,1) [v] [fill,label={[xshift=3pt]left:{\tiny $(-1,-1,1,0)$}}]{};
\node (---) at (-1,-1,-1) [v] [fill,label=left:{\tiny $(-1,-1,-1,0)$}]{};
\draw (---)--(+--)--(+-+)--(+++)--(-++)--(--+)--(---)--(-+-)--(-++) (--+)--(+-+);
\draw[dashed](++-)--(-+-) (+++)--(++-)--(+--);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.6149 | arxiv | 2014-12-16T02:18:43 |
|
Two eyes are linked to a modal box P that controls blinking. | \documentclass[11pt,oneside,article]{memoir}
\usepackage{amssymb}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,calc,positioning,scopes,cd,decorations.markings,fit}
\tikzset{
wiring diagram/.style={
every to/.style={out=0,in=180,draw},
label/.style={
font=\everymath\expandafter{\the\everymath\scriptstyle},
inner sep=0pt,
node distance=2pt and -2pt},
semithick,
node distance=1 and 1,
decoration={markings, mark=at position .5 with {\arrow{stealth};}},
ar/.style={postaction={decorate}},
execute at begin picture={\tikzset{
x=\bbx, y=\bby,
every fit/.style={inner xsep=\bbx, inner ysep=\bby}}}
},
bbx/.store in=\bbx,
bbx = 1.5cm,
bby/.store in=\bby,
bby = 1.75ex,
bb port sep/.store in=\bbportsep,
bb port sep=2,
% bb wire sep=1.75ex,
bb port length/.store in=\bbportlen,
bb port length=4pt,
bb min width/.store in=\bbminwidth,
bb min width=1cm,
bb rounded corners/.store in=\bbcorners,
bb rounded corners=2pt,
bb small/.style={bb port sep=1, bb port length=2.5pt, bbx=.4cm, bb min width=.4cm, bby=.7ex},
bbthick/.code n args={4}{
\pgfmathsetlengthmacro{\bbheight}{\bbportsep * (max(#1,#2)+1) * \bby}
\pgfkeysalso{draw,minimum height=\bbheight,minimum width=\bbminwidth,outer sep=0pt,
rounded corners=\bbcorners,thick,
prefix after command={\pgfextra{\let\fixname\tikzlastnode}},
append after command={\pgfextra{
\draw[#3]
\ifnum #1=0{} \else foreach \i in {1,...,#1} {
($(\fixname.north west)!{\i/(#1+1)}!(\fixname.south west)$) +(-\bbportlen,0) coordinate (\fixname_in\i) -- +(\bbportlen,0) coordinate (\fixname_in\i')}\fi;
\draw[#4]
\ifnum #2=0{} \else foreach \i in {1,...,#2} {
($(\fixname.north east)!{\i/(#2+1)}!(\fixname.south east)$) +(-\bbportlen,0) coordinate (\fixname_out\i') -- +(\bbportlen,0) coordinate (\fixname_out\i)}\fi;
}}}
},
bb/.code 2 args={\pgfkeysalso{bbthick={#1}{#2}{thin}{thin}}},
bb name/.style={append after command={\pgfextra{\node[anchor=north] at (\fixname.north) {#1};}}}
}
\begin{document}
\begin{tikzpicture}[wiring diagram,bb port sep=1, bb port length=2.5pt, bbx=.6cm, bb min width=.6cm, bby=1.3ex]
\node[bbthick={2}{1}{very thick}{very thick}, bb name=${E_1}$] (E1) {};
\node[bbthick={2}{1}{very thick}{very thick}, below= 3 of E1, bb name=${E_2}$] (E2) {};
\node[bbthick={2}{2}{very thick}{thin}, below right = 0 and 2 of E1, bb name=${P}$] (C) {};
\node[bb={2}{2}, fit={(E1) (E2) (C) ($(E1.north)+(0,0)$)},bb name =$$] (V) {};
\draw[ar, very thick] (E1_out1) to (C_in1);
\draw[ar, very thick] (E2_out1) to (C_in2);
\draw[ar] let \p1=(C.north east), \p2=(E1.north west), \n1={\y1+\bby}, \n2=\bbportlen in (C_out1) to[in=0] (\x1,\y2+\n2) -- (\x2-\n2,\y2+\n2) to[out=180] (E1_in1);
\draw[ar] let \p1=(C.south east), \p2=(E2.south west), \n1={\y1+\bby}, \n2=\bbportlen in (C_out2) to[in=0] (\x1,\y2-\n2) -- (\x2-\n2,\y2-\n2) to[out=180] (E2_in2);
\draw[ar, very thick] (V_in1) to (E1_in2);
\draw[ar, very thick] (V_in2) to (E2_in1);
\draw[ar, very thick] (E1_out1) to (V_out1);
\draw[ar, very thick] (E2_out1) to (V_out2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1502.07380 | arxiv | 2015-12-15T02:08:30 |
|
A discrete dynamical system of the visual pathway, interpreted over a mode-dependent network in O_MDN, the operad of mode-dependent networks. The thicker wires represent many parallel connections. | \documentclass[11pt,oneside,article]{memoir}
\usepackage{amssymb}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,calc,positioning,scopes,cd,decorations.markings,fit}
\tikzset{
wiring diagram/.style={
every to/.style={out=0,in=180,draw},
label/.style={
font=\everymath\expandafter{\the\everymath\scriptstyle},
inner sep=0pt,
node distance=2pt and -2pt},
semithick,
node distance=1 and 1,
decoration={markings, mark=at position .5 with {\arrow{stealth};}},
ar/.style={postaction={decorate}},
execute at begin picture={\tikzset{
x=\bbx, y=\bby,
every fit/.style={inner xsep=\bbx, inner ysep=\bby}}}
},
bbx/.store in=\bbx,
bbx = 1.5cm,
bby/.store in=\bby,
bby = 1.75ex,
bb port sep/.store in=\bbportsep,
bb port sep=2,
% bb wire sep=1.75ex,
bb port length/.store in=\bbportlen,
bb port length=4pt,
bb min width/.store in=\bbminwidth,
bb min width=1cm,
bb rounded corners/.store in=\bbcorners,
bb rounded corners=2pt,
bb small/.style={bb port sep=1, bb port length=2.5pt, bbx=.4cm, bb min width=.4cm, bby=.7ex},
bbthick/.code n args={4}{
\pgfmathsetlengthmacro{\bbheight}{\bbportsep * (max(#1,#2)+1) * \bby}
\pgfkeysalso{draw,minimum height=\bbheight,minimum width=\bbminwidth,outer sep=0pt,
rounded corners=\bbcorners,thick,
prefix after command={\pgfextra{\let\fixname\tikzlastnode}},
append after command={\pgfextra{
\draw[#3]
\ifnum #1=0{} \else foreach \i in {1,...,#1} {
($(\fixname.north west)!{\i/(#1+1)}!(\fixname.south west)$) +(-\bbportlen,0) coordinate (\fixname_in\i) -- +(\bbportlen,0) coordinate (\fixname_in\i')}\fi;
\draw[#4]
\ifnum #2=0{} \else foreach \i in {1,...,#2} {
($(\fixname.north east)!{\i/(#2+1)}!(\fixname.south east)$) +(-\bbportlen,0) coordinate (\fixname_out\i') -- +(\bbportlen,0) coordinate (\fixname_out\i)}\fi;
}}}
},
bb/.code 2 args={\pgfkeysalso{bbthick={#1}{#2}{thin}{thin}}},
bb name/.style={append after command={\pgfextra{\node[anchor=north] at (\fixname.north) {#1};}}}
}
\begin{document}
\begin{tikzpicture}[wiring diagram,bb port sep=1, bb port length=2.5pt, bbx=.6cm, bb min width=.6cm, bby=1.3ex]
\node[bbthick={2}{1}{thin}{very thick}, bb name=${E_1}$] (E1) {};
\node[bbthick={2}{1}{thin}{very thick}, below= 3 of E1, bb name=${E_2}$] (E2) {};
\node[bbthick={2}{2}{very thick}{thin}, below right = 0 and 2 of E1, bb name=${P}$] (P) {};
\node[bbthick={2}{1}{very thick}{thin}, right= 4 of P, bb name=$V$] (V) {};
\node[bb={2}{1}, fit={($(E2.south west)+(0,-2)$) (P) (V) ($(E1.north)+(0,2)$)},bb name =$VS$] (VS) {};
% "bold" arrows
\draw[ar, very thick] (E1_out1) to (P_in1);
\draw[ar, very thick] (E2_out1) to (P_in2);
\draw[ar] let \p1=(P.north east), \p2=(E1.north west), \n1={\y1+\bby}, \n2=\bbportlen in (P_out1) to[in=0] (\x1,\y2+\n2) -- (\x2-\n2,\y2+\n2) to[out=180] (E1_in1);
\draw[ar] let \p1=(P.south east), \p2=(E2.south west), \n1={\y1+\bby}, \n2=\bbportlen in (P_out2) to[in=0] (\x1,\y2-\n2) -- (\x2-\n2,\y2-\n2) to[out=180] (E2_in2);
\draw[ar] (VS_in1') to (E1_in2);
\draw[ar] (VS_in2') to (E2_in1);
% "bold" arrows
\draw[ar, very thick] (E1_out1) to (V_in1);
\draw[ar, very thick] (E2_out1) to (V_in2);
\draw[ar] (V_out1) to (VS_out1');
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1502.07380 | arxiv | 2015-12-15T02:08:30 |
|
The monoidal product of multiple mode-dependent networks, displayed with an instance of the mode-dependent network Eye(Nerve, Nerve, Nerve). | \documentclass[11pt,oneside,article]{memoir}
\usepackage{amssymb}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,calc,positioning,scopes,cd,decorations.markings,fit}
\tikzset{
wiring diagram/.style={
every to/.style={out=0,in=180,draw},
label/.style={
font=\everymath\expandafter{\the\everymath\scriptstyle},
inner sep=0pt,
node distance=2pt and -2pt},
semithick,
node distance=1 and 1,
decoration={markings, mark=at position .5 with {\arrow{stealth};}},
ar/.style={postaction={decorate}},
execute at begin picture={\tikzset{
x=\bbx, y=\bby,
every fit/.style={inner xsep=\bbx, inner ysep=\bby}}}
},
bbx/.store in=\bbx,
bbx = 1.5cm,
bby/.store in=\bby,
bby = 1.75ex,
bb port sep/.store in=\bbportsep,
bb port sep=2,
% bb wire sep=1.75ex,
bb port length/.store in=\bbportlen,
bb port length=4pt,
bb min width/.store in=\bbminwidth,
bb min width=1cm,
bb rounded corners/.store in=\bbcorners,
bb rounded corners=2pt,
bb small/.style={bb port sep=1, bb port length=2.5pt, bbx=.4cm, bb min width=.4cm, bby=.7ex},
bbthick/.code n args={4}{
\pgfmathsetlengthmacro{\bbheight}{\bbportsep * (max(#1,#2)+1) * \bby}
\pgfkeysalso{draw,minimum height=\bbheight,minimum width=\bbminwidth,outer sep=0pt,
rounded corners=\bbcorners,thick,
prefix after command={\pgfextra{\let\fixname\tikzlastnode}},
append after command={\pgfextra{
\draw[#3]
\ifnum #1=0{} \else foreach \i in {1,...,#1} {
($(\fixname.north west)!{\i/(#1+1)}!(\fixname.south west)$) +(-\bbportlen,0) coordinate (\fixname_in\i) -- +(\bbportlen,0) coordinate (\fixname_in\i')}\fi;
\draw[#4]
\ifnum #2=0{} \else foreach \i in {1,...,#2} {
($(\fixname.north east)!{\i/(#2+1)}!(\fixname.south east)$) +(-\bbportlen,0) coordinate (\fixname_out\i') -- +(\bbportlen,0) coordinate (\fixname_out\i)}\fi;
}}}
},
bb/.code 2 args={\pgfkeysalso{bbthick={#1}{#2}{thin}{thin}}},
bb name/.style={append after command={\pgfextra{\node[anchor=north] at (\fixname.north) {#1};}}}
}
\begin{document}
\begin{tikzpicture}[wiring diagram,bb port sep=1, bb port length=2.5pt, bbx=.6cm, bb min width=.6cm, bby=1.5ex]
\node[bb={1}{1}, bb name=$N_1$] (R) {};
\node[bb={1}{1}, fit={(R) ($(R.south)+(3,1)$)}, bb name=$R_1$] (box) {};
\draw[ar] (box_in1') to (R_in1);
\draw[ar] (R_out1) to (box_out1');
% second diagram below
\node[bb={0}{1}, below= 6 of R, bb name=$N_2$] (RK) {};
\node[bb={1}{1}, fit={(RK) ($(RK.south)+(3,1)$)}, bb name=$R_2$] (box2) {};
\draw[ar] (RK_out1) to (box2_out1');
\node[bb={1}{1}, below= 6 of RK, bb name=$N_3$] (RL) {};
\node[bb={1}{1}, fit={(RL) ($(RL.south)+(3,1)$)}, bb name=$R_3$] (box3) {};
\draw[ar] (box3_in1) to (RL_in1);
\draw[ar] (RL_out1) to (box3_out1');
\node[bb={1}{1}, right=8 of R, bb name=${N_1}$] (R1) {};
\node[bb={0}{1}, right=8 of RK, bb name=${N_2}$] (R2) {};
\node[bb={1}{1}, right=8 of RL, bb name=${N_3}$] (R3) {};
\node[bb={3}{3}, fit={(R1) (R2) (R3) ($(R1.north)+(3,0)$)},bb name =${E}$] (E) {};
\draw[ar] (E_in1) to (R1_in1);
\draw[ar] (E_in3) to (R3_in1);
\draw[ar] (R1_out1) to (E_out1);
\draw[ar] (R2_out1) to (E_out2);
\draw[ar] (R3_out1) to (E_out3);
\draw[label]
node[below = 10pt of box.south] {$\sqcup$};
\draw[label]
node[below = 10pt of box2.south] {$\sqcup$};
\draw[label]
node[right = 24pt of box2] {$=$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1502.07380 | arxiv | 2015-12-15T02:08:30 |
|
A feedforward network composed of three layers, written as a mode-dependent network V = (, _!) : (V_1, V_2, V_3) V in O_MDN. Note that the diagram pictured above is technically not a legal wiring diagram: typically multiple inputs cannot map into the same port, but we have used a shorthand here to represent the many input ports to each layer. | \documentclass[11pt,oneside,article]{memoir}
\usepackage{amssymb}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,calc,positioning,scopes,cd,decorations.markings,fit}
\tikzset{
wiring diagram/.style={
every to/.style={out=0,in=180,draw},
label/.style={
font=\everymath\expandafter{\the\everymath\scriptstyle},
inner sep=0pt,
node distance=2pt and -2pt},
semithick,
node distance=1 and 1,
decoration={markings, mark=at position .5 with {\arrow{stealth};}},
ar/.style={postaction={decorate}},
execute at begin picture={\tikzset{
x=\bbx, y=\bby,
every fit/.style={inner xsep=\bbx, inner ysep=\bby}}}
},
bbx/.store in=\bbx,
bbx = 1.5cm,
bby/.store in=\bby,
bby = 1.75ex,
bb port sep/.store in=\bbportsep,
bb port sep=2,
% bb wire sep=1.75ex,
bb port length/.store in=\bbportlen,
bb port length=4pt,
bb min width/.store in=\bbminwidth,
bb min width=1cm,
bb rounded corners/.store in=\bbcorners,
bb rounded corners=2pt,
bb small/.style={bb port sep=1, bb port length=2.5pt, bbx=.4cm, bb min width=.4cm, bby=.7ex},
bbthick/.code n args={4}{
\pgfmathsetlengthmacro{\bbheight}{\bbportsep * (max(#1,#2)+1) * \bby}
\pgfkeysalso{draw,minimum height=\bbheight,minimum width=\bbminwidth,outer sep=0pt,
rounded corners=\bbcorners,thick,
prefix after command={\pgfextra{\let\fixname\tikzlastnode}},
append after command={\pgfextra{
\draw[#3]
\ifnum #1=0{} \else foreach \i in {1,...,#1} {
($(\fixname.north west)!{\i/(#1+1)}!(\fixname.south west)$) +(-\bbportlen,0) coordinate (\fixname_in\i) -- +(\bbportlen,0) coordinate (\fixname_in\i')}\fi;
\draw[#4]
\ifnum #2=0{} \else foreach \i in {1,...,#2} {
($(\fixname.north east)!{\i/(#2+1)}!(\fixname.south east)$) +(-\bbportlen,0) coordinate (\fixname_out\i') -- +(\bbportlen,0) coordinate (\fixname_out\i)}\fi;
}}}
},
bb/.code 2 args={\pgfkeysalso{bbthick={#1}{#2}{thin}{thin}}},
bb name/.style={append after command={\pgfextra{\node[anchor=north] at (\fixname.north) {#1};}}}
}
\begin{document}
\begin{tikzpicture}[wiring diagram,bb port sep=1, bb port length=2.5pt, bbx=.6cm, bb min width=.6cm, bby=1.3ex]
\node[bbthick={1}{1}{very thick}{thin}, bb name=$$] (V11) {};
\node[bbthick={1}{1}{very thick}{thin}, below= 2 of V11, bb name=$$] (V12) {};
\node[bbthick={1}{1}{very thick}{thin}, below= 2 of V12, bb name=$$] (V13) {};
\node[bbthick={1}{1}{very thick}{thin}, below= 2 of V13, bb name=$$] (V14) {};
\node[bbthick={4}{4}{very thick}{thin}, fit={(V11) (V12) (V13) (V14) ($(V11.north)+(0,2)$) ($(V14.south)+(0,-2)$)}, bb name=${V_1}$] (V1) {};
\node[bbthick={1}{1}{very thick}{thin}, right= 5 of V12, bb name=$$] (V21) {};
\node[bbthick={1}{1}{very thick}{thin}, below= 2 of V21, bb name=$$] (V22) {};
\node[bbthick={2}{2}{very thick}{thin}, fit={(V21) (V22) ($(V21.north)+(0,2)$) ($(V22.south)+(0,-2)$)}, bb name=${V_2}$] (V2) {};
\node[bbthick={1}{1}{very thick}{thin}, above right= 0 and 5 of V22, bb name=$$] (V31) {};
\node[bbthick={1}{1}{very thick}{thin}, fit={(V31) ($(V31.north)+(0,2)$) ($(V31.south)+(0,-2)$)}, bb name=${V_3}$] (V3) {};
\node[bbthick={4}{1}{very thick}{thin}, fit={(V1) (V2) (V3)}, bb name=${V}$] (V) {};
% arrows from v to v1
\draw[ar, very thick] (V_in1') to (V1_in1);
\draw[ar, very thick] (V_in2') to (V1_in2);
\draw[ar, very thick] (V_in3') to (V1_in3);
\draw[ar, very thick] (V_in4') to (V1_in4);
% arrows from v1 to v2
\draw (V1_out1) to (V2_in1);
\draw (V1_out1) to (V2_in2);
\draw (V1_out2) to (V2_in1);
\draw (V1_out2) to (V2_in2);
\draw (V1_out3) to (V2_in1);
\draw (V1_out3) to (V2_in2);
\draw (V1_out4) to (V2_in1);
\draw (V1_out4) to (V2_in2);
% arrows from v2 to v3
\draw (V2_out1) to (V3_in1);
\draw (V2_out2) to (V3_in1);
% arrows from v3 to v
\draw[ar] (V3_out1) to (V_out1');
% arrows inside v1
\draw[very thick] (V1_in1') to (V11_in1);
\draw[very thick] (V1_in2') to (V12_in1);
\draw[very thick] (V1_in3') to (V13_in1);
\draw[very thick] (V1_in4') to (V14_in1);
\draw (V11_out1) to (V1_out1');
\draw (V12_out1) to (V1_out2');
\draw (V13_out1) to (V1_out3');
\draw (V14_out1) to (V1_out4');
% arrows inside v2
\draw[very thick] (V2_in1') to (V21_in1);
\draw[very thick] (V2_in2') to (V22_in1);
\draw (V21_out1) to (V2_out1');
\draw (V22_out1) to (V2_out2');
% arrows inside v3
\draw[very thick] (V3_in1') to (V31_in1);
\draw (V31_out1) to (V3_out1');
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1502.07380 | arxiv | 2015-12-15T02:08:30 |
|
Field inclusions for cases where there are one or more intermediate fields. The arrows run from the smaller field to the larger; numbers beside the arrows are the degrees of the extensions. | \documentclass[a4paper,oneside,reqno,11pt]{amsart}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{graphs,backgrounds,quotes,positioning,arrows,matrix,shapes}
\usetikzlibrary{arrows.meta}
\begin{document}
\begin{tikzpicture}
[auto, nd/.style={circle,minimum size = 13 mm,draw}]
\matrix[row sep=8mm,column sep=6mm] {
\node (15ac) [nd] {$15ac$};&&\node (19bc) [nd] {$19bc$}; &[7 mm] & &\node (35bcdg) [nd] {$35bcdg$};
\\
\node (15b) [nd] {$15b$}; &&\node (19d) [nd] {$19d$} ; &&\node (35e) [nd] {$35e$}; & \node (35af) [nd] {$35af$}; & \node (35h) [nd] {$35h$};
\\
\node(15d) [nd] {$15d$}; &&\node (19a) [nd] {$19a$}; & &&\node (35i) [nd] {$35i$};
\\
&& \node (19e) [nd] {$19e$}; & &&\node (35j) [nd] {$35j$};
\\[5 mm]
& \node (39acde) [nd] {$39acde$}; & & & & \node (48abcd) [nd] {$48abcd$};
\\
\node (39bf) [nd] {$39bf$}; & & \node (39gh) [nd] {$39gh$}; & & \node (48e) [nd] {$48e$}; & & \node (48f) [nd] {$48f$};
\\
& \node (39ij) [nd] {$39ij$}; &&&& \node (48g) [nd] {$48g$};
\\
};
\draw[->] (15d) to node{2} (15b);
\draw[->] (15b) to node{2} (15ac);
\draw[->] (19e) to node{3} (19a);
\draw[->] (19a) to node{2} (19d);
\draw[->] (19d) to node{2} (19bc);
\draw[->] (35j) to node[swap] {2} (35i);
\draw[->] (35i) to node[swap] {2} (35h);
\draw[->] (35j) to node{4} (35e);
\draw[->] (35i) to node[swap] {4} (35af);
\draw[->] (35e) to node{4} (35bcdg);
\draw[->] (35af) to node[swap] {2} (35bcdg);
\draw[->] (35h) to node[swap] {4} (35bcdg);
\draw[->] (39ij) to node{3} (39bf);
\draw[->] (39ij) to node[swap] {2} (39gh);
\draw[->] (39bf) to node{2} (39acde);
\draw[->] (39gh) to node[swap] {3} (39acde);
\draw[->] (48g) to node {8} (48e);
\draw[->] (48g) to node[swap] {3} (48f);
\draw[->] (48e) to node {3} (48abcd);
\draw[->] (48f) to node[swap] {8} (48abcd);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.05981 | arxiv | 2017-03-20T01:06:45 |
|
Invariant manifold for the 2-dimensional tandem case, where node 1 is the bottleneck. | \documentclass[10pt, conference]{IEEEtran}
\usepackage{amsfonts,amsthm,amssymb,amsmath}
\usepackage[usenames,dvipsnames]{color}
\usepackage{tikz}
\usetikzlibrary{arrows,shapes}
\begin{document}
\begin{tikzpicture}[scale=1]
% Draw axes
\draw [<->,thick] (0,5) node (yaxis) [above] {$x_1$}
|- (5,0) node (xaxis) [right] {$x_2$};
% Draw two intersecting lines
\draw (0,0) coordinate (a_1) -- (1.6,2) coordinate (a_2);
\draw (1.6,2) coordinate (b_1) -- (1.6,4.75) coordinate (b_2);
\coordinate (c) at (intersection of a_1--a_2 and b_1--b_2);
% Draw lines indicating intersection with y and x axis. Here we use
% the perpendicular coordinate system
\draw[dashed] (yaxis |- c) node[left] {$K_1$}
-| (xaxis -| c) node[below] {$\frac{\gamma_2\mu_1K_1}{\mu_2\gamma_1}$};
\draw[dashed] (2.2, 0.05) -- (2.2,0) node[above] {$K_2$};
% Draw a dot to indicate intersection point
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1404.6924 | arxiv | 2014-04-29T02:13:39 |
|
(a) Key showing four types of timelines (b) Progression of a poetry system (c) Progression of the HR system. | \documentclass{article}
\usepackage[dvipsnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{positioning}
\usetikzlibrary{shapes.multipart}
\usetikzlibrary{fit,backgrounds}
\usepackage{amssymb}
\usepackage{amsmath,amsthm}
\usepackage[colorinlistoftodos]{todonotes}
\begin{document}
\begin{tikzpicture}[
single/.style={draw, anchor=text, rectangle},
double/.style={draw, anchor=text, rectangle split,rectangle split parts=2},
triple/.style={draw, anchor=text, rectangle split,rectangle split parts=3},
quadruple/.style={draw, anchor=text, rectangle split,rectangle split parts=4}
]
%% beginning of FIRST box
\node[single,scale=0.3] (first) at (0, 0) {
\tikz{
\node[triple] (firstA) at (-2,0) {$A^{\beta,\gamma}_g = \langle T(\overline{C^{\beta}_g},\overline{C^{\gamma}_g})\rangle$
\nodepart{second}{$\langle E^{\epsilon}_g\rangle^* = \overline{C^{\epsilon}_p}(a^{\beta,\gamma}_g)$}
\nodepart{third}{$e^{\zeta}_g = \langle S[a^{\beta,\gamma}_g]({e^{\epsilon}}^*) \rangle$}
};
\node[single,right=6mm of firstA.three east] (firstB) {$\langle \overline{A^{\iota}_g}(e^{\zeta}_g)\rangle$
};
\draw [-latex] (firstA.third east) -- (firstB.west);
\node[above = 1cm of firstB,label={[label distance=1mm]10:{\textbf{P1}}},inner sep=1pt]{};
}
};
%% end of first box
%% beginning of SECOND box
\node[single,scale=0.3,right=3mm of first, inner sep=1mm] (second) {
\tikz{
\node[quadruple] (secondA) at (-2,0) {$C^{\iota}_p(\overline{t}(\overline{a^{\iota}_g})(e^\zeta_g))=\langle\overline{C^{\alpha}_m}\rangle$
\nodepart{second}{$A^{\beta,\gamma}_g = \langle T(C^{\beta}_g,C^{\gamma}_g)\rangle$}
\nodepart{third}{$\langle E^{\epsilon}_g\rangle^* = \overline{C^{\epsilon}_p}(a^{\beta,\gamma}_p)$}
\nodepart{fourth}{$e^{\zeta}_g = \langle S[a^{\beta,\gamma}_g]({e^{\epsilon}}^*) \rangle$}
};
\node[single,right=6mm of secondA.four east] (secondB) {$\langle \overline{T}[\overline{A^{\iota}_g}](e^{\zeta}_g)\rangle$
};
\draw [-latex] (secondA.four east) -- (secondB.west);
\draw [-latex,dashed] (secondB.north) to[out=90,in=0] (secondA.one east);
\node[above = 1.5cm of secondB,label={[label distance=3mm]10:{\textbf{P2}}},inner sep=1pt]{};
}
};;
%% end of second box
\draw[->] (first) -- (second);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.01770 | arxiv | 2016-03-08T02:10:21 |
|
[3^1+,4,3^1+]-diagram. | \documentclass{amsart}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[every node/.style={circle,draw,inner sep=2pt}]
\node [draw] (d) {};
\node [draw] (c) [right of=d] {} edge[dotted] (d);
\node [draw] (b) [right of=c] {} edge (c);
\node [draw] (a) [right of=b] {} edge (b);
\node [draw] (u) [right of=a] {} edge[double,thick]
(a);
\node [draw] (s) [right of=u] {} edge (u);
\node [draw] (v) [right of=s] {} edge (s);
\node [draw] (w) [right of=v] {} edge[dotted] (v);
\draw [decorate,decoration={brace,raise=3pt,transform={scale=1.5,xshift=-4pt}}] (c)--(d)
node[below,midway,draw=none]{\footnotesize $\nu\geq 0$};
\draw [decorate,decoration={brace,raise=3pt,transform={scale=1.5,xshift=-4pt}}] (w)--(v)
node[below,midway,draw=none]{\footnotesize $\mu\geq 0$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.01710 | arxiv | 2016-04-11T02:03:01 |
|
Affine Coxeter group F_4, nodes labelled by generators. | \documentclass{amsart}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[every node/.style={circle,draw,inner sep=2pt}]
\node [draw] (c) [label=$a$] {};
\node [draw] (b) [label=$b$,right of=c] {} edge (c);
\node [draw] (a) [label=$c$,right of=b] {} edge (b);
\node [draw] (u) [label=$d$,right of=a] {} edge[double,thick] (a);
\node [draw] (s) [label=$e$, right of=u] {} edge (u);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.01710 | arxiv | 2016-04-11T02:03:01 |
|
Coxeter group with diagram [3^2,4,3^2] from . | \documentclass{amsart}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[every node/.style={circle,draw,inner sep=2pt}]
\node [draw] (c) [label=$c_3$] {};
\node [draw] (b) [label=$b_3$,right of=c] {} edge (c);
\node [draw] (a) [label=$a$, right of=b] {} edge (b);
\node [draw] (u) [label=$b_1b_2$,right of=a] {}
edge[double,thick] (a);
\node [draw] (s) [label=$c_1c_2$, right of=u] {} edge (u);
\node [draw] (v) [label=$d_1 d_2$, right of=s] {} edge (s);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.01710 | arxiv | 2016-04-11T02:03:01 |
|
The presentation P for , nodes labelled by generators. | \documentclass{amsart}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[every node/.style={circle,draw,inner sep=2pt}]
\node [draw] (c) [label=$a$] {};
\node [draw] (b) [label=$b$,right of=c] {} edge (c);
\node [draw] (a) [label=$c$,right of=b] {} edge (b);
\node [draw] (u) [label=$d$,right of=a] {} edge[double,thick] (a);
\node [draw] (s) [label=$e$, right of=u] {} edge (u);
\node [draw] (t) [label=$f$, right of=s] {} edge (s);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.01710 | arxiv | 2016-04-11T02:03:01 |
|
IEEE~754 Floating-point memory layout; see Figure 3.1ieee08. | \documentclass[a4paper,bibliography=totoc,index=totoc]{scrbook}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\draw[rounded corners] (0, 0 ) rectangle (0.4,0.5) node[pos=.5] {$1$};
\draw[rounded corners] (0.4,0 ) rectangle (4.4,0.5) node[pos=.5] {$n_e$};
\draw[rounded corners] (4.4,0 ) rectangle (12.4,0.5) node[pos=.5] {$n_m$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.00722 | arxiv | 2017-01-04T02:05:36 |
|
For the same data shown in Figure~fig:motivation-breaksOnly, we computed the breakpointError function (E) and its components. False positives (FP) occur when there are more estimated than true breakpoints, and false negatives (FN) are the opposite. For the correct model size (3 segments = 2 breakpoints), the imprecision function (I) quantifies the distance between the true and estimated breakpoint positions. The breakpointError is the sum of the other components (E=FP+FN+I). | \documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amsthm,amsfonts,amssymb}
\usepackage{tikz}
\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 (433.62,144.54);
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (433.62,144.54);
\definecolor[named]{drawColor}{rgb}{1.00,1.00,1.00}
\definecolor[named]{fillColor}{rgb}{1.00,1.00,1.00}
\path[draw=drawColor,line width= 0.6pt,line join=round,line cap=round,fill=fillColor] ( 0.00, 0.00) rectangle (433.62,144.54);
\end{scope}
\begin{scope}
\path[clip] ( 39.69,119.86) rectangle (230.63,132.50);
\definecolor[named]{drawColor}{rgb}{0.50,0.50,0.50}
\definecolor[named]{fillColor}{rgb}{0.80,0.80,0.80}
\path[draw=drawColor,line width= 0.2pt,line join=round,line cap=round,fill=fillColor] ( 39.69,119.86) rectangle (230.63,132.50);
\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.96] at (135.16,122.87) {change in mean};
\end{scope}
\begin{scope}
\path[clip] (230.63,119.86) rectangle (421.57,132.50);
\definecolor[named]{drawColor}{rgb}{0.50,0.50,0.50}
\definecolor[named]{fillColor}{rgb}{0.80,0.80,0.80}
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\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.96] at (326.10,122.87) {change in variance};
\end{scope}
\begin{scope}
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cycle;
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cycle;
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cycle;
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cycle;
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\begin{scope}
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\definecolor[named]{drawColor}{rgb}{0.00,0.00,0.00}
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cycle;
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\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round,fill=fillColor] (209.55, 48.70) --
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cycle;
\definecolor[named]{fillColor}{rgb}{0.53,0.81,0.92}
\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round,fill=fillColor] (209.55,105.20) --
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cycle;
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cycle;
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\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 1.00] at ( 57.92, 46.09) {I};
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\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 1.00] at ( 57.92,106.92) {E};
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 1.00] at (212.40,111.25) {E};
\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 1.00] at ( 57.92, 35.76) {FP};
\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 1.00] at ( 57.92, 96.59) {FN};
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 1.00] at (212.40, 35.76) {FN};
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 1.00] at (212.40,100.92) {FP};
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\end{document} | https://arxiv.org/abs/1509.00368 | arxiv | 2015-09-02T02:10:54 |
|
For a small signal with 2 breakpoints, and for breakpoints i\{1, 2\}, we plot the _i functions that measure the precision of a guess in r_i = [ r_i, r_i]. The blue signal m^22 has 2 breakpoints: B=\{4,14\}. To emphasize the discrete nature of the data, N is drawn at each of the P=22 distinct positions at which data could be gathered. | \documentclass{article}
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|
Schema of R^* with the counter-clockwise orientation indicated by arrows (see Definition~def:pern). | \documentclass[a4paper,bibliography=totoc,index=totoc]{scrbook}
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\end{document} | https://arxiv.org/abs/1701.00722 | arxiv | 2017-01-04T02:05:36 |
|
Interpolated double floating-point evaluations (demarked by crosses) of the devil's sequence u_n(see (eq:devil)) for n\{2,,25\}(see listing~lst:devil). | \documentclass[a4paper,bibliography=totoc,index=totoc]{scrbook}
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\end{document} | https://arxiv.org/abs/1701.00722 | arxiv | 2017-01-04T02:05:36 |
|
Interpolated evaluations (demarked by crosses) of $f$ (see (\ref{eq:spike})) in the neighbourhood of $\frac{4}{3}$ for all possible double floating-point numbers in $\left[\frac{4}{3}-2.22\cdot 10^{-15},\frac{4}{3}+2.22\cdot 10^{-15} \right]$ (see listing~\ref{lst:spike}). | \documentclass[a4paper,bibliography=totoc,index=totoc]{scrbook}
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\end{document} | https://arxiv.org/abs/1701.00722 | arxiv | 2017-01-04T02:05:36 |
|
P_D(35,1)(demarked by crosses) in comparison with an exponential curve fitted to the endpoints (0,0) and (35,(P_D(35,1)). | \documentclass[a4paper,bibliography=totoc,index=totoc]{scrbook}
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|
Model selection error curves for 2 simulated signals. Minima are highlighted using circles. \\Signal: the log squared error E_signal of the estimated signal with respect to the true piecewise constant signal (see text). \\Breakpoint: exact breakpointError E^B_exact. %described in Section~\ref{sec:breakpoint_error}.\\Annotation: incomplete annotation error E^ A A^0_incomplete. %for the annotations shown in% Figure~\ref{fig:variable-density-annotation-cost}. | \documentclass{article}
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\end{document} | https://arxiv.org/abs/1509.00368 | arxiv | 2015-09-02T02:10:54 |
|
Comparison of annotation error functions as the set of annotations changes. Minima are highlighted using circles. \\Complete: annotation error %$E_{\text{incomplete}}^{\hat A\cup \hat A^0}$ for a complete set of 6 positive and 7 negative annotations. \\Zero-one: zero-one annotation error %$E_{01}^{\hat A\cup \hat A^0}$ for a complete set of 6 positive and 7 negative annotations. \\Incomplete: zero-one annotation error %$E_{01}^{\hat R,A}$ for 3 positive and 4 negative annotations. \\Positive: zero-one annotation error %%$E_{01}^{\hat R,A}$ for 3 positive annotations. | \documentclass{article}
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\end{scope}
\begin{scope}
\path[clip] ( 0.00, 0.00) rectangle (361.35,289.08);
\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= 1.09] at ( 18.16,148.90) {error};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1509.00368 | arxiv | 2015-09-02T02:10:54 |
|
Evaluation of the Unum Euler partial sums (eq:euler) for iterations n\{0,,20\} with (n_b,n_s)=(12,2)( demarks open/closed interval endpoints); see Listing~lst:euler. | \documentclass[a4paper,bibliography=totoc,index=totoc]{scrbook}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[xlabel=$n$, ylabel=$E_n$,
extra x ticks={0,20},
extra x tick style={xticklabel pos=right,
xtick pos=right},
extra y ticks={2.7182818284},
extra y tick style={yticklabel pos=right,
ytick pos=right},
extra y tick labels={e},
extra tick style={grid=major}]
\addplot[mark=*,draw=black] coordinates {(0 ,1.0)};
\addplot[mark=*,draw=black] coordinates {(1 ,2.0)};
\addplot[mark=*,draw=black] coordinates {(2 ,2.5)};
\addplot[mark=o,draw=black] coordinates {(3 ,2.6) (3 ,2.7)};
\addplot[mark=o,draw=black] coordinates {(4 ,2.6) (4 ,2.8)};
\addplot[mark=o,draw=black] coordinates {(5 ,2.6) (5 ,2.9)};
\addplot[mark=o,draw=black] coordinates {(6 ,2.6) (6 ,3.0)};
\addplot[mark=o,draw=black] coordinates {(7 ,2.6) (7 ,3.1)};
\addplot[mark=o,draw=black] coordinates {(8 ,2.6) (8 ,3.2)};
\addplot[mark=o,draw=black] coordinates {(9 ,2.6) (9 ,3.3)};
\addplot[mark=o,draw=black] coordinates {(10,2.6) (10,3.4)};
\addplot[mark=o,draw=black] coordinates {(11,2.6) (11,3.5)};
\addplot[mark=o,draw=black] coordinates {(12,2.6) (12,3.6)};
\addplot[mark=o,draw=black] coordinates {(13,2.6) (13,3.7)};
\addplot[mark=o,draw=black] coordinates {(14,2.6) (14,3.8)};
\addplot[mark=o,draw=black] coordinates {(15,2.6) (15,3.9)};
\addplot[mark=o,draw=black] coordinates {(16,2.6) (16,4.0)};
\addplot[mark=o,draw=black] coordinates {(17,2.6) (17,4.1)};
\addplot[mark=o,draw=black] coordinates {(18,2.6) (18,4.2)};
\addplot[mark=o,draw=black] coordinates {(19,2.6) (19,4.3)};
\addplot[mark=o,draw=black] coordinates {(20,2.6) (20,4.4)};
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.00722 | arxiv | 2017-01-04T02:05:36 |
|
Evaluation of the Unum spike function F(see (eq:spike-unum)) on all Unums in [11.2,1.9] with (n_b,n_s)=(12,2)( demarks open/closed interval endpoints); see Listing~lst:spikec-unum. | \documentclass[a4paper,bibliography=totoc,index=totoc]{scrbook}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{pgfplots}
\newcommand{\iffy}{\breve{\infty}}
\begin{document}
\begin{tikzpicture}
\begin{axis}[xlabel=$x$, ylabel=$F(x)$,
xmin=0.8,xmax=2.0,
ymin=-4.5,ymax=0.8,
extra x ticks={0.8333333333, 1.3333333333, 1.9},
extra x tick style={xticklabel pos=right,
xtick pos=right},
extra y ticks={},
extra y tick style={yticklabel pos=right,
ytick pos=right},
extra x tick labels={$\frac{1}{1.2}$, $\frac{4}{3}$, $1.9$},
extra tick style={grid=major}]
\draw [black, rounded corners]
(axis cs:0.8333, 0.1818) rectangle (axis cs:0.9091, 0.4167);
\addplot[mark=o,draw=black] coordinates {
(0.9091, 0.1818) (0.9091, 0.3448)
};
\draw [black, rounded corners]
(axis cs:0.9091, 0) rectangle (axis cs:1, 0.3448);
\addplot[mark=*,draw=black] coordinates {
(1, 0)
};
\draw [black, rounded corners]
(axis cs:1, -0.4167) rectangle (axis cs:1.1, 0);
\addplot[mark=o,draw=black] coordinates {
(1.1, -0.4167) (1.1, -0.3333)
};
\draw [black, rounded corners]
(axis cs:1.1, -1) rectangle (axis cs:1.2, -0.3333);
\addplot[mark=o,draw=black] coordinates {
(1.2, -1) (1.2, -0.8333)
};
\draw [black, rounded corners]
(axis cs:1.2, -2.4) rectangle (axis cs:1.3, -0.8333);
\addplot[mark=o,draw=black] coordinates {
(1.3, -2.4) (1.3, -1.7)
};
\draw [black, rounded corners]
(axis cs:1.3, -5) rectangle (axis cs:1.4, -1.1);
\node at (axis cs:1.35,-3.4) {$\iffy$};
\draw[->] (axis cs:1.35,-3.6) -- (axis cs: 1.35 ,-4.4)
node {};
\addplot[mark=o,draw=black] coordinates {
(1.4, -2.4) (1.4, -1.1)
};
\draw [black, rounded corners]
(axis cs:1.4, -2.4) rectangle (axis cs:1.5, -0.6667);
\addplot[mark=o,draw=black] coordinates {
(1.5, -0.7143) (1.5, -0.6667)
};
\draw [black, rounded corners]
(axis cs:1.5, -0.7143) rectangle (axis cs:1.6, -0.0909);
\addplot[mark=o,draw=black] coordinates {
(1.6, -0.4167) (1.6, -0.0909)
};
\draw [black, rounded corners]
(axis cs:1.6, -0.4167) rectangle (axis cs:1.7, 0.2632);
\addplot[mark=o,draw=black] coordinates {
(1.7, 0.2632)
};
\addplot[mark=none,draw=black] coordinates {
(1.7, 0) (1.7, 0.2632)
};
\addplot[mark=*,draw=black] coordinates {
(1.7, 0)
};
\draw [black, rounded corners]
(axis cs:1.7, 0) rectangle (axis cs:1.8, 0.4167);
\addplot[mark=o,draw=black] coordinates {
(1.8, 0.2564) (1.8, 0.4167)
};
\draw [black, rounded corners]
(axis cs:1.8, 0.2564) rectangle (axis cs:1.9, 0.5882);
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.00722 | arxiv | 2017-01-04T02:05:36 |
|
The duality between a cycle and a star. | \documentclass[11pt]{article}
\usepackage{amsmath,amsfonts,amssymb,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale=1]
\filldraw[gray] (0,0) circle (.1);
\draw[->] (-1,0)--(-.58,.78);
\draw[->] (-.5,.866)--(.4,.866);
\draw[->] (.5,.866)--(.92,.08);
\draw[->] (1,0)--(.58,-.78);
\draw[->] (.5,-.866)--(-.4,-.866);
\draw[->] (-.5,-.866)--(-.92,-.08);
\filldraw (-1,0) circle (.1);
\filldraw (-.5,.866) circle (.1);
\filldraw (.5,.866) circle (.1);
\filldraw (1,0) circle (.1);
\filldraw (.5,-.866) circle (.1);
\filldraw (-.5,-.866) circle (.1);
\draw[gray,->] (0,0) -- (-1.299,.75);
\draw[gray,->] (0,0) -- (0,1.5);
\draw[gray,->] (0,0) -- (1.299,.75);
\draw[gray,->] (0,0) -- (1.299,-.75);
\draw[gray,->] (0,0) -- (0,-1.5);
\draw[gray,->] (0,0) -- (-1.299,-.75);
\node at (.3,0) {$v'$};
\node at (1.6,.9) {$u'$};
\node at (-1.35,0) {$w_1$};
\node at (-.675,1.1691) {$w_2$};
\node at (.675,1.1691) {$w_3$};
\node at (1.35,0) {$w_4$};
\node at (.675,-1.1691) {$w_5$};
\node at (-.675,-1.1691) {$w_6$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.00765 | arxiv | 2017-04-05T02:00:56 |
|
Depiction of a depth-4 nand-tree as a two-player game. Let x be the input to nand_4 shown in the figure. This instance is A-winnable, and P_A(x) consists of the paths \{p_1,p_2,p_3,p_4\}, shown using solid lines. Fault nodes are those with double circles. Each path in P_A(x) encounters two faults at nodes where Player A makes decisions. Therefore, F_A(x)=4. | \documentclass[11pt]{article}
\usepackage{amsmath,amsfonts,amssymb,amsthm}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale=.65]
\tikzstyle{vertex} = [circle,draw,fill=white,minimum size=.5em]
\tikzstyle{vertexFault} = [circle,draw,fill=white,double,minimum size=.5em]
\tikzstyle{operator} = [rectangle,rounded corners,draw,%fill=cyan,
fill = black!20!white,
minimum size=1.5em]
\tikzstyle{turn} = [rectangle,draw,fill=white,minimum size=1.5em]
\node[vertex] (v0000) at (-7.5,0) {$1$};
\node[operator] (p1) at (-7.5,-1) {$p_1$};
\node[vertex] (v0001) at (-6.5,0) {$1$};
\node[operator] (p2) at (-6.5,-1) {$p_2$};
\node[vertex] (v0010) at (-5.5,0) {$1$};
\node[vertex] (v0011) at (-4.5,0) {$0$};
\node[vertex] (v0100) at (-3.5,0) {$0$};
\node[vertex] (v0101) at (-2.5,0) {$0$};
\node[vertex] (v0110) at (-1.5,0) {$1$};
\node[operator] (p3) at (-1.5,-1) {$p_3$};
\node[vertex] (v0111) at (-0.5,0) {$1$};
\node[operator] (p4) at (-0.5,-1) {$p_4$};
\node[vertex] (v1000) at (0.5,0) {$0$};
\node[vertex] (v1001) at (1.5,0) {$0$};
\node[vertex] (v1010) at (2.5,0) {$0$};
\node[vertex] (v1011) at (3.5,0) {$1$};
\node[vertex] (v1100) at (4.5,0) {$1$};
\node[vertex] (v1101) at (5.5,0) {$1$};
\node[vertex] (v1110) at (6.5,0) {$0$};
\node[vertex] (v1111) at (7.5,0) {$1$};
\node[vertex] (v000) at (-7,1.5) {$\wedge$};
\node[vertexFault] (v001) at (-5,1.5) {$\wedge$};
\node[vertex] (v010) at (-3,1.5) {$\wedge$};
\node[vertex] (v011) at (-1,1.5) {$\wedge$};
\node[vertex] (v100) at (1,1.5) {$\wedge$};
\node[vertexFault] (v101) at (3,1.5) {$\wedge$};
\node[vertex] (v110) at (5,1.5) {$\wedge$};
\node[vertexFault] (v111) at (7,1.5) {$\wedge$};
\node[vertexFault] (v00) at (-6,3) {$\vee$};
\node[vertexFault] (v01) at (-2,3) {$\vee$};
\node[vertex] (v10) at (2,3) {$\vee$};
\node[vertexFault] (v11) at (6,3) {$\vee$};
\node[vertex] (v0) at (-4,4.5) {$\wedge$};
\node[vertexFault] (v1) at (4,4.5) {$\wedge$};
\node[vertexFault] (v) at (0,6) {$\vee$};
\path (v000) edge[thick] (v0001);
\path (v000) edge[thick] (v0000);
\path[dashed] (v00) edge[thick] (v001);
\path (v00) edge[thick] (v000);
\path (v0) edge[thick] (v01);
\path (v0) edge[thick] (v00);
\path[dashed] (v001) edge[thick] (v0011);
\path[dashed] (v001) edge[thick] (v0010);
\path (v01) edge[thick] (v011);
\path[dashed] (v01) edge[thick] (v010);
\path[dashed] (v1) edge[thick] (v11);
\path (v011) edge[thick] (v0111);
\path (v011) edge[thick] (v0110);
\path[dashed] (v111) edge[thick] (v1110);
\path[dashed] (v111) edge[thick] (v1111);
\path[dashed] (v010) edge[thick] (v0101);
\path[dashed] (v010) edge[thick] (v0100);
\path[dashed] (v100) edge[thick] (v1001);
\path[dashed] (v100) edge[thick] (v1000);
\path[dashed] (v101) edge[thick] (v1011);
\path[dashed] (v101) edge[thick] (v1010);
\path[dashed] (v110) edge[thick] (v1101);
\path[dashed] (v110) edge[thick] (v1100);
\path[dashed] (v10) edge[thick] (v101);
\path[dashed] (v10) edge[thick] (v100);
\path[dashed] (v1) edge[thick] (v10);
\path[dashed] (v11) edge[thick] (v111);
\path[dashed] (v11) edge[thick] (v110);
\path[dashed] (v1) edge[thick] (v);
\path (v0) edge[thick] (v);
\node[turn] (p1m) at (10.1,6) {$\textrm{Player $A$'s First Turn}$};
\node[turn] (p1m) at (10.1,4.5) {$\textrm{Player $B$'s First Turn}$};
\node[turn] (p1m) at (10.1,3) {$\textrm{Player $A$'s Second Turn}$};
\node[turn] (p1m) at (10.1,1.5) {$\textrm{Player $B$'s Second Turn}$};
\node (h1) at (-8.3,0) {};
\node (h2) at (-8.3,5.3) {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.00765 | arxiv | 2017-04-05T02:00:56 |
|
2-relay MIMO Gaussian diamond channel: Each node has n antennas, Parameter = C_01C_02 - C_13C_23, C_012 and C_123 are the cut capacities of the respective cuts | \documentclass[conference]{IEEEtran}
\usepackage{amsthm,amssymb,graphicx,multirow,amsmath,amsfonts,cite}
\usepackage[usenames,dvipsnames]{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale=1]
\tikzset{vertex/.style = {shape=circle,very thick,draw,minimum size=1.1em}}
\tikzset{edge/.style = {> = latex', very thick}}
\node[vertex] (0) at (0,0) {0};
\node[vertex] (1) at (2,1.5) {1};
\node[vertex] (2) at (2,-1.5) {2};
\node[vertex] (3) at (4,0) {3};
\draw [edge] (0) to (1);
\draw [edge] (0) to (2);
\draw [edge] (1) to (3);
\draw [edge] (2) to (3);
\node[left] at (-0.25,0) {${\cal S}$ };
\node[right] at (4.22,0) {${\cal D}$};
\node[above] at (2,1.7) {${\cal R}_1$};
\node[below] at (2,-1.7) {${\cal R}_2$};
\node[above] at (1,0.85) {$C_{01}$};
\node[below] at (1,-0.8) {$C_{02}$};
\node[above] at (3,0.85) {$C_{13}$};
\node[below] at (3,-0.85) {$C_{23}$};
\node[right] at (3.5,0.9) {$C_{123}$};
\node[left] at (0.5,0.9) {$C_{012}$};
\draw[dashed] (0.5,1)-- (0.5,-1);
\draw[dashed] (3.5,1) -- (3.5,-1);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1602.01982 | arxiv | 2016-02-09T02:10:23 |
|
States of the diamond channel | \documentclass[conference]{IEEEtran}
\usepackage{amsthm,amssymb,graphicx,multirow,amsmath,amsfonts,cite}
\usepackage[usenames,dvipsnames]{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale=0.55]
\tikzset{vertex/.style = {shape=circle,very thick,draw,minimum size=2mm}}
\tikzset{edge/.style = {->,> = latex', very thick}}
\node[vertex] (0) at (0,0) {0};
\node[vertex] (1) at (2,1.5) {1};
\node[vertex] (2) at (2,-1.5) {2};
\node[vertex] (3) at (4,0) {3};
\path[->,>=stealth,draw,thick]
(0) edge node [above left] {${\mathbf H}_{01}$} (1)
(2) edge node [below right] {${\mathbf H}_{23}$} (3);
\node[right] at (1,-2.5) {\textbf{State 1}};
\node[vertex] (0) at (6,0) {0};
\node[vertex] (1) at (8,1.5) {1};
\node[vertex] (2) at (8,-1.5) {2};
\node[vertex] (3) at (10,0) {3};
\path[->,>=stealth,draw,thick]
(0) edge node [below left] {${\mathbf H}_{02}$} (2)
(1) edge node [above right] {${\mathbf H}_{13}$} (3);
\node[right] at (7,-2.5) {\textbf{State 2}};
%MAC
\node[vertex] (0) at (0,-6) {0};
\node[vertex] (1) at (2,-4.5) {1};
\node[vertex] (2) at (2,-7.5) {2};
\node[vertex] (3) at (4,-6) {3};
\path[->,>=stealth,draw,thick]
(1) edge node [above right] {${\mathbf H}_{13}$} (3)
(2) edge node [below right] {${\mathbf H}_{23}$} (3);
\node[right] at (1,-8.5) {\textbf{State 3}};
% BC
\node[vertex] (0) at (6,-6) {0};
\node[vertex] (1) at (8,-4.5) {1};
\node[vertex] (2) at (8,-7.5) {2};
\node[vertex] (3) at (10,-6) {3};
\path[->,>=stealth,draw,thick]
(0) edge node [above left] {${\mathbf H}_{01}$} (1)
(0) edge node [below left] {${\mathbf H}_{02}$} (2);
\node[right] at (7,-8.5) {\textbf{State 4}};
\draw[dashed] (5,-9)-- (5,3);
\draw[dashed] (-1,-3.2)-- (11,-3.2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1602.01982 | arxiv | 2016-02-09T02:10:23 |
|
An illustration of the rate regions for different choices of Q_1, Q_2 | \documentclass[conference]{IEEEtran}
\usepackage{amsthm,amssymb,graphicx,multirow,amsmath,amsfonts,cite}
\usepackage[usenames,dvipsnames]{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale=0.3]
\draw [<->] (0,20) -- (0,0) -- (20,0);
\node[below right] at (20,0) {$R_1$};
\node[above left] at (0,18) {$R_2$};
\node[below] at (0,0) {$0$};
\node[above right] at (2,2) {${\cal C}_{\text{MAC}}({\mathbf K}_{13}, {\mathbf K}_{23})$};
\draw[->,>=stealth,black] (5,4) -- (10.1,10.2);
\draw[black, thick] (0,0)--(17.8,0)--(17.8,2.5)--(4.8,15.5)--(0,15.5);
\draw[red, very thick, dashed] (17.8,0)--(17.8,5.7)--(9,14.5)--(0,14.5);
\draw[blue, very thick, dashed] (16.4,0)--(16.4,5.5)--(6.4,15.5)--(0,15.5);
\node[above right] at (10,17) {${\cal C}_{\text{MAC}}({\mathbf K}'_{13}, {\mathbf K}_{23})$};
\draw[->,>=stealth,black] (10,17) -- (8.9,13);
\node[above right] at (16,10) {${\cal C}_{\text{MAC}}({\mathbf K}_{13}, {\mathbf K}'_{23})$};
\draw[->,>=stealth,black] (16,10) -- (14.5,9);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1602.01982 | arxiv | 2016-02-09T02:10:23 |
|
The action of the 3-periodic matrix equation: 3-periodic matrix on the fan . | \documentclass[a4paper, 11pt, reqno]{amsart}
\usepackage{amsfonts, amsthm, amssymb, amsmath, stmaryrd, mathtools}
\usepackage{eucal,fullpage,times,color,enumerate,accents}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{calc}
\usetikzlibrary{fadings}
\usepackage[colorlinks,
%backref
]{hyperref}
\begin{document}
\begin{tikzpicture}
\fill[blue!15, path fading=north] (-2,2) -- (2,2) -- (2.5,2.5) -- (-2.5,2.5);
\fill[blue!15, path fading=south] (-2,-2) -- (2,-2) -- (2.5,-2.5) -- (-2.5,-2.5);
\fill[blue!15, path fading=east] (2,2) -- (2,-2) -- (2.5,-2.5) -- (2.5,2.5);
\fill[blue!15, path fading=west] (-2,2) -- (-2,-2) -- (-2.5,-2.5) -- (-2.5,2.5);
\fill[blue!15] (-2,-2) -- (2,-2) -- (2,2) -- (-2,2);
\draw[blue!50, ultra thick, ->] (0,0) -- (2.5,0);
\draw[blue!50, ultra thick, ->] (0,0) -- (0,2.5);
\draw[blue!50, ultra thick, ->] (0,0) -- (-2.5,-2.5);
\fill[blue!15] (1.7,0) circle (.15);
\fill[blue!15] (0,1.7) circle (.15);
\fill[blue!15] (-1.2,-1.2) circle (.15);
\fill[black!50!blue!50] (0,0) circle (.065);
\fill[black!50!blue!50] (1,0) circle (.065);
\fill[black!50!blue!50] (2,0) circle (.065);
\fill[black!50!blue!50] (-1,0) circle (.065);
\fill[black!50!blue!50] (-2,0) circle (.065);
\fill[black!50!blue!50] (0,1) circle (.065);
\fill[black!50!blue!50] (1,1) circle (.065);
\fill[black!50!blue!50] (2,1) circle (.065);
\fill[black!50!blue!50] (-1,1) circle (.065);
\fill[black!50!blue!50] (-2,1) circle (.065);
\fill[black!50!blue!50] (0,2) circle (.065);
\fill[black!50!blue!50] (1,2) circle (.065);
\fill[black!50!blue!50] (2,2) circle (.065);
\fill[black!50!blue!50] (-1,2) circle (.065);
\fill[black!50!blue!50] (-2,2) circle (.065);
\fill[black!50!blue!50] (0,-1) circle (.065);
\fill[black!50!blue!50] (1,-1) circle (.065);
\fill[black!50!blue!50] (2,-1) circle (.065);
\fill[black!50!blue!50] (-1,-1) circle (.065);
\fill[black!50!blue!50] (-2,-1) circle (.065);
\fill[black!50!blue!50] (0,-2) circle (.065);
\fill[black!50!blue!50] (1,-2) circle (.065);
\fill[black!50!blue!50] (2,-2) circle (.065);
\fill[black!50!blue!50] (-1,-2) circle (.065);
\fill[black!50!blue!50] (-2,-2) circle (.065);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.07593 | arxiv | 2017-03-31T02:04:26 |
|
Action of /3 on Trop(Y_) from Example example: Brauer-Severi A. | \documentclass[a4paper, 11pt, reqno]{amsart}
\usepackage{amsfonts, amsthm, amssymb, amsmath, stmaryrd, mathtools}
\usepackage{eucal,fullpage,times,color,enumerate,accents}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{calc}
\usetikzlibrary{fadings}
\usepackage[colorlinks,
%backref
]{hyperref}
\begin{document}
\begin{tikzpicture}
\fill[blue!15, ultra thick, line cap=round, rounded corners=.1mm] (0,0) -- ({2*cos(30)},{2*sin(30)}) to [out=120,in=-30] ({{2.5*cos(90)}},{{2.5*sin(90)}}) to [out=-150,in=60] ({{2*cos(150)}},{{2*sin(150)}}) -- (0,0);
\fill[blue!15, ultra thick, line cap=round, rounded corners=.1mm] (0,0) -- ({2*cos(30+120)},{2*sin(30+120)}) to [out=-120,in=90] ({{2.5*cos(90+120)}},{{2.5*sin(90+120)}}) to [out=-30,in=180] ({{2*cos(150+120)}},{{2*sin(150+120)}}) -- (0,0);
\fill[blue!15, ultra thick, line cap=round, rounded corners=.1mm] (0,0) -- ({2*cos(30-120)},{2*sin(30-120)}) to [out=0,in=-150] ({{2.5*cos(90-120)}},{{2.5*sin(90-120)}}) to [out=90,in=-60] ({{2*cos(150-120)}},{{2*sin(150-120)}}) -- (0,0);
\draw[blue!50, ultra thick, line cap=round, rounded corners=.1mm] ({2*cos(30)},{2*sin(30)}) to [out=120,in=-30] ({{2.5*cos(90)}},{{2.5*sin(90)}}) to [out=-150,in=60] ({{2*cos(150)}},{{2*sin(150)}});
\draw[blue!50, ultra thick, line cap=round, rounded corners=.1mm] ({2*cos(30+120)},{2*sin(30+120)}) to [out=-120,in=90] ({{2.5*cos(90+120)}},{{2.5*sin(90+120)}}) to [out=-30,in=180] ({{2*cos(150+120)}},{{2*sin(150+120)}});
\draw[blue!50, ultra thick, line cap=round, rounded corners=.1mm] ({2*cos(30-120)},{2*sin(30-120)}) to [out=0,in=-150] ({{2.5*cos(90-120)}},{{2.5*sin(90-120)}}) to [out=90,in=-60] ({{2*cos(150-120)}},{{2*sin(150-120)}});
\draw[blue!50, ultra thick, line cap=round, rounded corners=.1mm] (0,0) -- ({2*cos(30)},{2*sin(30)});
\draw[blue!50, ultra thick, line cap=round, rounded corners=.1mm] (0,0) -- ({2*cos(150)},{2*sin(150)});
\draw[blue!50, ultra thick, line cap=round, rounded corners=.1mm] (0,0) -- ({2*cos(-90)},{2*sin(-90)});
\fill[blue!15] ({1.175*cos(30)},{1.175*sin(30)}) circle (.15);
\fill[blue!15] ({1.175*cos(30+120)},{1.175*sin(30+120)}) circle (.15);
\fill[blue!15] ({1.195*cos(-90)},{1.195*sin(-90)}) circle (.15);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.07593 | arxiv | 2017-03-31T02:04:26 |
|
Galois-equivariant tropicalization of the degree-6 curve X Y_ in Example example: Brauer-Severi C. Note the /3-symmetry under the action in Figures figure: example of action and figure: example of tropical action. | \documentclass[a4paper, 11pt, reqno]{amsart}
\usepackage{amsfonts, amsthm, amssymb, amsmath, stmaryrd, mathtools}
\usepackage{eucal,fullpage,times,color,enumerate,accents}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{calc}
\usetikzlibrary{fadings}
\usepackage[colorlinks,
%backref
]{hyperref}
\begin{document}
\begin{tikzpicture}
\fill[blue!15, path fading=north] (-6,6) -- (6,6) -- (6.5,6.5) -- (-6.5,6.5);
\fill[blue!15, path fading=south] (-6,-6) -- (6,-6) -- (6.5,-6.5) -- (-6.5,-6.5);
\fill[blue!15, path fading=east] (6,6) -- (6,-6) -- (6.5,-6.5) -- (6.5,6.5);
\fill[blue!15, path fading=west] (-6,6) -- (-6,-6) -- (-6.5,-6.5) -- (-6.5,6.5);
\fill[blue!15] (-6,-6) -- (6,-6) -- (6,6) -- (-6,6);
\draw[blue!50, ultra thick, ->] (0,0) -- (6.5,0);
\draw[blue!50, ultra thick, ->] (0,0) -- (0,6.5);
\draw[blue!50, ultra thick, ->] (0,0) -- (-6.5,-6.5);
\fill[black!50!blue!50] (0,0) circle (.065);
\fill[black!50!blue!50] (1,0) circle (.065);
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\fill[black!50!blue!50] (5,0) circle (.065);
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\fill[black!50!blue!50] (-1,0) circle (.065);
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\fill[black!50!blue!50] (-1,1) circle (.065);
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\fill[black!50!blue!50] (6,-1) circle (.065);
\fill[black!50!blue!50] (-1,-1) circle (.065);
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\fill[black!50!blue!50] (-3,-1) circle (.065);
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\fill[black!50!blue!50] (-6,-1) circle (.065);
\fill[black!50!blue!50] (0,-2) circle (.065);
\fill[black!50!blue!50] (1,-2) circle (.065);
\fill[black!50!blue!50] (2,-2) circle (.065);
\fill[black!50!blue!50] (3,-2) circle (.065);
\fill[black!50!blue!50] (4,-2) circle (.065);
\fill[black!50!blue!50] (5,-2) circle (.065);
\fill[black!50!blue!50] (6,-2) circle (.065);
\fill[black!50!blue!50] (-1,-2) circle (.065);
\fill[black!50!blue!50] (-2,-2) circle (.065);
\fill[black!50!blue!50] (-3,-2) circle (.065);
\fill[black!50!blue!50] (-4,-2) circle (.065);
\fill[black!50!blue!50] (-5,-2) circle (.065);
\fill[black!50!blue!50] (-6,-2) circle (.065);
\fill[black!50!blue!50] (0,-3) circle (.065);
\fill[black!50!blue!50] (1,-3) circle (.065);
\fill[black!50!blue!50] (2,-3) circle (.065);
\fill[black!50!blue!50] (3,-3) circle (.065);
\fill[black!50!blue!50] (4,-3) circle (.065);
\fill[black!50!blue!50] (5,-3) circle (.065);
\fill[black!50!blue!50] (6,-3) circle (.065);
\fill[black!50!blue!50] (-1,-3) circle (.065);
\fill[black!50!blue!50] (-2,-3) circle (.065);
\fill[black!50!blue!50] (-3,-3) circle (.065);
\fill[black!50!blue!50] (-4,-3) circle (.065);
\fill[black!50!blue!50] (-5,-3) circle (.065);
\fill[black!50!blue!50] (-6,-3) circle (.065);
\fill[black!50!blue!50] (0,3) circle (.065);
\fill[black!50!blue!50] (1,3) circle (.065);
\fill[black!50!blue!50] (2,3) circle (.065);
\fill[black!50!blue!50] (3,3) circle (.065);
\fill[black!50!blue!50] (4,3) circle (.065);
\fill[black!50!blue!50] (5,3) circle (.065);
\fill[black!50!blue!50] (6,3) circle (.065);
\fill[black!50!blue!50] (-1,3) circle (.065);
\fill[black!50!blue!50] (-2,3) circle (.065);
\fill[black!50!blue!50] (-3,3) circle (.065);
\fill[black!50!blue!50] (-4,3) circle (.065);
\fill[black!50!blue!50] (-5,3) circle (.065);
\fill[black!50!blue!50] (-6,3) circle (.065);
%
\fill[black!50!blue!50] (0,4) circle (.065);
\fill[black!50!blue!50] (1,4) circle (.065);
\fill[black!50!blue!50] (2,4) circle (.065);
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\fill[black!50!blue!50] (5,4) circle (.065);
\fill[black!50!blue!50] (6,4) circle (.065);
\fill[black!50!blue!50] (-1,4) circle (.065);
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\fill[black!50!blue!50] (-3,4) circle (.065);
\fill[black!50!blue!50] (-4,4) circle (.065);
\fill[black!50!blue!50] (-5,4) circle (.065);
\fill[black!50!blue!50] (-6,4) circle (.065);
%
\fill[black!50!blue!50] (0,5) circle (.065);
\fill[black!50!blue!50] (1,5) circle (.065);
\fill[black!50!blue!50] (2,5) circle (.065);
\fill[black!50!blue!50] (3,5) circle (.065);
\fill[black!50!blue!50] (4,5) circle (.065);
\fill[black!50!blue!50] (5,5) circle (.065);
\fill[black!50!blue!50] (6,5) circle (.065);
\fill[black!50!blue!50] (-1,5) circle (.065);
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\fill[black!50!blue!50] (-3,5) circle (.065);
\fill[black!50!blue!50] (-4,5) circle (.065);
\fill[black!50!blue!50] (-5,5) circle (.065);
\fill[black!50!blue!50] (-6,5) circle (.065);
%
\fill[black!50!blue!50] (0,6) circle (.065);
\fill[black!50!blue!50] (1,6) circle (.065);
\fill[black!50!blue!50] (2,6) circle (.065);
\fill[black!50!blue!50] (3,6) circle (.065);
\fill[black!50!blue!50] (4,6) circle (.065);
\fill[black!50!blue!50] (5,6) circle (.065);
\fill[black!50!blue!50] (6,6) circle (.065);
\fill[black!50!blue!50] (-1,6) circle (.065);
\fill[black!50!blue!50] (-2,6) circle (.065);
\fill[black!50!blue!50] (-3,6) circle (.065);
\fill[black!50!blue!50] (-4,6) circle (.065);
\fill[black!50!blue!50] (-5,6) circle (.065);
\fill[black!50!blue!50] (-6,6) circle (.065);
%
\fill[black!50!blue!50] (0,-4) circle (.065);
\fill[black!50!blue!50] (1,-4) circle (.065);
\fill[black!50!blue!50] (2,-4) circle (.065);
\fill[black!50!blue!50] (3,-4) circle (.065);
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\fill[black!50!blue!50] (5,-4) circle (.065);
\fill[black!50!blue!50] (6,-4) circle (.065);
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\fill[black!50!blue!50] (-5,-4) circle (.065);
\fill[black!50!blue!50] (-6,-4) circle (.065);
%
\fill[black!50!blue!50] (0,-5) circle (.065);
\fill[black!50!blue!50] (1,-5) circle (.065);
\fill[black!50!blue!50] (2,-5) circle (.065);
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\fill[black!50!blue!50] (5,-5) circle (.065);
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\fill[black!50!blue!50] (-3,-5) circle (.065);
\fill[black!50!blue!50] (-4,-5) circle (.065);
\fill[black!50!blue!50] (-5,-5) circle (.065);
\fill[black!50!blue!50] (-6,-5) circle (.065);
%
\fill[black!50!blue!50] (0,-6) circle (.065);
\fill[black!50!blue!50] (1,-6) circle (.065);
\fill[black!50!blue!50] (2,-6) circle (.065);
\fill[black!50!blue!50] (3,-6) circle (.065);
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\fill[black!50!blue!50] (-3,-6) circle (.065);
\fill[black!50!blue!50] (-4,-6) circle (.065);
\fill[black!50!blue!50] (-5,-6) circle (.065);
\fill[black!50!blue!50] (-6,-6) circle (.065);
%
\draw[black, ultra thick, <->] (6.5,-5) -- (0,-5) -- (0,-4) -- (1,-3) -- (1,-2) -- (2,-1) -- (2,0) -- (3,1) -- (3,2) -- (4,3) -- (4,4) -- (5,5) -- (6.5,5);
\draw[black, ultra thick, <->] (-3.5,-6.5) -- (-1,-4) -- (-1,-3) -- (0,-2) -- (0,-1) -- (1,0) -- (1,1) -- (2,2) -- (2,3) -- (3,4) -- (3,6.5);
\draw[black, ultra thick, <->] (-5.5,-6.5) -- (-2,-3) -- (-2,-2) -- (-1,-1) -- (-1,0) -- (0,1) -- (0,2) -- (1,3) -- (1,6.5);
\draw[black, ultra thick, <->] (-6.5,-5.5) -- (-3,-2) -- (-3,-1) -- (-2,0) -- (-2,1) -- (-1,2) -- (-1,6.5);
\draw[black, ultra thick, <->] (-6.5,-3.5) -- (-4,-1) -- (-4,0) -- (-3,1) -- (-3,2) -- (-3,6.5);
\draw[black, ultra thick, <->] (-6.5,-1.5) -- (-5,0) -- (-5,6.5);
\draw[black, ultra thick, ->] (1,-3) -- (6.5,-3);
\draw[black, ultra thick, ->] (2,-1) -- (6.5,-1);
\draw[black, ultra thick, ->] (3,1) -- (6.5,1);
\draw[black, ultra thick, ->] (4,3) -- (6.5,3);
\draw[black, ultra thick, ->] (5,5) -- (5,6.5);
\draw[black, ultra thick, ->] (0,-5) -- (-1.5,-6.5);
\draw[black, ultra thick] (-1,-4) -- (0,-4);
\draw[black, ultra thick] (0,-2) -- (1,-2);
\draw[black, ultra thick] (1,0) -- (2,0);
\draw[black, ultra thick] (2,2) -- (3,2);
\draw[black, ultra thick] (3,4) -- (4,4);
\draw[black, ultra thick] (-2,-3) -- (-1,-3);
\draw[black, ultra thick] (-1,-1) -- (0,-1);
\draw[black, ultra thick] (0,1) -- (1,1);
\draw[black, ultra thick] (1,3) -- (2,3);
\draw[black, ultra thick] (-3,-2) -- (-2,-2);
\draw[black, ultra thick] (-2,0) -- (-1,0);
\draw[black, ultra thick] (-1,2) -- (0,2);
\draw[black, ultra thick] (-4,-1) -- (-3,-1);
\draw[black, ultra thick] (-3,1) -- (-2,1);
\draw[black, ultra thick] (-5,0) -- (-4,0);
\draw[black, ultra thick, dotted] (6.65,5) -- (7,5);
\fill[black] (7.1,5) circle (.08);
\draw[black, ultra thick, dotted] (6.65,3) -- (7,3);
\fill[black] (7.1,3) circle (.08);
\draw[black, ultra thick, dotted] (6.65,1) -- (7,1);
\fill[black] (7.1,1) circle (.08);
\draw[black, ultra thick, dotted] (6.65,-1) -- (7,-1);
\fill[black] (7.1,-1) circle (.08);
\draw[black, ultra thick, dotted] (6.65,-3) -- (7,-3);
\fill[black] (7.1,-3) circle (.08);
\draw[black, ultra thick, dotted] (6.65,-5) -- (7,-5);
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\fill[black] (5,7.1) circle (.08);
\draw[black, ultra thick, dotted] (3,6.65) -- (3,7);
\fill[black] (3,7.1) circle (.08);
\draw[black, ultra thick, dotted] (1,6.65) -- (1,7);
\fill[black] (1,7.1) circle (.08);
\draw[black, ultra thick, dotted] (-1,6.65) -- (-1,7);
\fill[black] (-1,7.1) circle (.08);
\draw[black, ultra thick, dotted] (-3,6.65) -- (-3,7);
\fill[black] (-3,7.1) circle (.08);
\draw[black, ultra thick, dotted] (-5,6.65) -- (-5,7);
\fill[black] (-5,7.1) circle (.08);
\draw[black, ultra thick, dotted] (-1.6,-6.6) -- (-1.85,-6.85);
\fill[black] (-1.925,-6.925) circle (.08);
\draw[black, ultra thick, dotted] (-3.6,-6.6) -- (-3.85,-6.85);
\fill[black] (-3.925,-6.925) circle (.08);
\draw[black, ultra thick, dotted] (-5.6,-6.6) -- (-5.85,-6.85);
\fill[black] (-5.925,-6.925) circle (.08);
\draw[black, ultra thick, dotted] (-6.6,-1.6) -- (-6.85,-1.85);
\fill[black] (-6.925,-1.925) circle (.08);
\draw[black, ultra thick, dotted] (-6.6,-3.6) -- (-6.85,-3.85);
\fill[black] (-6.925,-3.925) circle (.08);
\draw[black, ultra thick, dotted] (-6.6,-5.6) -- (-6.85,-5.85);
\fill[black] (-6.925,-5.925) circle (.08);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.07593 | arxiv | 2017-03-31T02:04:26 |
|
Automaton generating the set (a_n)_n 0 in Lemma %lem2. | \documentclass[reqno]{amsart}
\usepackage{amsfonts,amssymb}
\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{positioning,arrows,automata,shadows,petri}
\begin{document}
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,>=stealth,every state/.style={draw=blue!50,very thick,fill=blue!20}]
\node[state,initial] (q_0) {$q_0/0$};
\node[state] (q_1) [below left=of q_0,yshift=-1.5cm,xshift=-2cm] {$q_1/1$};
\node[state] (q_2) [below right=of q_0,yshift=-1.5cm,xshift=2cm] {$q_2/0$};
\path[->]
(q_0) edge [bend right=15] node [above left] {1} (q_1)
edge node [above right] {$b,\cdots,2b-2$} (q_2)
(q_1) edge [bend right=15] node [below right] {$0,2,\cdots,b-1$} (q_0)
edge node [below ] {$b,\cdots,2b-2$} (q_2)
(q_0) edge [loop above] node {$0,2,\cdots,b-1$} ()
(q_1) edge [loop below] node {1} ()
(q_2) edge [loop below] node {$0,1,\cdots,2b-2$} ();
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1405.6493 | arxiv | 2014-11-12T02:12:32 |
|
Class Vectors model. While training each class vector is represented by an id. Every word in the sentence of that class co-occurs with its class vector. Class vectors and words vectors are jointly trained using skip-gram approach. | \documentclass[11pt]{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usepackage{amsmath, amssymb, amsfonts}
\begin{document}
\begin{tikzpicture}[
roundnode/.style={circle, draw=green!60, fill=green!5, very thick, minimum size=7mm},
squarednode/.style={rectangle, draw=red!60, fill=red!5, very thick, minimum width=5mm, minimum height = 3mm},
myrect/.style={rectangle, draw, inner sep=0pt, fit=#1}
]
%Nodes
\node[squarednode] (class) {class\_id};
\node[squarednode] (word1) [right=of class] {sen1};
\node[squarednode] (word2) [right=of word1] {sen2};
\node[squarednode] (word3) [right=of word2] {sen3};
%Lines
\draw[bend right, ->] (class.south) to node [auto] {} (word1.west);
\draw[bend right, ->] (class.south) to node [auto] {} (word2.west);
\draw[bend right, ->] (class.south) to node [auto] {} (word3.west);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1508.00189 | arxiv | 2015-08-04T02:08:49 |
|
B(2,3) does not contain any vertices at distance 3 from 011. | \documentclass[12pt]{article}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[-,>=stealth',auto,node distance=2cm,
thick,main node/.style={circle,draw,font=\sffamily\bfseries,scale=0.75},new node/.style={circle,fill=black,text=white,draw,font=\sffamily\bfseries,scale=0.75}]
\node[main node] (0) {000};
\node[main node] (1) [above right of=0] {001};
\node[main node] (2) [below right of=1] {010};
\node[main node] (4) [below right of=0] {100};
\node[main node] (5) [right of=2] {101};
\node[main node] (6) [below right of=5] {110};
\node[new node] (3) [above right of=5] {011};
\node[main node] (7) [below right of=3] {111};
\path[every node/.style={font=\sffamily\small}]
(0) edge node [left] {} (1)
edge [loop left] node {} (0)
(1) edge node [left] {} (3)
edge node [right] {} (2)
(2) edge [bend right] node{} (5)
edge node [right] {} (4)
(3) edge node [right] {} (6)
edge node [right] {} (7)
(4) edge node [left] {} (0)
edge node [right] {} (1)
(5) edge [bend right] node{} (2)
edge node [right] {} (3)
(6) edge node [right] {} (5)
edge node [right] {} (4)
(7) edge [loop right] node{} (7)
edge node [right] {} (6);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1508.00403 | arxiv | 2015-08-04T02:15:54 |
|
A gadget in a distributive lattice. | \documentclass[12pt]{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[scale = 1.25]
\node (u) at (0,0) {$u$};
\node (t) at (-1,-1) {$t$};
\node (z) at (1,-1) {$z$};
\node (y) at (0,-2) {$y$};
\node (s) at (-2,-2) {$s$};
\node (x) at (-1,-3) {$x$};
\draw (u) -- (t) -- (s);
\draw (x) -- (y) -- (z);
\draw (s) -- (x);
\draw (t) -- (y);
\draw (u) -- (z);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.05124 | arxiv | 2016-05-27T02:05:21 |
|
The lattice FD(\{a,b,c\}) | \documentclass[12pt]{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[scale = 2.1]
\node (1) at (0,0) {$a \vee b \vee c$};
\node (a+b) at (-1,-0.5) {$a \vee b$};
\node (a+c) at (0,-0.5) {$a \vee c$};
\node (b+c) at (1,-0.5) {$b \vee c$};
\node (a+b-) at (-1,-1) {$\circ$};
\node (a+c-) at (0,-1) {$\circ$};
\node (b+c-) at (1,-1) {$\circ$};
\node (z) at (0,-1.5) {$z$};
\node (ab+) at (-1,-2) {$(a \wedge b) \vee (a \wedge c)$};
\node (ac+) at (0,-2) {$\circ$};
\node (bc+) at (1,-2) {$(a \wedge c) \vee (b \wedge c)$};
\node (ab) at (-1,-2.5) {$a \wedge b$};
\node (ac) at (0,-2.5) {$a \wedge c$};
\node (bc) at (1,-2.5) {$b \wedge c$};
\node (0) at (0,-3) {$a \wedge b \wedge c$};
\node (a) at (-1.25,-1.5) {$a$};
\node (b) at (0.5,-1.5) {$b$};
\node (c) at (1.25,-1.5) {$c$};
\draw (1) -- (a+b);
\draw (1) -- (a+c);
\draw (1) -- (b+c);
\draw (z) -- (a+b-);
\draw (z) -- (a+c-);
\draw (z) -- (b+c-);
\draw (z) -- (ab+);
\draw (z) -- (ac+);
\draw (z) -- (bc+);
\draw (0) -- (ab);
\draw (0) -- (ac);
\draw (0) -- (bc);
\draw (a+b) -- (a+b-);
\draw (b+c) -- (b+c-);
\draw (a+b) -- (a+c-);
\draw (a+b-) -- (a+c);
\draw (a+c-) -- (b+c);
\draw (a+c) -- (b+c-);
\draw (ab) -- (ab+);
\draw (bc) -- (bc+);
\draw (ab) -- (ac+);
\draw (ab+) -- (ac);
\draw (ac+) -- (bc);
\draw (ac) -- (bc+);
\draw (ab+) -- (a) -- (a+b-);
\draw (ac+) -- (b) -- (a+c-);
\draw (bc+) -- (c) -- (b+c-);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.05124 | arxiv | 2016-05-27T02:05:21 |
|
The lattice FL(1 + 2). | \documentclass[12pt]{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[scale = 1.25]
\node (A+C) at (0,3) {$a \vee c$};
\node (A+B) at (-1,2) {$a \vee b$};
\node (C) at (1,2) {$c$};
\node (A+B C) at (0,1) {$(a \vee b) \wedge c$};
\node (A) at (-2.5, 0.5) {$a$};
\node (AC+B) at (0,0) {$(a \wedge c) \vee b$};
\node (AC) at (-1,-1) {$a \wedge c$};
\node (B) at (1,-1) {$b$};
\node (AB) at (0,-2) {$a \wedge b$};
\draw (A+B) -- (A+B C);
\draw (A+C) -- (A+B) -- (A) -- (AC) -- (AC+B) -- (A+B C) -- (C) -- (A+C);
\draw (AC) -- (AB) -- (B) -- (AC+B);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.05124 | arxiv | 2016-05-27T02:05:21 |
|
Long initial fragments of the two paths are also equal in M but we are never going to use this fact, and it is not indicated on the picture. | \documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{amssymb}
\usepackage{graphicx,amsmath, amsfonts}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{color}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=1.25]
\usetikzlibrary{calc}
\foreach \n in {0} {
\foreach \m in {0,1,2,3,4,5} {
\node[fill=gray, circle, scale=0.3] (n\m\n) at (\m,\n) {$ $};
}
}
\filldraw [gray, opacity=0.30] (4,0) rectangle (5,1);
\filldraw [gray, opacity=0.25] (3,1) rectangle (4,2);
\filldraw [gray, opacity=0.20] (2,2) rectangle (3,3);
\foreach \n in {0,1,2,3} {
\foreach \m in {5} {
\node[fill=gray, circle, scale=0.3] (n\m\n) at (\m,\n) {$ $};
}
}
\path[draw, ->, line width=1pt] (n00) -- (n10) node [pos =0.5, above] {$\alpha$};
\path[draw, ->, line width=1pt] (n20) -- (n10) node [pos =0.5, above] {$\beta_1$};
\path[draw, ->, line width=1pt] (n20) -- (n30) node [pos =0.5, above] {$\beta_0$};
\path[draw, ->, line width=1pt] (n40) -- (n30) node [pos =0.5, above] {$\beta_1$};
\path[draw, ->, line width=1pt] (n40) -- (n50) node [pos =0.5, above] {$\beta_0$};
\path[draw, ->, line width=1pt] (n53) -- (n52) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=1pt] (n51) -- (n52) node [pos =0.5, right] {$\beta_1$};
\path[draw, ->, line width=1pt] (n51) -- (n50) node [pos =0.5, right] {$\beta_0$};
\node at (-0.3,0) {\small $h(a)$};
\node at (5.3,3) {\small $h(a)$};
\node at (5.78,0) {\small $h(b_t)$=$h(b_{t'})$};
\draw [help lines] (0,0) grid (5,3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1512.01681 | arxiv | 2015-12-08T02:07:01 |
|
Grid M_3. No 1-2 pattern. | \documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{amssymb}
\usepackage{graphicx,amsmath, amsfonts}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{color}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=1]
\usetikzlibrary{calc}
\foreach \n in {0,1,2,3,4,5} {
\foreach \m in {0,1,2,3,4,5} {
\node[fill=gray, circle, scale=0.3] (n\m\n) at (\m,\n) {$$};
}
}
\path[draw, ->, line width=1pt] (n35) -- (n34) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=1pt] (n33) -- (n34) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=3pt] (n15) -- (n14) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=3pt] (n13) -- (n14) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=3pt] (n04) -- (n05) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=1pt] (n04) -- (n03) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n24)--(n25) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=3pt] (n24)--(n23) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n44)--(n45) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=1pt] (n44)--(n43) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n00) -- (n10) node [pos =0.5, above] {$\alpha$};
\path[draw, ->, line width=1pt] (n20) -- (n10) node [pos =0.5, above] {$\beta_1$};
\path[draw, ->, line width=1pt] (n20) -- (n30) node [pos =0.5, above] {$\beta_0$};
\path[draw, ->, line width=1pt] (n40) -- (n30) node [pos =0.5, above] {$\beta_1$};
\path[draw, ->, line width=1pt] (n40) -- (n50) node [pos =0.5, above] {$\beta_0$};
\path[draw, ->, line width=1pt] (n55) -- (n54) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=1pt] (n53) -- (n54) node [pos =0.5, right] {$\beta_1$};
\path[draw, ->, line width=1pt] (n53) -- (n52) node [pos =0.5, right] {$\beta_0$};
\path[draw, ->, line width=1pt] (n51) -- (n52) node [pos =0.5, right] {$\beta_1$};
\path[draw, ->, line width=1pt] (n51) -- (n50) node [pos =0.5, right] {$\beta_0$};
\path[draw,dashed, ->, line width=1pt] (n00) -- (n01) node [pos =0.5, right] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n11) -- (n10) node [pos =0.5, right] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n20) -- (n21) node [pos =0.5, right] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n31) -- (n30) node [pos =0.5, right] {$\beta$};
\path[draw,dashed, ->, line width=3pt] (n40) -- (n41) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n02) -- (n01) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n11) -- (n12) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n22) -- (n21) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=3pt] (n31) -- (n32) node [pos =0.5, right] {$\beta$};
\path[draw,->, line width=3pt] (n42) -- (n41) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n02) -- (n03) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n13) -- (n12) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=3pt] (n22) -- (n23) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=3pt] (n33) -- (n32) node [pos =0.5, right] {$\beta$};
\path[draw,->, line width=1pt] (n42) -- (n43) node [pos =0.5, right] {$\beta$};
\path[draw,dashed, ->, line width=3pt] (n51) -- (n41) node [pos =0.5, above] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n42) -- (n52) node [pos =0.5, above] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n53) -- (n43) node [pos =0.5, above] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n44) -- (n54) node [pos =0.5, above] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n55) -- (n45) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n31) -- (n41) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n42) -- (n32) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n33) -- (n43) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n44) -- (n34) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n35) -- (n45) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n31) -- (n21) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n22) -- (n32) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n33) -- (n23) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n24) -- (n34) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n35) -- (n25) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n11) -- (n21) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n22) -- (n12) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n13) -- (n23) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n24) -- (n14) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n15) -- (n25) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n11) -- (n01) node [pos =0.5, above] {$\alpha$};
\path[draw, ->, line width=1pt] (n02) -- (n12) node [pos =0.5, above] {$\alpha$};
\path[draw, ->, line width=1pt] (n13) -- (n03) node [pos =0.5, above] {$\alpha$};
\path[draw, ->, line width=3pt] (n04) -- (n14) node [pos =0.5, above] {$\alpha$};
\path[draw, ->, line width=3pt] (n15) -- (n05) node [pos =0.5, above] {$\alpha$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1512.01681 | arxiv | 2015-12-08T02:07:01 |
|
Grid constructed by T_. Diagonal (``d'') edges are bold and border (``b'') edges are dashed. Labels of the edges in the NW-corner are n,,d,b and w,,d,b so they form a 1-2 pattern. | \documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{amssymb}
\usepackage{graphicx,amsmath, amsfonts}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{color}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=1.65]
\usetikzlibrary{calc}
\foreach \n in {0,1,2,3} {
\foreach \m in {0,1,2,3,4,5} {
\node[fill=gray, circle, scale=0.3] (n\m\n) at (\m,\n) {$$};
}
}
\path[draw, ->, line width=1pt] (n00) -- (n10) node [pos =0.5, above] {$\alpha$};
\path[draw, ->, line width=1pt] (n20) -- (n10) node [pos =0.5, above] {$\beta_1$};
\path[draw, ->, line width=1pt] (n20) -- (n30) node [pos =0.5, above] {$\beta_0$};
\path[draw, ->, line width=1pt] (n40) -- (n30) node [pos =0.5, above] {$\beta_1$};
\path[draw, ->, line width=1pt] (n40) -- (n50) node [pos =0.5, above] {$\beta_0$};
\path[draw, ->, line width=1pt] (n53) -- (n52) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=1pt] (n51) -- (n52) node [pos =0.5, right] {$\beta_1$};
\path[draw, ->, line width=1pt] (n51) -- (n50) node [pos =0.5, right] {$\beta_0$};
\path[draw,dashed, ->, line width=1pt] (n00) -- (n01) node [pos =0.5, right] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n11) -- (n10) node [pos =0.5, right] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n20) -- (n21) node [pos =0.5, right] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n31) -- (n30) node [pos =0.5, right] {$\beta$};
\path[draw,dashed, ->, line width=3pt] (n40) -- (n41) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n02) -- (n01) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n11) -- (n12) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n22) -- (n21) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=3pt] (n31) -- (n32) node [pos =0.5, right] {$\beta$};
\path[draw,->, line width=3pt] (n42) -- (n41) node [pos =0.5, right] {$\beta$};
\path[draw, ->, line width=1pt] (n02) -- (n03) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=1pt] (n13) -- (n12) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=3pt] (n22) -- (n23) node [pos =0.5, right] {$\alpha$};
\path[draw, ->, line width=3pt] (n33) -- (n32) node [pos =0.5, right] {$\alpha$};
\path[draw,->, line width=1pt] (n42) -- (n43) node [pos =0.5, right] {$\alpha$};
\path[draw,dashed, ->, line width=3pt] (n51) -- (n41) node [pos =0.5, above] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n42) -- (n52) node [pos =0.5, above] {$\beta$};
\path[draw,dashed, ->, line width=1pt] (n53) -- (n43) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n31) -- (n41) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n42) -- (n32) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n33) -- (n43) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n31) -- (n21) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n22) -- (n32) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n33) -- (n23) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n11) -- (n21) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n22) -- (n12) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=3pt] (n13) -- (n23) node [pos =0.5, above] {$\beta$};
\path[draw, ->, line width=1pt] (n11) -- (n01) node [pos =0.5, above] {$\alpha$};
\path[draw, ->, line width=1pt] (n02) -- (n12) node [pos =0.5, above] {$\alpha$};
\path[draw, ->, line width=1pt] (n13) -- (n03) node [pos =0.5, above] {$\alpha$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1512.01681 | arxiv | 2015-12-08T02:07:01 |
|
Layered structure of verifiable FT computation. | \documentclass[twocolumn,footinbib,floatfix,reprint]{revtex4-1}
\usepackage{graphicx,amsmath,amsfonts,algorithm}
\usepackage{amssymb}
\usepackage{color}
\usepackage[colorlinks=true,citecolor=red,linkcolor=brown,urlcolor=orange]{hyperref}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes}
\usetikzlibrary{calc,3d, arrows.meta, decorations.markings,math}
\begin{document}
\begin{tikzpicture}[every node/.style={%
rectangle,
rounded corners=0.4cm,
align=center,
draw,
thick,
minimum height=2cm,
shade,
shading=radial,
inner color=lightgray!20,
outer color=lightgray!50,font=\large
}]
\node [minimum width=13.7cm] at (0,2.10) {Ising Sampler and Test Computations MBQC \\ (Logical layer)};
\node [minimum width=6.8cm] at (-3.45,0) {Non-adaptive `teleported' gates \\ (Logical layer)};
\node [minimum width=6.8cm] at (3.45,0) {Distillation of magic and X states \\ (Logical layer)};
\node [minimum width=13.7cm] at (0,-2.10) {Blindness on 3D cluster-state MBQC \\ (Physical layer)};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.09568 | arxiv | 2017-03-29T02:08:23 |
|
%The left-hand side illustrates the%procedure for implementing a logical $Z$ rotation on a double-well%qubit by smoothly varying the depths of the wells. The right-hand side%illustrates the procedure for implementing an $X$ rotation by%temporarily lowering the barrier height. The variation of well depths implements a Z rotation (left-hand side), while lowering the barrier height implements an X rotation (right-hand side). | \documentclass[12pt]{article}
\usepackage{graphicx, amssymb, amsmath, fullpage, dsfont, bm, epsfig, multirow, amsthm, url, authblk, MnSymbol}
\usepackage{tikz}
\usetikzlibrary{backgrounds,fit,decorations.pathreplacing,calc}
\begin{document}
\begin{tikzpicture}
\draw [thick, blue] (0,0) to [out=0,in=180] (1,-1)
to [out=0,in=180] (2,0) to [out=0,in=180] (3,-1) to [out=0,in=180] (4,0) ;
\draw [thick, blue] (6,0) to [out=0,in=180] (7,-1)
to [out=0,in=180] (8,0) to [out=0,in=180] (9,-1) to [out=0,in=180] (10,0) ;
%2nd line
\draw [thick, blue] (0,-2) to [out=0,in=180] (1,-2.5)
to [out=0,in=180] (2,-2) to [out=0,in=180] (3,-3) to [out=0,in=180] (4,-2) ;
\draw [thick, blue] (6,-2) to [out=0,in=180] (7,-2.5)
to [out=0,in=180] (8,-2) to [out=0,in=180] (9,-2.5) to [out=0,in=180]
(10,-2) ;
%3rd line
\draw [thick, blue] (0,-4) to [out=0,in=180] (1,-5)
to [out=0,in=180] (2,-4) to [out=0,in=180] (3,-5) to [out=0,in=180] (4,-4) ;
\draw [thick, blue] (6,-4) to [out=0,in=180] (7,-5)
to [out=0,in=180] (8,-4) to [out=0,in=180] (9,-5) to [out=0,in=180]
(10,-4) ;
%Time arrow
\draw [->] (5,-3.5) -- (5,-1);
\node at (5,-4) {time};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.00454 | arxiv | 2017-03-03T02:00:17 |
|
%Illustration of Our implementation of an entangling two-qubit gate. If the center two wells are occupied (corresponding to the logical 10 state), the attraction between particles induces a phase rotation. In the case that exactly one of the two center wells is occupied, there is a tunneling amplitude into the noncoding subspace. | \documentclass[12pt]{article}
\usepackage{graphicx, amssymb, amsmath, fullpage, dsfont, bm, epsfig, multirow, amsthm, url, authblk, MnSymbol}
\usepackage{tikz}
\usetikzlibrary{backgrounds,fit,decorations.pathreplacing,calc}
\begin{document}
\begin{tikzpicture}
\coordinate (a) at (1,0);
\draw [thick, blue] ($(a) + (0,0)$) to [out=0,in=180] ($(a) + (1,-1)$)
to [out=0,in=180] ($(a) + (2,0)$) to [out=0,in=180] ($(a) + (3,-1)$) to
[out=0,in=180] ($(a) + (4,0)$) to [out=0,in=180] ($(a) + (5,-1)$)
to [out=0,in=180] ($(a) + (6,0)$) to [out=0,in=180] ($(a) + (7,-1)$) to
[out=0,in=180] ($(a) + (8,0)$) ;
%2nd line
\draw [thick, blue] ($(a) + (0,-2)$) to [out=0,in=180] ($(a) + (1,-3)$)
to [out=0,in=180] ($(a) + (2,-2)$) to [out=0,in=180] ($(a) + (3.5,-3)$)
to [out=0,in=180] ($(a) + (4,-2)$) to [out=0,in=180] ($(a) + (4.5,-3)$)
to [out=0,in=180] ($(a) + (6,-2)$) to [out=0,in=180] ($(a) + (7,-3)$) to
[out=0,in=180] ($(a) + (8,-2)$) ;
%3rd line
\draw [thick, blue] ($(a) + (0,-4)$) to [out=0,in=180] ($(a) + (1,-5)$)
to [out=0,in=180] ($(a) + (2,-4)$) to [out=0,in=180] ($(a) + (3,-5)$) to
[out=0,in=180] ($(a) + (4,-4)$) to [out=0,in=180] ($(a) + (5,-5)$)
to [out=0,in=180] ($(a) + (6,-4)$) to [out=0,in=180] ($(a) + (7,-5)$) to
[out=0,in=180] ($(a) + (8,-4)$) ;
% Time
\draw [->] (0,-4) -- (0,0);
\node at (0,-4.5) {time};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.00454 | arxiv | 2017-03-03T02:00:17 |
|
Hierarchy of the main functions in CANONICA. Each block lists the public functions called by the function in the blocks title. | \documentclass[preprint,12pt]{elsarticle}
\usepackage[%
pdftex,%
colorlinks=true,%
hyperindex,%
plainpages=false,%
pagebackref=false,%
bookmarksopen,%
bookmarksnumbered %
]{hyperref}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning, calc}
\begin{document}
\begin{tikzpicture}[thick,scale=0.9, every node/.style={scale=0.9}]
\clip(-4,-2) rectangle (11,8);
\def\frow{0}
\def\srow{7}
\def\mrow{\frow*0.5+\srow*0.5}
\def\vadd{-4}
\def\vvadd{-4}
\def\vvvadd{3}
\small
\tikzset{
bignodeone/.style={rectangle,rounded corners, draw=black, top color=white, inner sep=1em,minimum width=5.80cm, minimum height=1.2cm, text centered},
regnodeone/.style={rectangle,draw=black, top color=white, inner sep=1pt,minimum width=5.8cm, minimum height=1cm, text centered},
bignode/.style={rectangle,rounded corners, draw=black, top color=white, inner sep=1em,minimum width=5.80cm, minimum height=3cm, text centered},
regnode/.style={rectangle,draw=black, top color=white, inner sep=1pt,minimum width=5.8cm, minimum height=1cm, text centered},
nregnode/.style={rectangle,draw=white, top color=white, inner sep=1pt,minimum width=1.2cm, minimum height=0.4cm,text width=5cm}
}
\node[bignodeone] (axiif) at (\mrow,3.5+\vvvadd) {};
\node[regnode] (RecursivelyTransformSectors) at (\mrow, 4.5+\vvvadd) {\texttt{RecursivelyTransformSectors}};
\node[nregnode] (pTransformNextSector) at (\mrow,3.6+\vvvadd) {\texttt{TransformNextSector}};
\node[bignode] (axiif) at (\mrow,3.5) {};
\node[regnode] (sTransformNextSector) at (\mrow, 4.5) {\texttt{TransformNextSector}};
\node[nregnode] (pTransformNextDiagonalBlock) at (\mrow,3.6) {\texttt{TransformNextDiagonalBlock}};
\node[nregnode] (pTransformOffDiagonalBlock) at (\mrow,3.0) {\texttt{TransformOffDiagonalBlock}};
\node[nregnode] (pTransformDlogToEpsForm) at (\mrow,2.4) {\texttt{TransformDlogToEpsForm}};
\node[bignode] (axiif) at (\frow,3.5+\vadd) {};
\node[regnode] (sTransformNextDiagonalBlock) at (\frow, 4.5+\vadd) {\texttt{TransformNextDiagonalBlock}};
\node[nregnode] (pCalculateNexta) at (\frow,3.6+\vadd) {\texttt{CalculateNexta}};
\node[nregnode] (pTransformDiagonalBlock) at (\frow,3.0+\vadd) {\texttt{TransformDiagonalBlock}};
\node[bignodeone] (axiif) at (\srow,3.5+\vvadd) {};
\node[regnode] (sTransformOffDiagonalBlock) at (\srow, 4.5+\vvadd) {\texttt{TransformOffDiagonalBlock}};
\node[nregnode] (pCalculateNextSubsectorD) at (\srow,3.6+\vvadd) {\texttt{CalculateNextSubsectorD}};
\draw[draw=black,line width=0.5mm,solid, -triangle 90] (\mrow-3,3.6+\vvvadd) .. controls (\mrow-4.5,3.6+\vvvadd-0.3) and (\mrow-4.5,3.6+\vvvadd-1.7) .. (\mrow-3, 4.5);
\draw[draw=black,line width=0.5mm,solid, -triangle 90] (\mrow-3,3.6) .. controls (\mrow-4.5,3.6) and (\frow-6,3.6+\vvvadd-3.6) .. (\frow-3, 4.5+\vadd);
\draw[draw=black,line width=0.5mm,solid, -triangle 90] (\mrow+3,3.0) .. controls (\srow+4.5,3.0) and (\srow+4.5,\vvvadd-1) .. (\srow+3, 4.5+\vadd);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1705.06252 | arxiv | 2017-05-18T02:10:20 |
|
A u-iceberg J. | \documentclass[12pt,a4paper,reqno]{amsart}
\usepackage{amsmath,amssymb,amsthm,calc,verbatim,enumitem,tikz,url,hyperref,mathrsfs,cite}
\usetikzlibrary{shapes.misc,calc,intersections,patterns,decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[>=latex,scale=0.9]
\draw (0,0) -- (12,0) (0,0) -- (12,3);
\draw (3,0.75) -- (4,2.25) -- (9,2.25);
\draw [<->,densely dashed] (3,2.75) -- node [above] {$O\big(\gamma/\sigma(u)\big)$} (9,2.75);
\draw [<->,densely dashed] (1.5,0.75) -- node [left] {$O(\gamma)$} (1.5,2.25);
\node at (4.5,1.7) {$J$};
\draw [->] (11,2.75) -- ($(11,2.75)!0.5cm!(10,6.75)$);
\node at ($(11,2.75)!0.8cm!(10,6.75)$) {$u$};
\draw [->] (11,0) -- (11,0.5);
\node at (11,0.8) {$u^*$};
\draw [->] (3.5,1.5) -- ($(3.5,1.5)!0.5cm!(2,2.5)$);
\node at ($(3.5,1.5)!0.9cm!(2,2.5)$) {$u_0$};
\draw (3.5,0) arc (0:atan(0.25):3.5);
\pgfmathparse{atan(0.125)};
\node at (\pgfmathresult:4.4) {$\sigma(u)$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1406.6680 | arxiv | 2015-07-23T02:08:06 |
|
The partial order on the polytopes P_431,w with different w. | \documentclass{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb,amsthm,mathrsfs,latexsym,mathtools,mathdots,enumerate,tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[>=triangle 45,xscale=1.6,y=-1cm, yscale=1.2]
\node[draw] (n422) at (1,0) {422};
\node[draw] (n332) at (2,0) {332};
\node[draw] (n431) at (3,0) {431};
\node[draw,dashed] (n2222) at (0,1) {2222};
\node[draw,dashed] (n3221) at (1,1) {3221};
\node[draw] (n4211) at (2,1) {4211};
\node[draw] (n3311) at (3,1) {3311};
\node[draw,dotted] (n22211) at (1,2) {22211};
\node[draw,dashed] (n32111) at (2,2) {32111};
\node[draw] (n41111) at (3,2) {41111};
\node[draw,dotted] (n221111) at (2,3) {221111};
\node[draw,dotted] (n311111) at (3,3) {311111};
\node[draw,dotted] (n2111111) at (2,4) {2111111};
\node[draw,dotted] (n11111111) at (2,5) {11111111};
%Arrows 1 lvlv
\draw [->] (n422) -- (n2222);
\draw [->] (n422) -- (n3221);
\draw [->] (n422) -- (n4211);
\draw [->] (n332) -- (n3221);
\draw [->] (n332) -- (n3311);
\draw [->] (n431) -- (n3221);
\draw [->] (n431) -- (n4211);
\draw [->] (n431) -- (n3311);
%Arrows 2 lvlv
\draw [->] (n2222) -- (n22211);
\draw [->] (n3221) -- (n22211);
\draw [->] (n3221) -- (n32111);
\draw [->] (n4211) -- (n22211);
\draw [->] (n4211) -- (n32111);
\draw [->] (n4211) -- (n41111);
\draw [->] (n3311) -- (n32111);
%Arrows 3 lvlv
\draw [->] (n22211) -- (n221111);
\draw [->] (n32111) -- (n221111);
\draw [->] (n32111) -- (n311111);
\draw [->] (n41111) -- (n311111);
\draw [->] (n41111) -- (n221111);
%Arrows 4 lvlv
\draw [->] (n221111) -- (n2111111);
\draw [->] (n311111) -- (n2111111);
%Arrows 5 lvlv
\draw [->] (n2111111) -- (n11111111);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1405.4718 | arxiv | 2015-11-26T02:12:17 |
|
The growth mechanism in the unbalanced setting. | \documentclass[12pt,a4paper,reqno]{amsart}
\usepackage{amsmath,amssymb,amsthm,calc,verbatim,enumitem,tikz,url,hyperref,mathrsfs,cite}
\usetikzlibrary{shapes.misc,calc,intersections,patterns,decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[>=latex]
\draw (0,0) rectangle (0.5,3) (0.5,0) rectangle (8,3) (8,0) rectangle (8.5,6);
\draw (11,0) -- (8,0) -- (8,6) -- (11,6);
\draw [dashed] (11,0) -- (12,0) (11,6) -- (12,6) (8,3) -- (9.5,3);
\draw (0,3) -- (8,6);
\begin{scope}
\clip (0.5,0) rectangle (12,3);
\foreach \x in {0,0.5,...,2}
\draw (\x,3) -- (\x+0.8,2) -- (\x+0.9,1) -- (\x,0);
\end{scope}
\begin{scope}
\clip (8.5,0) rectangle (12,6);
\foreach \x in {7,7.5,...,9}
\draw (\x,6) -- (\x+1.6,4) -- (\x+1.8,2) -- (\x,0);
\end{scope}
\draw [->] (5,1.7) -- node [below] {1} (6,1.7);
\draw [->] (6.5,3.5) -- node [right] {2} (6.5,4.5);
\draw [->] (11,3) -- node [below] {3} (12,3);
\draw [->] (0.5,5) -- (0.5,5.8) node [above] {$u^*$};
\draw [->] (0.5,5) -- (1.3,5) node [right] {$u^\perp$};
\draw (0.25,2) -- (-0.5,2) node [left] {$R_0$};
\node at (3.5,1.5) {$R_1$};
\node at (11.5,4.5) {$R_3$};
\draw (8.25,0.6) -- (7.75,0.6) node [left] {$R_2$};
\node at (5,4) {$T$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1406.6680 | arxiv | 2015-07-23T02:08:06 |
|
The sequence of droplets D_0 D_1 D_2. | \documentclass[12pt,a4paper,reqno]{amsart}
\usepackage{amsmath,amssymb,amsthm,calc,verbatim,enumitem,tikz,url,hyperref,mathrsfs,cite}
\usetikzlibrary{shapes.misc,calc,intersections,patterns,decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[>=latex]
\path [name path=C1] (10:7*7/6) circle (3);
\path [name path=C2] (-5:7*7/6) circle (3);
\path [name path=C3] (-20:7) circle (3);
\pgfresetboundingbox
\draw (0:0) -- (20:8);
\draw [densely dashed] (0:0) -- (10:9);
\draw [densely dashed] (0:0) -- (-5:9);
\draw (0:0) -- (-20:8);
\foreach \x in {3,4,...,7}
\draw (20:\x) -- (10:\x*7/6) -- (-5:\x*7/6) -- (-20:\x);
\draw (-15:2) -- ++(0,-1) node[below] {$D_0$};
\draw (-15:3.5) -- ++(0,-1) node[below] {$D_1\setminus D_0$};
\node at (-0.4,0) {$x_0$};
\node at (-5:10) {$L_u^+=L_v^-$};
\draw [->] (20:6.5) -- ++(110:0.5);
\path (20:6.5) -- ++(110:0.8) node {$u^+$};
\draw [->] (-20:6.5) -- ++(-110:0.5);
\path (-20:6.5) -- ++(-110:0.8) node {$u^-$};
\path [name intersections={of=C2 and C1,by=Q1}];
\path [name intersections={of=C2 and C3,by=Q2}];
\coordinate (P1) at ($(10:7*7/6) !0.5! (-5:7*7/6)$);
\coordinate (P2) at ($(-5:7*7/6) !0.5! (-20:7)$);
\draw [->] (P1) -- ($(P1)!0.5cm!(Q1)$);
\draw [->] (P2) -- ($(P2)!-0.5cm!(Q2)$);
\node at ($(P1)!0.8cm!(Q1)$) {$v$};
\node at ($(P2)!-0.8cm!(Q2)$) {$u$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1406.6680 | arxiv | 2015-07-23T02:08:06 |
|
A u^r-crossed u^r-strip S together with a possible (u^r,)-partition for S A in which a_1=a_2=a_4=a_5=1 and a_3=3. | \documentclass[12pt,a4paper,reqno]{amsart}
\usepackage{amsmath,amssymb,amsthm,calc,verbatim,enumitem,tikz,url,hyperref,mathrsfs,cite}
\usetikzlibrary{shapes.misc,calc,intersections,patterns,decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[>=latex,scale=0.9]
\draw (-0.1,-0.6) -- (0,0) (1,6) -- (1.1,6.6);
\fill [pattern=north west lines] (-0.3,-0.6) -- (-0.1,-0.6) -- (1.1,6.6) -- (0.9,6.6) -- cycle;
\draw (8.4,0) -- (0,0) -- (1,6) -- (9.4,6) -- cycle;
\foreach \x in {1,2,...,6}
\draw [densely dotted] (1.2*\x,0) -- (1.2*\x+1,6);
\node [circle,draw] at (0.9,1.8) {$\gamma$};
\node [circle,draw] at (2.6,4.8) {$\gamma$};
\node [circle,draw] at (7.2,3.6) {$\gamma$};
\node [circle,draw] at (8,1.2) {$\gamma$};
\draw (3.3,4.2) -- (6.4,4.2) -- (6,1.8) -- (4.5,1.8) -- cycle;
\node at (5,3.1) {$D$};
\draw [->] (8.9,3) -- ++(0.6,-0.1);
\path (8.9,3) ++(0.9,-0.15) node {$u^r$};
\node at (-0.5,3) {$\H_{u^r}$};
\path [name path=P1] (2.6,1.2) -- ++(1.8,-0.3);
\path [name path=P2] (3.6,0) -- (4,2.4);
\path [name intersections={of=P1 and P2,by=I}];
\draw [<->] (2.6,1.2) -- node [above] {$\lambda$} (I);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1406.6680 | arxiv | 2015-07-23T02:08:06 |
|
Since $w$ is unstable, there exists $X \in \U$ with $X\subset\H_w$. If $x\in X$ lies in the region between $\ell_w$ and $\ell_u$, then the direction $w'$ would be in $\qquasi$, by construction, which contradicts $u$ and $v$ being consecutive in $\stab\cup\qquasi$. Thus $X \subset (\H_u\cup\ell_u\big)\cap\big(\H_v\cup\ell_v\big)$, as required. | \documentclass[12pt,a4paper,reqno]{amsart}
\usepackage{amsmath,amssymb,amsthm,calc,verbatim,enumitem,tikz,url,hyperref,mathrsfs,cite}
\usetikzlibrary{shapes.misc,calc,intersections,patterns,decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[>=latex]
\node[circle,fill,inner sep=0pt,minimum size=0.15cm] at (0,0) {};
\draw (30:1) -- (-150:6) ++(-150:0.4) node {$\ell_v$};
\draw (160:1) -- (-20:6) ++(-20:0.4) node {$\ell_u$};
\draw[->] (-150:5) -- ++(120:1);
\path (-150:5) ++(120:1.4) node {$v$};
\draw[->] (-20:5) -- ++(70:1);
\path (-20:5) ++(70:1.4) node {$u$};
\draw[densely dashed] (-175:4) -- (5:4) ++(5:0.4) node {$\ell_w$};
\draw[->] (-175:2) -- ++(95:1);
\path (-175:2) ++(95:1.4) node {$w$};
\draw[densely dashed] (175:0.7) -- (-5:2.5);
\node at (-5:2.9) {$x$};
\draw[->] (-5:2.5) -- ++(85:1);
\path (-5:2.5) ++(85:1.4) node {$w'$};
\node[circle,fill,inner sep=0pt,minimum size=0.15cm] at (-5:2.5) {};
\node at (-85:2) {$\big(\H_u\cup\ell_u\big)\cap\big(\H_v\cup\ell_v\big)$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1406.6680 | arxiv | 2015-07-23T02:08:06 |
|
The figure depicts the application of Lemma~\ref{le:halfcrossed} in the proof of Lemma~\ref{le:indvert} assuming $\alpha^-(u^*)=\infty$. Included are the $\stabu$-droplets $D_{i-1}$, $D_i$ and $D_{i+1}$; the set $L_i$, which is such that $D_{i-1}\cup L_i$ is a strongly connected component of $\big[D_{i-1}\cup(D_i\cap A)\big]$; the site $x_i$ at the bottom-left corner of $D_i$; the half plane $\H_u(x_i)$, where $\sigma(u)=p^{1-\eta}$; and the minimal $u$-strip $T_i$ such that $L_i\subset T_i\cup\H_u(x_i)$, which is $u$-crossed. | \documentclass[12pt,a4paper,reqno]{amsart}
\usepackage{amsmath,amssymb,amsthm,calc,verbatim,enumitem,tikz,url,hyperref,mathrsfs,cite}
\usetikzlibrary{shapes.misc,calc,intersections,patterns,decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[>=latex,scale=1.2]
\begin{scope}
\clip (0,0) -- (5,0) -- (5.3,1.8) -- (-0.6,1.8) -- cycle;
\fill [pattern=north west lines] (-0.6,1.8) -- (5.3,1.8) -- (5.3,1.6) -- (-0.6,1.6) -- cycle;
\end{scope}
\begin{scope}
\clip (6,6) -- (-2,6) -- (-1.4,4.2) -- (5.7,4.2) -- cycle;
\fill [pattern=north west lines] (-1.6,4.2) -- (5.9,4.2) -- (5.9,4.4) -- (-1.6,4.4) -- cycle;
\end{scope}
% overall droplet
\draw (0,0) -- (5,0) -- (6,6) -- (-2,6) -- cycle;
% droplet division lines
\draw (-0.6,1.8) -- (5.3,1.8) (-1.4,4.2) -- (5.7,4.2);
% three conn comps of L
\draw (0,1.8) -- (0.3,2.4) -- (0.5,2.1) -- (0.6,2.2) -- (0.9,1.8);
\draw (1.5,1.8) -- (1.8,2) -- (2.1,1.8);
\draw (2.5,1.8) -- (3,3.5) -- (3.9,2.7) -- (4.3,1.8);
\draw [dashed,name path=H] (-2,1.66) -- (7,2.56);
% path/coordinate names
\path [name path=S1] (0,1.8) -- (0.3,2.4);
\path [name path=S2] (3.9,2.7) -- (4.3,1.8);
\path [name intersections={of=H and S1,by=P1}];
\path [name intersections={of=H and S2,by=P2}];
\path [name path=T] (0,3.2) -- (3,3.5) -- (5,3.7);
\path [name path=V1] (P1) -- ++(0,3);
\path [name path=V2] (P2) -- ++(0,3);
\path [name intersections={of=T and V1,by=Q1}];
\path [name intersections={of=T and V2,by=Q2}];
% the strip
\draw [dashed] (P1) -- (Q1) -- (Q2) -- (P2);
% labels
\node at (2.5,0.8) {$D_{i-1}=D_{u^*}$};
\node at (2.5,5.2) {$D_{i+1}=D_{-u^*}$};
\node at (-0.4,3.7) {$D_i$};
\draw (P2) ++(0,1) -- ++(0.5,0) node [right] {$T_i$};
\draw (2.9,2.4) -- ++(-1,0.3) node [left] {$L_i$};
\draw (0.3,2.1) -- (1.3,2.7) (1.8,1.9) -- (1.7,2.4);
\draw (-0.6,1.8) node [circle,fill,inner sep=0pt,minimum size=0.1cm] {} -- (-1,1.3) node [below left] {$x_i$};
\node at (7,2.2) {$\H_u(x_i)$};
\draw [->] (2.5,0) -- ++(0,-0.5);
\node at (2.5,-0.8) {$-u^*$};
\draw [->] (2.5,6) -- ++(0,0.5);
\node at (2.5,6.8) {$u^*$};
\draw [->] (5.8,4.8) -- ($(5.8,4.8)!0.5cm!(7,4.6)$);
\node at ($(5.8,4.8)!0.8cm!(7,4.6)$) {$u^r$};
\draw [->] (-1.6,4.8) -- ($(-1.6,4.8)!0.5cm!(-2.2,4.6)$);
\node at ($(-1.6,4.8)!0.8cm!(-2.2,4.6)$) {$u^l$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1406.6680 | arxiv | 2015-07-23T02:08:06 |
|
The situation in the proof of Claim~\ref{cl:partitions} is depicted assuming $z\in Z$. The size of the projection $\big|\<D-\H_u,u\>\big|$ is at most the total length of the dashed line in the $u$-norm (see \eqref{eq:partcl2}). | \documentclass[12pt,a4paper,reqno]{amsart}
\usepackage{amsmath,amssymb,amsthm,calc,verbatim,enumitem,tikz,url,hyperref,mathrsfs,cite}
\usetikzlibrary{shapes.misc,calc,intersections,patterns,decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[>=latex,scale=1.2]
\draw (-0.1,-0.6) -- (0,0) (1,6) -- (1.1,6.6);
\fill [pattern=north west lines] (-0.3,-0.6) -- (-0.1,-0.6) -- (1.1,6.6) -- (0.9,6.6) -- cycle;
\draw (5,0) -- (0,0) -- (1,6) -- (6,6);
\draw [dashed] (5,0) -- (6,0) (6,6) -- (7,6);
% droplet
\draw (3.3,4.2) -- (6.4,4.2) -- (6,1.8) -- (4.5,1.8) -- cycle;
% mountains
\draw (0.1,0.6) -- (1.5,0.8) -- (1.9,1.1) -- (1.7,1.2) -- (2,1.4) -- (1.2,1.8) -- (1.4,2) -- (1,2.4) -- (0.45,2.7);
\draw (0.5,3) -- (0.7,3.15) -- (0.55,3.3);
\draw (0.6,3.6) -- (0.9,4) -- (0.9,4.1) -- (1.1,4.3) -- (0.95,4.7) -- (0.8,4.8);
\draw (0.85,5.1) -- (1.3,5.3) -- (1.4,5.5) -- (0.95,5.7);
% nodes and labels of sites
\node [inner sep=0pt,minimum size=0.1cm,circle,fill,label=below:$x$] at (5.7,3.3) {};
\node [inner sep=0pt,minimum size=0.1cm,circle,fill,label=right:$w$] at (4.7,2.1) {};
\node [inner sep=0pt,minimum size=0.1cm,circle,fill] at (1.7,1.4) {};
\draw (1.7,1.4) -- ++(0,0.5) node [above] {$z$};
\node [inner sep=0pt,minimum size=0.1cm,circle,fill] at (1.1,1.05) {};
\draw (1.1,1.05) -- ++(0,-0.5) node [below] {$y$};
% lengths
\draw [dashed] (4.7,2.1) -- (1.7,1.4) -- (1.1,1.05) -- (0.2,1.2);
% nodes and labels of sets
\draw (0.8,2.2) -- (1.5,3.1) node [above] {$Z$};
\draw (0.6,3.15) -- (1.3,3.3) (0.9,4.4) -- (1.5,3.6);
\node at (4.2,3.7) {$D$};
\node at (5.5,0.6) {$S$};
\node at (-0.5,3) {$\H_u$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1406.6680 | arxiv | 2015-07-23T02:08:06 |
|
Power of a point Z with respect to the unit circle. | \documentclass[12pt,twocolumn]{article}
\usepackage[utf8]{inputenc}
\usepackage{standalone, tikz, pgf}
\usetikzlibrary{plotmarks}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[scale=2]
\draw (-1.2,0) -- (2.2,0);
\draw (0,0) circle (1) node [above left=40pt] {$\omega$};
% The points on the line
\draw [fill=black] (0,0) circle (0.025) node [below left] {$C$};
\draw [fill=black] (0.5,0) circle (0.025) node [below left] {$Z$};
\draw [fill=black] (2,0) circle (0.025) node [below left] {$Z'$};
\draw [fill=black] (-1,0) circle (0.025) node [below left] {$X$};
\draw [fill=black] (1,0) circle (0.025) node [below left] {$Y$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1511.05060 | arxiv | 2015-11-17T02:21:55 |
|
Roots of the first elimination ideals for the examples with respect to the unit circle S. | \documentclass[12pt,twocolumn]{article}
\usepackage[utf8]{inputenc}
\usepackage{standalone, tikz, pgf}
\usetikzlibrary{plotmarks}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[scale=2]
% Grid
% The Axis
\draw[->] (-1.2,0) -- (2.1,0) node [right] {$\mathrm{Re}$};
\draw[->] (0,-1.2) -- (0,1.4) node [above] {$\mathrm{Im}$};
% The unit circle
\draw (0,0) circle (1) node [above left=37pt] {$\mathbb{S}$};
% The Points
% The Points on the imaginary axes:
% Tick marks
\foreach \x in {-1,1}
\draw(\x,2pt) -- (\x,-2pt) node [below=1pt, right=-1pt] {\x};
\draw(2pt,1) -- (-2pt,1) node [left, below=-1pt] {$\mathrm{i}$};
\draw(2pt,-1) -- (-2pt,-1) node [left=3pt, below=-1pt] {$-\mathrm{i}$};
% The roots
\node[mark size=2pt,color=black] at (0.549,0) {\pgfuseplotmark{*}};
\node[mark size=2pt,color=black] at (1.822,0) {\pgfuseplotmark{*}};
\node[mark size=2pt,color=black] at (0.944,-0.329) {\pgfuseplotmark{*}};
\node[mark size=2pt,color=black] at (0.944,0.329) {\pgfuseplotmark{*}};
% % Example 2
\node[mark size=2pt,color=gray] at (-0.298,-0.954) {\pgfuseplotmark{square*}};
\node[mark size=2pt,color=gray] at (-0.298,0.954) {\pgfuseplotmark{square*}};
\node[mark size=2pt,color=gray] at (0.953,-0.302) {\pgfuseplotmark{square*}};
\node[mark size=2pt,color=gray] at (0.953,0.302) {\pgfuseplotmark{square*}};
%legend box
\draw[thick] (1.4,1) -- (2.8,1);
\draw[thick] (2.8,1) -- (2.8,1.7);
\draw[thick] (2.8,1.7) -- (1.4,1.7);
\draw[thick] (1.4,1.7) -- (1.4,1);
%legends
\node[mark size=2pt,color=black] at (1.6,1.5) {\pgfuseplotmark{*}};
\node at (1.6,1.5) [right=2pt] {Example 1};
\node[mark size=2pt,color=gray] at (1.6,1.2) {\pgfuseplotmark{square*}};
\node at (1.6,1.2) [right=2pt] {Example 2};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1511.05060 | arxiv | 2015-11-17T02:21:55 |
|
The six-point lattice. | \documentclass[a4paper]{article}
\usepackage{cite, amssymb}
\usepackage{amsmath}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture}
\node (nml) at (0,0) [circle,fill,label=-135:{$(n-1,l)$}] {};
\node (nmlp) at (0,2.5) [circle,fill,label=135:{$(n-1,l+1)$}] {};
\node (nl) at (2.5,0) [circle,fill,label=-90:{$(n,l)$}] {};
\node (nlp) at (2.5,2.5) [circle,fill,label=90:{$(n,l+1)$}] {};
\node (nplp) at (5,2.5) [circle,fill,label=45:{$(n+1,l+1)$}] {};
\node (npl) at (5,0) [circle,fill,label=-45:{$(n+1,l)$}] {};
\draw[thick] (nlp)--(nmlp)--(nml)--(nl)--(npl)--(nplp)--(nlp)--(nl);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.05805 | arxiv | 2017-04-20T02:09:07 |
|
(6) (7,3) (9,5,2) (9,7,3,1) (10, 8, 6, 2, 1) | \documentclass{article}
\usepackage{tikz, amsmath, amsthm, amssymb}
\usetikzlibrary{calc,decorations.pathmorphing,decorations.markings, decorations.pathreplacing,patterns,shapes,arrows}
\begin{document}
\begin{tikzpicture}[scale=0.35]
\draw[thick, smooth] (-1,0)--(4,5);
\draw[thick, smooth] (-1,0)--(4,-5);
\foreach \x in {0,...,4} {
\draw[thick, smooth] (\x, {-\x-1})--(5, {-2*\x+4});
\draw[thick, smooth] (\x, {\x+1})--(5, {2*\x-4});
}
\node at (0,0) {$6$};
\node at (1,1) {$7$};
\node at (1,-1) {$3$};
\node at (2,2) {$9$};
\node at (2,0) {$5$};
\node at (2,-2) {$2$};
\node at (3,3) {$9$};
\node at (3,1) {$7$};
\node at (3,-1) {$3$};
\node at (3,-3) {$1$};
\node at (4,4) {$10$};
\node at (4,2) {$8$};
\node at (4,0) {$6$};
\node at (4,-2) {$2$};
\node at (4,-4) {$1$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.05809 | arxiv | 2017-04-20T02:09:09 |
|
A plane overpartition % $\emptyset \prec (1) \prec' (2) \prec (2,2) \prec' (3,3,1) \prec (5,3,1) \prec' (5,4,1) \prec (5,4,1,1) \prec' (5,4,2,1)$.%} | \documentclass{article}
\usepackage{tikz, amsmath, amsthm, amssymb}
\usetikzlibrary{calc,decorations.pathmorphing,decorations.markings, decorations.pathreplacing,patterns,shapes,arrows}
\begin{document}
\begin{tikzpicture}[scale=0.5]
\draw[thick, smooth] (0,0)--(0,4)--(5,4);
\draw[thick, smooth] (0,0)--(1,0);
\draw[thick, smooth] (0,1)--(2,1);
\draw[thick, smooth] (0,2)--(4,2);
\draw[thick, smooth] (0,3)--(5,3);
\draw[thick, smooth] (1,0)--(1,4);
\draw[thick, smooth] (2,1)--(2,4);
\draw[thick, smooth] (3,2)--(3,4);
\draw[thick, smooth] (4,2)--(4,4);
\draw[thick, smooth] (5,3)--(5,4);
\node at (0.5,0.5) { 1};
\node at (0.5,1.5) {$\overline{3}$};
\node at (0.5,2.5) { 3};
\node at (0.5,3.5) { 4};
\node at (1.5,1.5) { $\overline{1}$};
\node at (1.5,2.5) { 3};
\node at (1.5,3.5) { $\overline{4}$};
\node at (2.5,2.5) { $\overline{3}$};
\node at (2.5,3.5) { $\overline{3}$};
\node at (3.5,2.5) {$\overline{2}$};
\node at (3.5,3.5) { 2};
\node at (4.5,3.5) {2};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.05809 | arxiv | 2017-04-20T02:09:09 |
|
Derivation tree for the grammar in examplegrammar with yield abab. | \documentclass{amsart}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{tikz-qtree}
\begin{document}
\begin{tikzpicture}
\tikzset{level distance=25pt}
\Tree [ .{$S$}
[ .{$Sf$}
[ .{$Sgf$}
[ .{$Ugf$}
[ .{$Bf$}
[ .{$Uf$}
[ .{$A$}
[ .{$U$}
[ .{$\varepsilon$} ] ]
[ .{$a$} ] ] ]
[ .{$b$} ] ] ]
[ .{$Ugf$}
[ .{$Bf$}
[ .{$Uf$}
[ .{$A$}
[ .{$U$}
[ .{$\varepsilon$} ] ]
[ .{$a$} ] ] ]
[ .{$b$} ] ] ] ] ] ]
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1503.01068 | arxiv | 2015-06-02T02:20:21 |
|
Slice tree arising from the derivation tree in derivationtreeslices. Each edge label indicates the slice that induces the edge. | \documentclass{amsart}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{tikz-qtree}
\begin{document}
\begin{tikzpicture}[
sibling distance=40pt,
level 3/.style={sibling distance=100pt},
slicenode/.style={circle,draw,fill=black,inner sep=1pt}
]
\Tree [ .\node[slicenode] {};
\edge node[midway] (1 i a) {} node[near start, auto=left]{$\alpha$};
[ .\node[slicenode] {};
\edge node[midway] (1 i b) {} node[near start, auto=left]{$\beta$};
[ .\node[slicenode] {};
\edge node[midway] (2 ii c) {} node[auto=left]{$\gamma$};
[ .\node[slicenode] {};
\edge node[midway] (2 iii d) {} node[near start, auto=left]{$\delta$};
[ .\node[slicenode] {};
\edge node[midway] (3 iv e) {} node[auto=left]{$\epsilon$};
[ .\node[slicenode] {};
\edge node[midway] (3 iv f) {} node[auto=left]{$\zeta$};
[ .\node[slicenode] {};
]
]
\edge node[midway] (4 v g) {} node[auto=right]{$\eta$};
[ .\node[slicenode] {};
\edge node[midway] (4 v h) {} node[auto=right]{$\theta$};
[ .\node[slicenode] {};
]
]
]
]
\edge node[midway] (5 vi i) {} node[auto=right]{$\iota$};
[ .\node[slicenode] {};
\edge node[midway] (6 vii j) {} node[auto=left]{$\kappa$};
[ .\node[slicenode] {};
\edge node[midway] (6 vii k) {} node[auto=left]{$\lambda$};
[ .\node[slicenode] {};
]
]
\edge node[midway] (7 viii l) {} node[auto=right]{$\mu$};
[ .\node[slicenode] {};
\edge node[midway] (7 viii m) {} node[auto=right]{$\nu$};
[ .\node[slicenode] {};
]
]
]
]
]
]
\draw[->] (1 i a) .. controls +(180:2cm) and +(180:2cm) .. (3 iv f);
\draw[->] (1 i a) .. controls +(180:1.7cm) and +(0:1.7cm) .. (4 v h);
\draw[->] (1 i a) .. controls +(0:1.5cm) and +(180:1.5cm) .. (6 vii k);
\draw[->] (1 i a) .. controls +(0:2cm) and +(0:2cm) .. (7 viii m);
\draw[->] (1 i b) .. controls +(180:1pt) and +(100:1cm) .. (2 ii c);
\draw[->] (1 i b) .. controls +(0:2cm) and +(70:1cm) .. (7 viii l);
\draw[->] (1 i b) .. controls +(0:1cm) and +(180:2.5cm) .. (6 vii j);
\draw[->] (2 iii d) .. controls +(180:1pt) and +(110:1cm) .. (3 iv e);
\draw[->] (2 iii d) .. controls +(0:1pt) and +(70:1cm) .. (4 v g);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1503.01068 | arxiv | 2015-06-02T02:20:21 |
|
Example of a derivation tree and two possible shortcut trees. The trees above are two drawings of the same derivation tree. In each of the derivation trees, the boxed nodes induce nodes in the shortcut tree below it. The shading of each boxed node indicates the level of its corresponding node in the shortcut tree. Here, A,B,C,D are nonterminals, f,g,h are index symbols, and a,b,c are terminals. | \documentclass{amsart}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{tikz-qtree}
\begin{document}
\begin{tikzpicture}[
level distance=25pt,
inner sep=2pt,
shortcut1/.style={rectangle,draw=black,fill=gray!0},
shortcut2/.style={rectangle,draw=black,fill=gray!20},
shortcut3/.style={rectangle,draw=black,fill=gray!90}]
\Tree [ .\node[shortcut1](r1){$Afg$};
[ .{$Bfg$}
[ .{$Dfg$}
[ .\node[shortcut2](r21){$Cg$};
[ .\node[shortcut3](r31){$a$};
]
[ .{$Ag$}
[ .\node[shortcut3](r32){$B$};
[ .{$b$}
]
]
]
]
]
[ .\node[shortcut2](r22){$b$};
]
]
[ .{$Cfg$}
[ .{$Chfg$}
[ .{$Bfg$}
[ .{$Afg$}
[ .\node[shortcut2](r23){$Dg$};
[ .{$Ag$}
[ .\node[shortcut3](r33){$B$};
[ .{$b$}
]
]
]
[ .{$Cg$}
[ .\node[shortcut3](r34){$D$};
[ .{$b$}
]
]
]
]
]
[ .{$Cfg$}
[ .\node[shortcut2](r24){$c$};
]
[ .{$Bfg$}
[ .\node[shortcut2](r25){$Ag$};
[ .\node[shortcut3](r35){$C$};
[ .{$c$}
]
]
]
]
]
]
]
]
]
\begin{scope}[level distance=25pt, shift={(0cm,-8cm)}]
\Tree [ .\node(s1){$A$};
[ .\node(s21){$C$};
[ .\node(s31){$a$};
]
[ .\node(s32){$B$};
]
]
[ .\node(s22){$b$};
]
[ .\node(s23){$D$};
[ .\node(s33){$B$};
]
[ .\node(s34){$D$};
]
]
[ .\node(s24){$c$};
]
[ .\node(s25){$A$};
[ .\node(s35){$C$};
]
]
]
\node at (-2cm,0) {$\bar{t}_1$};
\end{scope}
\begin{scope}[shift={(6cm, 0cm)}]
\Tree [ .\node[shortcut1](r1){$Afg$};
[ .{$Bfg$}
[ .{$Dfg$}
[ .{$Cg$}
[ .\node[shortcut2](r21){$a$};
]
[ .\node[shortcut2](r22){$Ag$};
[ .\node[shortcut3](r32){$B$};
[ .{$b$}
]
]
]
]
]
[ .\node[shortcut2](r23){$b$};
]
]
[ .{$Cfg$}
[ .{$Chfg$}
[ .{$Bfg$}
[ .{$Afg$}
[ .\node[shortcut2](r24){$Dg$};
[ .{$Ag$}
[ .\node[shortcut3](r33){$B$};
[ .{$b$}
]
]
]
[ .{$Cg$}
[ .\node[shortcut3](r34){$D$};
[ .{$b$}
]
]
]
]
]
[ .{$Cfg$}
[ .\node[shortcut2](r25){$c$};
]
[ .{$Bfg$}
[ .\node[shortcut2](r26){$Ag$};
[ .\node[shortcut3](r35){$C$};
[ .{$c$}
]
]
]
]
]
]
]
]
]
\end{scope}
\begin{scope}[level distance=25pt, shift={(6cm,-8cm)}]
\Tree [ .\node(s1){$A$};
[ .\node(s21){$a$};
]
[ .\node(s22){$A$};
[ .\node(s32){$B$};
]
]
[ .\node(s23){$b$};
]
[ .\node(s24){$D$};
[ .\node(s33){$B$};
]
[ .\node(s34){$D$};
]
]
[ .\node(s25){$c$};
]
[ .\node(s26){$A$};
[ .\node(s35){$C$};
]
]
]
\node at (-2cm,0) {$\bar{t}_2$};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1503.01068 | arxiv | 2015-06-02T02:20:21 |
|
Graphical representation of the correlation of the specific factor loadings obtained with the MSFA. Darker grey lines correspond to higher correlations. Correlations smaller than .25 are not shown. | \documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows,shapes, positioning}
\usepackage{amssymb}
\usepackage{color}
\usepackage{colortbl}
\begin{document}
\begin{tikzpicture}
[scale=.8,auto=left]
% con draw fai il contorno, con bottom color fai dentro
%GSE9891
\node[, ] at (-10.5,3) {GSE9891};
\node[rectangle split,rectangle split horizontal, rectangle split parts=6, draw=gray!60] (n1) at (-10.5,2) {$\phi_1$ \nodepart{two} $\lambda_{11}$ \nodepart{three} $\lambda_{21}$ \nodepart{four} $\lambda_{31}$ \nodepart{five} $\lambda_{41}$ \nodepart{six} $\lambda_{51}$};
\draw[line width=0.8mm] (-13.6,1.6) -- (-13.6,2.4);
\draw[line width=0.8mm] (-13.6,1.6) -- (-12.7,1.6);
\draw[line width=0.8mm] (-12.7,1.6) -- (-12.7,2.4);
\draw[line width=0.8mm] (-13.6,2.4) -- (-12.7,2.4);
%destra 3studio GSE26712
\node[, ] at (-1,3) {GSE26712};
\node[rectangle split,rectangle split horizontal, rectangle split parts=10, draw=gray!60] (n1) at (-1,2) {$\phi_1$ \nodepart{two} $\lambda_{13}$ \nodepart{three} $\lambda_{23}$ \nodepart{four} $\lambda_{33}$ \nodepart{five} $\lambda_{43}$ \nodepart{six} $\lambda_{53}$ \nodepart{seven} $\lambda_{63}$ \nodepart{eight} $\lambda_{73}$ \nodepart{nine} $\lambda_{83}$ \nodepart{ten} $\lambda_{93}$ };
\draw[line width=0.8mm] (-6.2,1.6) -- (-6.2,2.4);
\draw[line width=0.8mm] (-6.2,1.6) -- (-5.3,1.6);
\draw[line width=0.8mm] (-5.3,1.6) -- (-5.3,2.4);
\draw[line width=0.8mm] (-5.3,2.4) -- (-6.2,2.4);
%GSE20565
\node[, ] at (-10.5,-3) {GSE20565};
\node[rectangle split,rectangle split horizontal, rectangle split parts=7, draw=gray!60] (n2) at (-10.5,-2) {$\phi_1$ \nodepart{two} $\lambda_{12}$ \nodepart{three} $\lambda_{22}$ \nodepart{four} $\lambda_{32}$ \nodepart{five} $\lambda_{42}$ \nodepart{six} $\lambda_{52}$ \nodepart{seven} $\lambda_{62}$};
%bordino fattore comune
\draw[line width=0.8mm] (-14.1,-1.6) -- (-14.1,-2.4);
\draw[line width=0.8mm] (-14.1,-1.6) -- (-13.2,-1.6);
\draw[line width=0.8mm] (-13.2,-1.6) -- (-13.2,-2.4);
\draw[line width=0.8mm] (-14.1,-2.4) -- (-13.2,-2.4);
%TCGA
\node[, ] at (-1,-3) {TCGA};
\node[rectangle split,rectangle split horizontal, rectangle split parts=9, draw=gray!60] (n1) at (-1,-2) {$\phi_1$ \nodepart{two} $\lambda_{14}$ \nodepart{three} $\lambda_{24}$ \nodepart{four} $\lambda_{34}$ \nodepart{five} $\lambda_{44}$ \nodepart{six} $\lambda_{54}$ \nodepart{seven} $\lambda_{64}$ \nodepart{eight} $\lambda_{74}$ \nodepart{nine} $\lambda_{84}$ };
\draw[line width=0.8mm] (-5.65,-1.6) -- (-5.65,-2.4);
\draw[line width=0.8mm] (-5.65,-1.6) -- (-4.75,-1.6);
\draw[line width=0.8mm] (-4.75,-1.6) -- (-4.75,-2.4);
\draw[line width=0.8mm] (-4.75,-2.4) -- (-5.65,-2.4);
%tra studio 1 e 2
\draw[gray!100,line width=0.4mm] (-12.5,-1.5) -- (-12.1,1.5);
\draw[gray!100,line width=0.4mm] (-11.5,-1.5) -- (-11.1,1.5);
\draw[gray!30,line width=0.1mm] (-10.5,-1.5) -- (-9.1,1.5);
\draw[gray!30,line width=0.1mm] (-10.3,-1.5) -- (-8,1.5);
\draw[gray!70,line width=0.3mm] (-8.5,-1.5) -- (-7.9,1.5);
%tra studio 3 e 4
\draw[gray!30,line width=0.1mm] (-3.2,-1.5) -- (3.6,1.5);
\draw[gray!10,line width=0.01mm] (-2.2,-1.5) -- (-1.6,1.5);
%tra 1 e 3
\draw[gray!30,line width=0.1mm] (-10.9,1.5) to [out = -20, in=200] (-3.6,1.5);
%tra 1 e 4
\draw[gray!10,line width=0.01mm] (-11.9,1.5) -- (-1.2,-1.5);
\draw[gray!30,line width=0.1mm] (-8.9,1.5) -- (-1,-1.5);
%tra 2 e 4
\draw[gray!30,line width=0.1mm] (-11.5,-1.5) to [out = 25, in=150] (0,-1.5);
\draw[gray!10,line width=0.01mm] (-8.4,-1.5) to [out = 20, in=150] (2,-1.5);
%tra 2 e 3
\draw[gray!30,line width=0.1mm] (-12.6,-1.5) -- (2.5,1.5);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1611.06350 | arxiv | 2017-01-05T02:03:28 |
|
A hallway with four doorways and the slope- tube T=_^-1(D)([0,4]) along with a line of sight having slope greater than . | \documentclass[12pt]{amsart}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=1.5]
\draw[very thick] (0,0) -- (0,1);
\draw[very thick] (0,2) -- (0,4);
\draw[very thick] (1,0) -- (1,1);
\draw[very thick] (1,2) -- (1,4);
\draw[very thick] (2,0) -- (2,2);
\draw[very thick] (2,3) -- (2,4);
\draw[very thick] (3,0) -- (3,2);
\draw[very thick] (3,3) -- (3,4);
\path[fill=blue!15] (0,1) -- (3, 2.5) -- (3, 3) -- (0,1.5) -- cycle;
\draw[dashed, blue!30] (-.5,.75) -- (3.5,2.75);
\draw[dashed, blue!30] (-.5,1.25) -- (3.5,3.25);
\draw (2.75,2.75) node[yshift=-3mm] {$T$};
\draw (3,2.75) node[below right,xshift=4mm] {slope $\alpha$};
\draw[dash pattern=on 8pt off 3pt, red!60, very thick] (-2,0) -- (4.9,4);
\draw (-1,.5) node[above,yshift=1mm] {$\ell$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1705.00699 | arxiv | 2017-05-03T02:01:18 |
|
The partition P_5. | \documentclass[12pt]{amsart}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=6]
\draw[thick] (0,0) grid (1,1);
\draw[] (0,1) -- (1,0);
\draw[] (0,1) -- (1/2,0);
\draw[] (1/2,1) -- (1,0);
\draw[] (0,1) -- (1/3,0);
\draw[] (1/3,1) -- (2/3,0);
\draw[] (2/3,1) -- (1,0);
\draw[] (0,1) -- (1/4,0);
\draw[] (1/4,1) -- (2/4,0);
\draw[] (2/4,1) -- (3/4,0);
\draw[] (3/4,1) -- (1,0);
\draw[] (0,1) -- (1/5,0);
\draw[] (1/5,1) -- (2/5,0);
\draw[] (2/5,1) -- (3/5,0);
\draw[] (3/5,1) -- (4/5,0);
\draw[] (4/5,1) -- (1,0);
\draw[] (0,0) -- (1,0) node[right] {$\alpha$};
\draw[] (0,0) -- (0,1) node[above] {$t$};
\draw[] (1/2,.02) -- (1/2,0) node[below, yshift=-1] {$\frac{1}{2}$};
\draw[] (1/3,.02) -- (1/3,0) node[below, yshift=-1] {$\frac{1}{3}$};
\draw[] (2/3,.02) -- (2/3,0) node[below, yshift=-1] {$\frac{2}{3}$};
\draw[] (0,.02) -- (0,0) node[below, yshift=-1] {$0$};
\draw[] (1,.02) -- (1,0) node[below, yshift=-1] {$1$};
\draw[] (.02,1) -- (0,1) node[left, xshift=-1] {$1$};
\draw[] (.02,1/2) -- (0,1/2) node[left, xshift=-1] {$\frac{1}{2}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1705.00699 | arxiv | 2017-05-03T02:01:18 |
|
The regret equals the vertical distance between curve and tangent. | \documentclass[10pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{pgf}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=10.0cm,y=10.0cm]
\clip(-0.06431,-0.5008779149519884) rectangle (1.1419478737997253,0.15580246913580265);
\draw[line width=1.2pt,color=blue,smooth,samples=100,domain=0:1.1419478737997253] plot(\x,{(\x)*ln((\x)+1.0E-4)});
\draw[->,color=black,line width=1.2pt] (0.,0.) -- (1.1419478737997253,0.);
\draw[->,color=black,line width=1.2pt] (0.,-0.5) -- (0.,0.15580246913580265);
\draw [color=green] (0.3868, -0.4994) -- (1.1362, 0.0827);
\draw [dash pattern=on 4pt off 4pt, color=brown] (0.8,0.)-- (0.8,-0.178414847300847);
\draw [line width=2.pt, color=brown] (0.45,-0.450314607074793)-- (0.45,-0.35922847440746253);
\draw [dash pattern=on 4pt off 4pt, color=brown] (0.45,0.)-- (0.45,-0.35922847440746253);
\draw (0.4343468211923174,0.07152263374485619) node[anchor=north west,color=brown] {$s_1$};
\draw (0.790781098312178,0.0680109739369001) node[anchor=north west,color=brown] {$s_2$};
\draw (0.23,-0.38) node[anchor=north west, color=brown] {$D_{F}(s_1 ,s_2)$};
\draw (1.0330861733985859,0.1540466392318246) node[anchor=north west, color=blue] {$F$};
\draw [fill=blue] (0.8,-0.178414847300847) circle (2pt);
\draw [fill=blue] (0.45,-0.35922847440746253) circle (2pt);
\draw [fill=green] (0.45,-0.450314607074793) circle (2pt);
\draw [fill=brown] (0.45,0.) circle (2pt);
\draw [fill=brown] (0.8,0.) circle (2pt);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1701.01010 | arxiv | 2017-01-05T02:05:32 |