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Elements of the Network-Based Architecture (net-arch) wherein components interact by sending data through communications connectors. | \documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes}
\usetikzlibrary{positioning,calc}
\usetikzlibrary{arrows,decorations.markings}
\begin{document}
\begin{tikzpicture}
\node [draw, ultra thick, circle, fill=blue!05!white, minimum size=60, align=center] (top) at (0,0) {Component};
\node [draw, ultra thick, circle, fill=blue!05!white, minimum size=60, align=center] (left) at (-3,-3) {Component};
\node [draw, ultra thick, circle, fill=blue!05!white, minimum size=60, align=center] (right) at (3,-3) {Component};
\draw [very thick] (top) -- (left);
\draw [very thick] (top) -- (right);
\draw [very thick, ->, dashed] (2.0,-1.5) -- (1.5,-1.0);
\draw [very thick, ->, dashed] (1.0,-1.5) -- (1.5,-2.0);
\draw [very thick, ->, dashed] (-2.0,-1.5) -- (-1.5,-1.0);
\draw [very thick, ->, dashed] (-1.0,-1.5) -- (-1.5,-2.0);
\node [align=center] (conn) at (-2.5,0.5) {Connector};
\node [align=center] (data) at (2.5,-0.5) {Data};
\draw [thick] (data) -- (1.75,-1.25);
\draw [thick] (conn) -- (-0.9,-0.9);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.07642 | arxiv | 2016-04-27T02:11:04 |
|
The Ozy Architecture. Ozy does not define a new services interface; industry standard SOAP or RESTful interfaces should still be employed, but the Ozy Architecture does provide a better separation of concern between interface and implementation. | \documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes}
\usetikzlibrary{positioning,calc}
\usetikzlibrary{arrows,decorations.markings}
\begin{document}
\begin{tikzpicture}
\node [draw, ultra thick, circle, fill=blue!05, minimum size=60, align=center] (service) at (0,5) {Service \\\footnotesize{(Tenant)}};
\node [draw=gray, ultra thick, rectangle, fill=yellow!10, minimum width=250, minimum height=175, align=center] (bigbox) at (0,-1.1) {};
\node [draw, ultra thick, rectangle, fill=blue!05, minimum width=200, minimum height=50, align=center] (soap) at (0,2) {SOAP, REST, Database Driver, Other\\\\Component Interfaces};
\node [draw, ultra thick, circle, fill=blue!05, minimum size=60, align=center] (serviceleft) at (-2,-1) {Service\\\footnotesize{(Process)}};
\node [draw, ultra thick, circle, fill=blue!05, minimum size=60, align=center] (serviceright) at (2,-1) {Service\\\footnotesize{(Process)}};
\node [draw=gray, ultra thick, rectangle, minimum width=75, minimum height=30, align=center, text=black!80] (soap) at (2,-3.2) {Private State};
\node [draw=gray, ultra thick, rectangle, minimum width=75, minimum height=30, align=center, text=black!80] (soap) at (-2,-3.2) {Private State};
\draw [very thick] (service) -- (0,2.88) ;
\draw [dashed, very thick, ->] (0.2,3.75) -- (0.2,3.2);
\draw [dashed, very thick, <-] (-0.2,3.75) -- (-0.2,3.2);
\draw [gray, very thick, ->] (serviceleft) -- (-2,-2.65);
\draw [gray, very thick, ->] (-2,-2.65) -- (serviceleft);
\draw [gray, very thick, ->] (serviceright) -- (2,-2.65) ;
\draw [gray, very thick, ->] (2,-2.65) -- (serviceright) ;
\draw [very thick] (serviceright) -- (2,1.05) ;
\draw [very thick] (-2,1.05) -- (serviceleft) ;
\draw [dashed, very thick, ->] (-2.2,0.85) -- (-2.2,0.3);
\draw [dashed, very thick, <-] (-1.8,0.85) -- (-1.8,0.3);
\draw [dashed, very thick, ->] (2.2,0.85) -- (2.2,0.3) ;
\draw [dashed, very thick, <-] (1.8,0.85) -- (1.8,0.3);
\draw [dotted, very thick] (-3.55,1.97) -- (3.55,1.97);
\node [] (component) at (3,5.5) {Component};
\draw [thick] (component.west) -- (1,5);
\node [] (data) at (2,4) {Data};
\draw [thick] (data.west) -- (0.3,3.5);
\node [] (conn) at (-2.5,4.0) {Connector};
\draw [thick] (conn.east) -- (-0.01,3.85);
\node [text=gray] (record) at (-3.5,0.15) {record};
\draw [gray, thick] (record.east) -- (-2.2,0.55);
\node [text=gray] (functors) at (-0.5,0.4) {functors};
\draw [gray, thick] (functors.north) -- (0,1.35);
\node [text=gray] (proc) at (3.5,0.2) {procedure};
\draw [gray, thick] (proc.south) -- (2.98,-0.6);
\node [text=gray, rotate=-90] (cont) at (-4.1,-1.2) {Ozy Container};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.07642 | arxiv | 2016-04-27T02:11:04 |
|
Message routing in Ozy. Message routing is based on the Ozy Architecture where the net-arch components are Root, Tenant, Process and Thread. | \documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes}
\usetikzlibrary{positioning,calc}
\usetikzlibrary{arrows,decorations.markings}
\begin{document}
\begin{tikzpicture}
\node [] (in) at (-1.6,2.2) (in) {Message In};
\node [] (out) at (2.0,2.2) (out) {Message Out};
\draw [dashed, ultra thick, ->] (-0.2,2.0) -- (-0.2,1.35);
\draw [dashed, ultra thick, <-] (0.4,2.0) -- (0.4,1.35);
\draw [] (in) -- (-0.4,1.75);
\draw [] (out) -- (0.6,1.75);
\node [draw, circle, fill=blue!09, inner sep=2] (r) at (0.1,1.0) {R};
\draw [thick] (r.north) -- (0.1,1.9);
\draw [thick, dotted] (0.1,1.9) -- (0.1,2.3);
\node [draw, circle, fill=blue!09, inner sep=2] (tl) at (-1.3,0.0) {T};
\node [draw, circle, fill=blue!09, inner sep=2] (tc) at (0.1,0.15) {T};
\draw [gray, dotted, very thick] (tc) -- (0.1, -0.3);
\node [draw, circle, fill=blue!09, inner sep=2] (tr) at (1.5,0) {T};
\draw [gray, very thick] (r) -- (tl);
\draw [gray, very thick] (r) -- (tc);
\draw [gray, very thick] (r) -- (tr);
\node [draw, circle, fill=blue!09, inner sep=2] (pl) at (-2.3,-1.0) {P};
\draw [gray, dotted, very thick] (pl) -- (-2.3, -1.5);
\node [draw, circle, fill=blue!09, inner sep=2, dashed] (plc) at (-2.0,-1.8) {P};
\node [draw, circle, fill=blue!09, inner sep=2] (pc) at (-1.3,-1.0) {P};
\draw [gray, dotted, very thick] (pc) -- (-1.3, -1.5);
\node [draw, circle, fill=blue!09, inner sep=2] (prc) at (-0.5,-1.8) {P};
\node [draw, circle, fill=blue!09, inner sep=2] (pr) at (-0.3,-1.0) {P};
\draw [gray, dotted, very thick] (pr) -- (-0.3, -1.5);
\draw [gray, very thick] (tl) -- (pl);
\draw [gray, very thick] (tl) -- (plc);
\draw [gray, very thick] (tl) -- (pc);
\draw [gray, very thick] (tl) -- (prc);
\draw [gray, very thick] (tl) -- (pr);
\node [draw, circle, fill=blue!09, inner sep=2] (prr) at (1.5,-1.0) {P};
\draw [gray, dotted, very thick] (prr) -- (1.5, -1.5);
\draw [gray, very thick] (tr) -- (prr);
\node [draw, circle, fill=blue!09, inner sep=1, dashed] (thll) at (-2.0,-3.5) {Th};
\node [draw, circle, fill=blue!09, inner sep=1, dashed] (thlc) at (-2.4,-2.8) {Th};
\node [draw, circle, fill=blue!09, inner sep=1, dashed] (thlr) at (-1.6,-2.8) {Th};
\draw [gray, very thick] (plc) -- (thll);
\draw [gray, very thick] (plc) -- (thlc);
\draw [gray, very thick] (plc) -- (thlr);
\node [draw, circle, fill=blue!09, inner sep=1] (thrl) at (-0.9,-2.8) {Th};
\node [draw, circle, fill=blue!09, inner sep=1] (thrr) at (-0.1,-2.8) {Th};
\draw [gray, very thick] (prc) -- (thrr);
\draw [gray, very thick] (prc) -- (thrl);
\node [draw, circle, fill=blue!09, inner sep=1.5] (r) at (-3.9,-4.5) {R};
\node [] (r) at (-3.2,-4.5) {Root};
\node [draw, circle, fill=blue!09, inner sep=1.5] (r) at (-2.1,-4.5) {T};
\node [] (r) at (-1.1,-4.5) {Tenant};
\node [draw, circle, fill=blue!09, inner sep=1.5] (r) at (0.3,-4.5) {P};
\node [] (r) at (1.2,-4.5) {Process};
\node [draw, circle, fill=blue!09, inner sep=0.1] (r) at (2.5,-4.5) {Th};
\node [] (r) at (3.4,-4.5) {Thread};
\node [draw, circle, fill=blue!09, minimum width=14, dashed, thick] (r) at (-3.5,-5.3) {};
\node [] (r) at (-1.6,-5.3) {Partially Terminated};
\node [draw, circle, fill=blue!09, minimum width=14, thick] (r) at (0.5,-5.3) {};
\node [] (r) at (2.3,-5.3) {Partially Activated};
\draw [gray, very thick] (-2.7, -6.1) -- (-1.9, -6.1);
\node [] (r) at (-0.9,-6.1) {Connector};
\draw [ultra thick, ->, dashed] (0.5, -6.1) -- (1.3, -6.1);
\node [] (r) at (2.2,-6.1) {Message};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.07642 | arxiv | 2016-04-27T02:11:04 |
|
Heterogeneous services on an enterprise system. The Ozy container aims to elegantly orchestrate these diverse services. | \documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes}
\usetikzlibrary{positioning,calc}
\usetikzlibrary{arrows,decorations.markings}
\begin{document}
\begin{tikzpicture}
\node [cloud, fill=blue!02, draw,cloud puffs=12,cloud puff arc=140, aspect=2, inner ysep=7em] {};
\node[draw, ultra thick, fill=white, inner sep=.8em, rectangle, font=\large] (catavolt) {\textbf{RMAD}};
\node[draw, thick, fill=white, rectangle, align=center, minimum height=.8cm,minimum width=2.6cm, inner sep=0cm] (sap) at (-3.1,-5.5) {SAP};
\node[draw, thick, fill=white, rectangle, align=center, minimum height=.8cm,minimum width=2.6cm, inner sep=0cm] (erp) at (0,-5.5) {Legacy ERP};
\node[draw, thick, fill=white, rectangle, align=center, minimum height=.8cm,minimum width=2.6cm, inner sep=0cm] (dataextraction) at (3.1,-5.5) {Data Extraction\\\{external use only\}};
\node[draw, thick, fill=white, rectangle, align=center, minimum height=.8cm,minimum width=2.6cm, inner sep=0cm] (media) at (-5.0,1) {Media};
\node[draw, thick, fill=white, rectangle, align=center, minimum height=.8cm,minimum width=2.6cm, inner sep=0cm] (bigdata) at (-5.0,-1) {Big Data};
\node[draw, thick, fill=white, rectangle, align=center, minimum height=.8cm,minimum width=2.6cm, inner sep=0cm] (social) at (5.0,1) {Social Networking\\for Business};
\node[draw, thick, fill=white, cylinder, shape border rotate=90, aspect=0.2, align=center, minimum height=1cm,minimum width=2.6cm, inner sep=0cm] at (5.0,-1) (metadata) {Metadata};
\node[draw, thick, rectangle, align=center, minimum height=.8cm,minimum width=2.6cm, inner sep=0cm] (phone) at (-3.1,5.5) {Phone};
\node[draw, thick, rectangle, align=center, minimum height=.8cm,minimum width=2.6cm, inner sep=0cm] (tablet) at (0,5.5) {Tablet};
\node[draw, thick, rectangle, align=center, minimum height=.8cm,minimum width=2.6cm, inner sep=0cm] (thing) at (3.1,5.5) {Thing};
\draw [thick] (catavolt) -- (media);
\draw [thick] (catavolt) -- (bigdata);
\draw [thick] (catavolt) -- (social);
\draw [thick] (catavolt) -- (metadata);
\draw [thick] (catavolt) -- (sap);
\draw [thick] (catavolt) -- (erp);
\draw [thick] (catavolt) -- (dataextraction);
\draw [thick] (catavolt) -- (phone);
\draw [thick] (catavolt) -- (tablet);
\draw [thick] (catavolt) -- (thing);
\node[draw, thick, fill=white, ellipse, minimum height=.8cm,minimum width=1.4cm] at (-2.2,.6) {File};
\node[draw, thick, fill=white, ellipse, align=center, minimum height=.8cm, minimum width=1.4cm, inner sep=0cm] at (-2.2,-.6) {Custom\\Driver};
\node[draw, thick, fill=white, ellipse, align=center, minimum height=.8cm,minimum width=1.4cm, inner sep=0cm] at (2.2,.6) {REST};
\node[draw, thick, fill=white, ellipse, align=center, minimum height=.8cm,minimum width=1.4cm, inner sep=0cm] at (2.2,-.6) {JDBC};
\node[draw, thick, fill=white, ellipse, align=center, minimum height=.8cm,minimum width=1.4cm, inner sep=0cm] at (-1.6,-2.5) {BAPI};
\node[draw, thick, fill=white, ellipse, align=center, minimum height=.8cm,minimum width=1.4cm, inner sep=0cm] at (0,-2.5) {SOAP};
\node[draw, thick, fill=white, ellipse, align=center, minimum height=.8cm,minimum width=1.4cm, inner sep=0cm] at (1.6,-2.5) {JDBC};
\node[draw, thick, fill=white, ellipse, align=center, minimum height=.8cm,minimum width=1.4cm, inner sep=0cm] at (0,2.5) {UI Services\\Custom HTTP/JSON};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.07642 | arxiv | 2016-04-27T02:11:04 |
|
Ozy Computation. If we zoom-in on Process and Thread from Fig.~fig:msgrouting, we see the intersection of message routing and computation. Process and Thread implement the Oz Computation Model. | \documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes}
\usetikzlibrary{positioning,calc}
\usetikzlibrary{arrows,decorations.markings}
\begin{document}
\begin{tikzpicture}
\node [draw=gray, ultra thick, rectangle, fill=yellow!10, minimum width=200, minimum height=220, align=center] (bigbox) at (0,-1.1) {};
\node [draw=gray, ultra thick, rectangle, dotted, fill=yellow!01, minimum width=155, minimum height=45, align=left] (createthread) at (-4.75,1.3) {\textbf{createThread(stmt)}\\\textbf{saveProcessTo(stream)}\\\textbf{restoreProcessFrom(stream)}};
\node [draw=gray, ultra thick, rectangle, dotted, fill=yellow!01, minimum width=155, minimum height=45, align=left] (these) at (-4.75,-0.75) {These components comprise an\\interpreter that implements\\the Oz Computation Model.};
\node [draw=gray, ultra thick, rectangle, dotted, fill=yellow!01, minimum width=140, minimum height=15, align=left] (pterm) at (4.75,1.8) {\textbf{partiallyTerminated()}};
\node [draw=gray, ultra thick, rectangle, dotted, fill=yellow!01, minimum width=140, minimum height=15, align=left] (startthread) at (4.75,0.5) {\textbf{startThread(stmt, env)}\\\textbf{runTimeSlice(duration)}};
\node [draw=gray, ultra thick, rectangle, dotted, fill=yellow!01, minimum width=140, minimum height=15, align=left] (runtime) at (4.75,-0.75) {\textbf{runTimeSlideEnded()}};
\node [align=left] (orch) at (-2.1,2.4) {\textbf{Ozy Container}};
\node [draw, circle, fill=blue!09, inner sep=6] (p) at (0.1,1.0) {P};
\node [draw, circle, fill=blue!09, inner sep=6] (tl) at (-1.3,-2.0) {Th};
\node [draw, circle, fill=blue!09, inner sep=6] (tc) at (1.5,-2) {Th};
\draw [ultra thick] (p) -- (0.1,1.7);
\draw [ultra thick] (0.1,1.7) -- (0.1,2.2);
\draw [ultra thick] (p) -- (tl);
\draw [ultra thick] (p) -- (tc);
\draw [ultra thick, dashed, ->] (0.4,1.5) -- (0.4,2.2);
\draw [ultra thick, dashed, ->] (-0.2,2.2) -- (-0.2,1.5);
\draw [gray] (createthread) -- (-0.2,2.2);
\draw [gray] (pterm) -- (0.4,1.5);
\draw [ultra thick, dashed, ->] (1.0,-0.1) -- (1.3,-0.8);
\draw [ultra thick, dashed, ->] (0.6,-1.0) -- (0.3,-0.3);
\draw [ultra thick, dashed, ->] (-0.8,-0.1) -- (-1.2,-0.8);
\draw [ultra thick, dashed, ->] (-0.4,-1.0) -- (-0.1,-0.3);
\draw [gray] (startthread) -- (1.0,-0.1);
\draw [gray] (runtime) -- (0.6,-1.0);
\node [draw=gray, thick, rectangle, fill=blue!10, minimum width=140, minimum height=25, align=left] (runtime) at (0.1,-4.35) {Dataflow Memory};
\node [draw=gray, thick, rectangle, fill=blue!10, inner sep=4, align=left, rotate=-90] (sr) at (0.5,-3) {Stack};
\node [draw=gray, thick, rectangle, fill=blue!10, inner sep=4, align=left, rotate=-90] (sl) at (-2.3,-3) {Stack};
\draw [] (tl.west) -- +(0,0)-| (sl);
\draw [] (tc.west) -- +(0,0)-| (sr);
\draw [very thick, <->] (tc.south) -- (1.5,-3.9);
\draw [very thick, <->] (tl.south) -- (-1.3,-3.9);
\draw [gray] (these) -- (tl);
\draw [gray] (these) -- (sl);
\draw [gray] (these.south) -- (runtime.west);
\draw [ultra thick] (-2.7, -5.5) -- (-1.9, -5.5);
\node [] (r) at (-0.9,-5.5) {Connector};
\draw [ultra thick, ->, dashed] (0.5, -5.5) -- (1.3, -5.5);
\node [] (r) at (2.2,-5.5) {Message};
\draw [very thick, <->] (-1.1, -6.0) -- (-0.3, -6.0);
\node [] (r) at (1.0,-6.0) {Private Access};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.07642 | arxiv | 2016-04-27T02:11:04 |
|
Encoded bytes corresponding to integer values 1024,12,10,512 using VarIntGB\@. The result occupies seven bytes. | \documentclass[preprint, 3p, twocolumn, times,sort]{elsarticle}
\usepackage{pgfplots}
\pgfplotsset{width=7cm,compat=1.3}
\usepackage{tikz}
\usepackage{color}
\usetikzlibrary{chains,positioning,arrows}
\usepackage[colorlinks,bookmarksopen,bookmarksnumbered,citecolor=red,urlcolor=red,draft]{hyperref}
\begin{document}
\begin{tikzpicture}[node distance=0cm,start chain=1 going right] \tikzstyle{mytape}=[draw,minimum height=1cm]
\node [on chain=1,mytape,fill=red!20] {01|00|00|01};
\node [on chain=1,mytape,fill=green!20] {0x0004};
\node [on chain=1,mytape,fill=green!20] {0xc};
\node [on chain=1,mytape,fill=green!20] {0xa};
\node [on chain=1,mytape,fill=green!20] {0x0200};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1611.05428 | arxiv | 2016-11-17T02:09:11 |
|
Graph topology analyzed in Example~ex:network | \documentclass[11pt,letterpaper]{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usetikzlibrary{arrows}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsmath,amsfonts, amssymb,color}
\begin{document}
\begin{tikzpicture}[-,>=stealth',shorten >=1pt,auto,thick,main node/.style={circle,draw,minimum size = 0.6cm,inner sep=0pt}]
\node[main node] (1) {$1$};
\node[main node] (2) [below = 0.4cm of 1] {$2$};
\node[main node] (3) [below = 0.4cm of 2] {$3$};
\node[main node] (4) [right = 0.8cm of 1] {$4$};
\node[main node] (5) [right = 1.5cm of 2] {$5$};
\node[main node] (6) [right = 0.8cm of 3] {$6$};
\node[main node] (7) [right = 1cm of 5] {$7$};
\node[main node] (8) [right = 1cm of 7] {$8$};
\node[main node] (9) [above = 0.4cm of 8] {$9$};
\node[main node] (10) [below = 0.4cm of 8] {$10$};
\path[every node/.style={font=\sffamily\small}]
(1) edge (4)
(2) edge (5)
(3) edge (6)
(4) edge (5)
(4) edge [bend right] (6)
(5) edge (6)
(4) edge (7)
(5) edge (7)
(6) edge (7)
(7) edge (8)
(8) edge (9)
(8) edge (10);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1510.09106 | arxiv | 2016-08-16T02:00:16 |
|
Case (n,m+1) | \documentclass[11pt]{book}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{cd}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{arrows}
\usetikzlibrary{matrix}
\tikzset{sdiag/.style={decorate,decoration={snake,amplitude=.3mm,segment length=1.5mm,post length=1mm}}}
\tikzcdset{sdiag/.style={
arrows={decorate,decoration={snake,amplitude=.3mm,segment length=1.5mm,post length=1mm}},
labels={font=\small},
column sep=large,
row sep=large}}
\newcommand{\Sm}[1]{\mathbf{S}^{#1}}
\newcommand{\Sn}[1]{\mathbb{S}^{#1}}
\newcommand{\id}{\mathsf{id}}
\begin{document}
\begin{tikzpicture}[commutative diagrams/every diagram]
\node (P0) at (0:8em) {$\Sm{n+m+1}$};
\node (P1) at (60:8em) {$\Sm{n+m+1}$};
\node (P2) at (120:8em) {$\Sm{n+m+1}$};
\node (P3) at (180:8em) {$\Sm{n+m+1}$};
\node (P4) at (240:8em) {$\Sm{n+m+1}$};
\node (P5) at (300:8em) {$\Sm{n+m+1}$};
\node (T0) at ($(0:8em)+(330:8em)$) {$\Sn1\wedge(\Sm{m}\wedge\Sm{n})$};
\node (T1) at ($(60:8em)+(90:8em)$) {$(\Sn1\wedge \Sm{m})\wedge\Sm{n}$};
\node (T2) at ($(120:8em)+(90:8em)$) {$\Sm{n}\wedge(\Sn1\wedge\Sm{m})$};
\node (T3) at ($(180:8em)+(210:8em)$) {$(\Sm{n}\wedge \Sn1)\wedge\Sm{m}$};
\node (T4) at ($(240:8em)+(210:8em)$) {$(\Sn1\wedge \Sm{n})\wedge\Sm{m}$};
\node (T5) at ($(300:8em)+(330:8em)$) {$\Sn1\wedge(\Sm{n}\wedge \Sm{m})$};
\path[commutative diagrams/.cd, every arrow, every label]
(P1) edge node[swap] {$\id$} (P0)
(P2) edge node[swap] {$(-1)^{n(m+1)}$} (P1)
(P3) edge node[swap] {$\id$} (P2)
(P3) edge node {$(-1)^n$} (P4)
(P4) edge node {$\id$} (P5)
(P5) edge node {$(-1)^{nm}$} (P0)
(T1) edge[bend left] node {$\alpha_{\Sn1,\Sm m,\Sm n}$} (T0)
(T2) edge node {\raisebox{0.7em}{$\sigma_{\Sm{n},\Sn1\wedge \Sm{m}}$}} (T1)
(T3) edge[bend left] node {$\alpha_{\Sm n,\Sn1,\Sm m}$} (T2)
(T3) edge node[swap] {$\sigma_{\Sm{n},\Sn1}\wedge\id_{\Sm m}$} (T4)
(T4) edge[bend right] node[swap] {$\alpha_{\Sn1,\Sm{n},\Sm m}$} (T5)
(T5) edge node[swap] {$\id_{\Sn1}\wedge\sigma_{\Sm n,\Sm m}$} (T0)
(T1) edge (P1)
(T2) edge (P2)
(T3) edge (P3)
(T4) edge (P4)
(T5) edge (P5)
(T0) edge (P0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1606.05916 | arxiv | 2016-06-21T02:10:49 |
|
The MC~ C of the reduction from NMF to~ MC MDP_m. | \documentclass[envcountsame]{llncs}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows, automata, positioning}
\usepackage{pgf, verbatim,eurosym}
\usetikzlibrary{arrows,automata}
\RequirePackage{tikz}
\usetikzlibrary{arrows,snakes}
\newcommand{\inn}{{\mathit{in}}}
\newcommand{\fin}{{\mathit{fi}}}
\begin{document}
\begin{tikzpicture}[xscale=.6,>=latex',shorten >=1pt,node distance=3cm,on grid,auto]
\node[state,initial,initial text={}] (qin) at (0,2) {$q_{\inn}$};
\node[state] (q1) at (2,4) {$q_{1}$};
\node[label] at (1,2.1) {$\vdots$};
\node[state] (qn) at (2,0) {$q_{n}$};
\node[state] (qfi) at (8,2) {$q_{\fin}$};
\path[->] (qin) edge node [midway, left] {$\frac{1}{n},a_1$} (q1);
\path[->] (qin) edge node [midway, left] {$\frac{1}{n},a_n$} (qn);
\path[->] (q1) edge [bend left=15] node [midway, right] {$b_1,M[1,1]$} (qfi);
\node[label] at (4.8,3.3) {$\vdots$};
\path[->] (q1) edge [bend right=15] node [midway, left] {$b_m,M[1,m]$} (qfi);
\path[->] (qn) edge [bend left=15] node [midway, left] {$b_1,M[n,1]$} (qfi);
\node[label] at (4.8,.8) {$\vdots$};
\path[->] (qn) edge [bend right=15] node [midway, right] {$b_m,M[n,m]$} (qfi);
\path[->] (qfi) edge [loop right] node [right, midway] {$c,1$} (qfi);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1510.09102 | arxiv | 2016-01-11T02:05:26 |
|
The even (top row) and odd (bottom row) 8-vertex model weights, with bond states shown in terms of line type, dashed or solid. | \documentclass{article}
\usepackage{tikz}
\usepackage{amssymb}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\draw[dashed,line width = 2pt] (0,1) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (0,-1);
\draw[dashed,line width = 2pt] (-1,0) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $w_1$}};
\begin{scope}[shift={(3,0)}]
\draw[line width = 2pt] (0,1) -- (0,0);
\draw[line width = 2pt] (0,0) -- (0,-1);
\draw[line width = 2pt] (-1,0) -- (0,0);
\draw[line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $w_2$}};
\end{scope}
\begin{scope}[shift={(6,0)}]
\draw[line width = 2pt] (0,1) -- (0,0);
\draw[line width = 2pt] (0,0) -- (0,-1);
\draw[dashed,line width = 2pt] (-1,0) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $w_3$}};
\end{scope}
\begin{scope}[shift={(9,0)}]
\draw[dashed,line width = 2pt] (0,1) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (0,-1);
\draw[line width = 2pt] (-1,0) -- (0,0);
\draw[line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $w_4$}};
\end{scope}
\begin{scope}[shift={(12,0)}]
\draw[dashed,line width = 2pt] (0,1) -- (0,0);
\draw[line width = 2pt] (0,0) -- (0,-1);
\draw[dashed,line width = 2pt] (-1,0) -- (0,0);
\draw[line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $w_5$}};
\end{scope}
\begin{scope}[shift={(15,0)}]
\draw[line width = 2pt] (0,1) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (0,-1);
\draw[line width = 2pt] (-1,0) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $w_6$}};
\end{scope}
\begin{scope}[shift={(18,0)}]
\draw[dashed,line width = 2pt] (0,1) -- (0,0);
\draw[line width = 2pt] (0,0) -- (0,-1);
\draw[line width = 2pt] (-1,0) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $w_7$}};
\end{scope}
\begin{scope}[shift={(21,0)}]
\draw[line width = 2pt] (0,1) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (0,-1);
\draw[dashed,line width = 2pt] (-1,0) -- (0,0);
\draw[line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $w_8$}};
\end{scope}
%
\begin{scope}[shift={(0,-3)}]
\draw[dashed,line width = 2pt] (0,1) -- (0,0);
\draw[line width = 2pt] (0,0) -- (0,-1);
\draw[dashed,line width = 2pt] (-1,0) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $v_1$}};
\begin{scope}[shift={(3,0)}]
\draw[line width = 2pt] (0,1) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (0,-1);
\draw[line width = 2pt] (-1,0) -- (0,0);
\draw[line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $v_2$}};
\end{scope}
\begin{scope}[shift={(6,0)}]
\draw[line width = 2pt] (0,1) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (0,-1);
\draw[dashed,line width = 2pt] (-1,0) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $v_3$}};
\end{scope}
\begin{scope}[shift={(9,0)}]
\draw[dashed,line width = 2pt] (0,1) -- (0,0);
\draw[line width = 2pt] (0,0) -- (0,-1);
\draw[line width = 2pt] (-1,0) -- (0,0);
\draw[line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $v_4$}};
\end{scope}
\begin{scope}[shift={(12,0)}]2
\draw[dashed,line width = 2pt] (0,1) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (0,-1);
\draw[dashed,line width = 2pt] (-1,0) -- (0,0);
\draw[line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $v_5$}};
\end{scope}
\begin{scope}[shift={(15,0)}]
\draw[line width = 2pt] (0,1) -- (0,0);
\draw[line width = 2pt] (0,0) -- (0,-1);
\draw[line width = 2pt] (-1,0) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $v_6$}};
\end{scope}
\begin{scope}[shift={(18,0)}]
\draw[dashed,line width = 2pt] (0,1) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (0,-1);
\draw[line width = 2pt] (-1,0) -- (0,0);
\draw[dashed,line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $v_7$}};
\end{scope}
\begin{scope}[shift={(21,0)}]
\draw[line width = 2pt] (0,1) -- (0,0);
\draw[line width = 2pt] (0,0) -- (0,-1);
\draw[dashed,line width = 2pt] (-1,0) -- (0,0);
\draw[line width = 2pt] (0,0) -- (1,0);
\node at (-.7,.6) {{\Large $v_8$}};
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.02110 | arxiv | 2017-02-08T02:07:39 |
|
The weak-graph transformation. Spins on each bond are split into two, separated by the dashed lines, and a local map between spins variables and vertex weights is used around each vertex. The constraint that the split spin variables are equal is equivalent to the bond sharing of vertex weight variables. | \documentclass{article}
\usepackage{tikz}
\usepackage{amssymb}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\foreach \x in {2,4}
\draw (\x,0.4) -- (\x,5.6);
\foreach \y in {2,4}
\draw (0.4,\y) -- (5.6,\y);
\foreach \y in {1,3,5}
\draw[dashed] (1.5,\y) -- (2.5,\y);
\foreach \y in {1,3,5}
\draw[dashed] (3.5,\y) -- (4.5,\y);
\foreach \x in {1,3,5}
\draw[dashed] (\x,1.5) -- (\x,2.5);
\foreach \x in {1,3,5}
\draw[dashed] (\x,3.5) -- (\x,4.5);
\foreach \position in {(1.7,2.6),(3.7,4.6)}
\node at \position {$\sigma_A^{(1)}$};
\foreach \position in {(1.5,1.65),(3.5,3.65)}
\node at \position {$\sigma_B^{(1)}$};
\foreach \position in {(2.35,1.4),(4.35,3.4)}
\node at \position {$\sigma_C^{(1)}$};
\foreach \position in {(2.6,2.3),(4.6,4.3)}
\node at \position {$\sigma_D^{(1)}$};
\foreach \position in {(2.35,4.6),(4.35,2.6)}
\node at \position {$\sigma_C^{(2)}$};
\foreach \position in {(1.5,4.3),(3.5,2.3)}
\node at \position {$\sigma_D^{(2)}$};
\foreach \position in {(1.7,3.4),(3.7,1.4)}
\node at \position {$\sigma_A^{(2)}$};
\foreach \position in {(2.6,3.65),(4.6,1.65)}
\node at \position {$\sigma_B^{(2)}$};
\draw (1.9,1.9) rectangle (2.1,2.1);
\draw (3.9,3.9) rectangle (4.1,4.1);
\fill[black] (2,4) circle (0.115cm);
\fill[black] (4,2) circle (0.115cm);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.02110 | arxiv | 2017-02-08T02:07:39 |
|
\documentclass{article}
\usepackage{tikz}
\usepackage{amssymb}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\draw[line width = 1pt] (-2.25,0) -- (2.25,0);
\draw[line width = 1pt] (0,-2.25) -- (0,2.25);
\draw[line width = 1pt] (0,-1) -- (1,0) -- (0,1) -- (-1,0) -- (0,-1);
\node[above=4.5pt, right=-2pt] at (0,1) {\large\textbf{U}};
\node[below=5.5pt, right=-2pt] at (0,-1) {\large\textbf{D}};
\node[above=5.5pt, left=-2pt] at (-1,0) {\large\textbf{L}};
\node[above=5.5pt, right=-2.5pt] at (1,0) {\large\textbf{R}};
\node[above=5.5pt, right=-2.5pt] at (0,0) {\large\textbf{C}};
\node[above=3.5pt, left=-3.5pt] at (-0.5,0.5) {$z_1$};
\node[below=3.5pt, right=-3.5pt] at (0.5,-0.5) {$z_2$};
\node[above=3.5pt, right=-3.5pt] at (0.5,0.5) {$z_3$};
\node[below=3.5pt, left=-3.5pt] at (-0.5,-0.5) {$z_4$};
\node[below=3.5pt, left=-3.5pt] at (-0.5,-0.5) {$z_4$};
\node[below=1pt,left=-3.5pt] at (0,0.5) {$z_5$};
\node[above=1pt,left=-3pt] at (0,-0.5) {$z_6$};
\node[above=-2.5pt] at (-0.4,0) {$z_7$};
\node[below=-1.5pt] at (0.4,0) {$z_8$};
\node[above=4.5pt, right=-2pt] at (0,1.6) {1};
\node[below=5.5pt, right=-2pt] at (0,-1.6) {1};
\node[above=5.5pt, left=-2pt] at (-1.6,0) {1};
\node[above=5.5pt, right=-2.5pt] at (1.6,0) {1};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1702.02110 | arxiv | 2017-02-08T02:07:39 |
||
An annulus with four marked points and two non-isomorphic skeletons with their cilium structure. | \documentclass[12pt]{amsart}
\usepackage{amsmath,amsthm,amssymb, amsxtra, amsfonts, amscd}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{calc,positioning,intersections}
\newcommand{\ra}{\rangle}
\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro{\ra}{0.5}
\pgfmathsetmacro{\rb}{1.3}
\begin{scope}[shift={(-3,0)}]
\draw [fill=lightgray] (0,0) circle [radius=\rb];
\draw [fill=white] (0,0) circle [radius=\ra];
\draw [fill=black] (0,\ra) circle [radius=0.05];
\draw [fill=black] (180:\rb) circle [radius=0.05];
\draw [fill=black] (60:\rb) circle [radius=0.05];
\draw [fill=black] (-60:\rb) circle [radius=0.05];
\draw [black] (180:\rb) to [out=60, in=180] (60:\rb);
\draw [black] (60:\rb) to [out=-60, in=60] (-60:\rb);
\draw [black] (180:\rb) to [out=-60, in=180] (-60:\rb);
\draw [black] (0,\ra) to (60:\rb);
\draw [black] (180:\rb) to (180:\rb+0.2);
\draw [black] (0,\ra) to (0,\ra-0.2);
\draw [black] (60:\rb) to (60:\rb+0.2);
\draw [black] (-60:\rb) to (-60: \rb+0.2);
\end{scope}
\begin{scope}[shift={(3,0)}]
\draw [fill=lightgray] (0,0) circle [radius=\rb];
\draw [fill=white] (0,0) circle [radius=\ra];
\draw [fill=black] (0,\ra) circle [radius=0.05];
\draw [fill=black] (180:\rb) circle [radius=0.05];
\draw [fill=black] (60:\rb) circle [radius=0.05];
\draw [fill=black] (-60:\rb) circle [radius=0.05];
\draw [black] (180:\rb) to [out=60, in=180] (60:\rb);
\draw [black] (180:\rb) to [out=-60, in=180] (-60:\rb);
\draw [black] (0,\ra) to (60:\rb);
\draw [black] (0,\ra) to [out=0, in=30] (-60:\rb);
\draw [black] (180:\rb) to (180:\rb+0.2);
\draw [black] (0,\ra) to (0,\ra-0.2);
\draw [black] (60:\rb) to (60:\rb+0.2);
\draw [black] (-60:\rb) to (-60: \rb+0.2);
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.01782 | arxiv | 2016-10-07T02:03:27 |
|
The marked surface (_3, V). | \documentclass[12pt]{amsart}
\usepackage{amsmath,amsthm,amssymb, amsxtra, amsfonts, amscd}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{calc,positioning,intersections}
\newcommand{\ra}{\rangle}
\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro{\ra}{0.5}
\pgfmathsetmacro{\rb}{1.8}
\pgfmathsetmacro{\ry}{0.8}
\draw [fill=lightgray] (0,0) circle [radius=\rb];
\draw [fill=white] (0,\ry) circle [radius=\ra];
\draw [fill=white] (0,-\ry) circle [radius=\ra];
\draw [fill=black] (-\rb,0) circle [radius=0.05];
\draw [fill=black] (\rb, 0) circle [radius=0.05];
\node [left] at (-\rb,0) {$v_1$};
\node [right] at (\rb, 0) {$v_2$};
\draw [->] (180:\rb) to [out=60, in=180] (90:1.6) to [out=0, in=120] (0:\rb);
\draw [->] (180:\rb) to [out=300, in=180] (270:1.6) to [out=0, in=240] (0:\rb);
\draw [->] (180:\rb) to (\rb, 0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.01782 | arxiv | 2016-10-07T02:03:27 |
|
An annulus with three marked points obtained by fusing three disks with two marked points each. | \documentclass[12pt]{amsart}
\usepackage{amsmath,amsthm,amssymb, amsxtra, amsfonts, amscd}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{calc,positioning,intersections}
\newcommand{\ra}{\rangle}
\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro{\ra}{1.5}
\pgfmathsetmacro{\rb}{0.8}
\begin{scope}[shift={(-3,0)}]
\coordinate (v0) at (5: \ra); \coordinate (v1) at (115: \ra); \coordinate (v2) at (125: \ra); \coordinate (v3) at (235: \ra); \coordinate (v4) at (245: \ra); \coordinate (v5) at (-5: \ra);
\draw [fill=black] (v0) circle [radius= 0.05];
\draw [fill=black] (v1) circle [radius= 0.05];
\draw [fill=black] (v2) circle [radius= 0.05];
\draw [fill=black] (v3) circle [radius= 0.05];
\draw [fill=black] (v4) circle [radius= 0.05];
\draw [fill=black] (v5) circle [radius= 0.05];
\draw [fill=lightgray](v0) to [out=40,in=-90] (20:\ra+ 0.3) to [out=90,in=80] (v1) to [out=-30,in=150] (100: \ra-0.2) to [out=-10,in=120] (v0);
\draw [very thick] (v0) to [out=40,in=-90] (20:\ra+ 0.3); \draw [very thick] (v1) to [out=-30,in=150] (100: \ra-0.2);
\draw [fill=lightgray] (v5) to [out=-10,in=90] (-20: \ra+0.4) to [out=-95,in=-80] (v4) to [out=20,in=200] (260: \ra-0.3) to [out=25,in=210] (v5);
\draw [very thick] (v5) to [out=-10,in=90] (-20: \ra+0.4); \draw [very thick] (v4) to [out=20,in=200] (260: \ra-0.3);
\draw [fill=lightgray] (v2) to [out=-100,in=80] (140: \ra -0.3) to [out=-90,in=95] (220:\ra-0.3) to (v3) to [out=200,in=-90] (180:\ra+0.4) to [out=90,in=160] (v2);
\draw [very thick] (v2) to [out=-100,in=80] (140: \ra -0.3); \draw [very thick] (220:\ra-0.3) to (v3);
\draw (v0) arc (5:115:\ra); \draw (v2) arc (125: 235:\ra); \draw (v4) arc (245:355:\ra);
\end{scope}
\node at (0,0) {$\stackrel{{\rm fusion}}{\longrightarrow}$};
\begin{scope}[shift={(3,0)}]
\draw [fill=lightgray] (0,0) circle [radius=\ra];
\draw [fill=white] (0,0) circle [radius=\rb];
\draw [fill=black] (0:\rb) circle [radius= 0.05];
\draw [fill=black] (120:\ra) circle [radius= 0.05];
\draw [fill=black] (240:\ra) circle [radius= 0.05];
\draw (0:\rb) to [out=75,in=0] (120:\ra) to [out=-115,in=115] (240:\ra) to [out=-25,in=-75] (0:\rb);
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.01782 | arxiv | 2016-10-07T02:03:27 |
|
The ratio c_Na^(i)/c_Na^(o) for sodium ion depletion in the cell over resting potential V_m. z_i=-0.5,-1,-2 from right to left. | \documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage[latin1]{inputenc}
\usepackage[svgnames]{xcolor}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{amsmath}
\usetikzlibrary{calc,fadings,decorations}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{shapes.symbols}
\usetikzlibrary{shadows}
\usetikzlibrary{spy}
\usetikzlibrary{patterns}
\usetikzlibrary{circuits}
\usetikzlibrary{intersections}
\usetikzlibrary{positioning}
\usetikzlibrary{plotmarks}
\usetikzlibrary{circuits.ee.IEC}
\usepgfplotslibrary{groupplots}
\usepgfplotslibrary{external}
\tikzset{external/force remake}
\pgfkeys{/pgf/number format/.cd,
1000 sep={}}
\pgfplotsset{clip marker paths=true,compat=newest}
\begin{document}
\begin{tikzpicture}[thick]
\begin{axis}[axis lines=middle, samples=400,width=7cm,height=7cm,xmin=-80,xmax=5, domain=-100:0, xtick={0, -10, -20, -30, -40, -50, -60, -70, -80}, ytick={0, 0.25, 0.5, 0.75, 1}, every tick/.style={
black,
ymin=0,
ymax=1.2,
thick,
},minor x tick num=0, minor y tick num=0,yticklabel style={anchor=west,xshift=0.25cm},xticklabel style={yshift=0.5ex,
anchor=north},xlabel={$V_m$ [mV]},ylabel={$c_{\mathrm{Na}}^{(\mathrm{i})}/c_{\mathrm{Na}}^{(\mathrm{o})}$},ymin=-25,ymax=15,every axis x label/.style={at={(current axis.right of origin)},anchor=west}, every axis y label/.style={at={(current axis.above origin)},anchor=south}]
% Delta = 1/3
\addplot [thick, dashed] {-0.073*exp(-x/25.3)+1.073*(1-1/3*(1-exp(x/25.3)))};
% Delta = 0
\addplot [thick] {-0.073*exp(-x/25.3)+1.073*(1-0*(1-exp(x/25.3)))};
% Delta = -1/3
\addplot [thick, dashed] {-0.073*exp(-x/25.3)+1.073*(1-(-1/3)*(1-exp(x/25.3)))};
\addplot[mark=+,mark size=5,thick] coordinates {
(-65, 0.11)
};
\node (Z) at (axis cs:0,0) {};
\end{axis}
\node at (Z) {$0$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.03766 | arxiv | 2017-03-13T01:08:54 |
|
The function s(V_m)(eq. g1) for V_m 0 and three different values of z_i(from below: z_i=-0.5, -1, -2). (Temperature 20 C) | \documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage[latin1]{inputenc}
\usepackage[svgnames]{xcolor}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{amsmath}
\usetikzlibrary{calc,fadings,decorations}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{shapes.symbols}
\usetikzlibrary{shadows}
\usetikzlibrary{spy}
\usetikzlibrary{patterns}
\usetikzlibrary{circuits}
\usetikzlibrary{intersections}
\usetikzlibrary{positioning}
\usetikzlibrary{plotmarks}
\usetikzlibrary{circuits.ee.IEC}
\usepgfplotslibrary{groupplots}
\usepgfplotslibrary{external}
\tikzset{external/force remake}
\pgfkeys{/pgf/number format/.cd,
1000 sep={}}
\pgfplotsset{clip marker paths=true,compat=newest}
\begin{document}
\begin{tikzpicture}[thick]
\begin{axis}[axis lines=middle, samples=400,width=6cm,height=6cm,xmin=-65,xmax=15, domain=-100:0, xtick={25, 0, -25, -50, -75, -100},ytick={0,-5, -10, -15, -20, -25}, every tick/.style={
black,
ymin=-15,
ymax=5,
thick,
},minor x tick num=4, minor y tick num=1,xticklabel style={yshift=0.5ex,
anchor=south},xlabel={$V_m$ [mV]},ylabel={$s(V_m)$},ymin=-25,ymax=15,every axis x label/.style={at={(current axis.right of origin)},anchor=west}, every axis y label/.style={at={(current axis.above origin)},anchor=south}]
\addplot [thick] {-exp(-x/25.3)-2*(-0.5)/(1-(-0.5))+(1+(-0.5))/(1-(-0.5))*exp(x/25.3)};
\addplot [thick,dashed] {-exp(-x/25.3)-2*(-1)/(1-(-1))+(1+(-1))/(1-(-1))*exp(x/25.3)};
\addplot [thick] {-exp(-x/25.3)-2*(-2)/(1-(-2))+(1+(-2))/(1-(-2))*exp(x/25.3)};
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1703.03766 | arxiv | 2017-03-13T01:08:54 |
|
Modeling Languages, Intermediate and Flat Formats. | \documentclass[10pt]{report}
\usepackage[table]{xcolor}
\usepackage{mathrsfs,amssymb,amsmath}
\usepackage{tikz}
\usetikzlibrary{shapes,calc,positioning,automata,arrows,trees}
\usepackage[tikz]{bclogo}
\usepackage[skins,breakable,xparse]{tcolorbox}
\tikzset{
dirtree/.style={
grow via three points={one child at (0.8,-0.7) and two children at (0.8,-0.7) and (0.8,-1.45)},
edge from parent path={($(\tikzparentnode\tikzparentanchor)+(.4cm,0cm)$) |- (\tikzchildnode\tikzchildanchor)}, growth parent anchor=west, parent anchor=south west},
}
\begin{document}
\begin{tikzpicture}[scale=0.8, every node/.style={scale=0.8}]
\tikzstyle{sn}=[draw,rounded corners,minimum height=12mm,fill=blue!30,text width=6cm,text centered]
\node[draw=none,text centered,text width=2.3cm] (1) at (0,0) {Modeling Languages};
\node[draw=none,text centered,text width=2.3cm] (2) at (0,-2.5) {Intermediate\\ Format};
\node[draw=none,text centered,text width=2.3cm] (2) at (0,-5) {Flat\\ Formats};
\node[draw=none] (l) at (0,-1.25) {};
\node[draw=none] (r) at (9.5,-1.25) {};
\node[draw=none] (l2) at (0,-3.75) {};
\node[draw=none] (r2) at (9.5,-3.75) {};
\node[draw=none] (a1) at (10,0.5) {$+$};
\node[draw=none] (a2) at (10,-5.5) {$-$};
\node[sn] (a) at (5,0) {OPL, ESRA, MiniZinc, Essence, ...};
\node[sn] (b) at (5,-2.5) {XCSP3};
\node[sn] (c) at (5,-5) {XCSP 2.1, FlatZinc, wcsp};
\draw[->,>=latex] (a1) -- (a2);
\node[draw=none,rotate=-90] at (10.6,-2.2) {Abstraction};
\draw[dotted] (l) -- (r);
\draw[dotted] (l2) -- (r2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1611.03398 | arxiv | 2016-11-11T02:07:41 |
|
X_1 X_2 Coordinate Plane | \documentclass{amsproc}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[scale=.6]
\draw[->] (-3.5,0)-- (12.5,0)
node[below right] {$X_1$};
\draw[->] (4.5,0)-- (4.51,0)
node[below right] {$X_1$};
\draw[->] (0.5,-3)-- (0.5,3)
node[right] {$X_2$};
\draw[->] (8.5,-3)-- (8.5,3)
node[right] {$X_2$};
\draw[step=.25cm,gray,thick] (0.5+0,2)-- (0.5+4,2)node[above] {$(2\pi,\pi)$}-- (0.5+0,-2)node[below right] {$(0.-\pi)$}-- (0.5-4,-2)node[below] {$(-2\pi,-\pi)$}-- (0.5+0,2)node[above left] {$(0,\pi)$};
\draw[step=.25cm,gray,thick] (6.5,2)-- (10.5,2)node[above right] {$(\pi,\pi)$}-- (8.5+2,-2)node[below right] {$(\pi,-\pi)$}-- (6.5,-2)node[below left] {$(-\pi,-\pi)$}-- (6.5+0,2)node[above] {$(-\pi,\pi)$};
\draw[fill=gray!15] (0.5-4,-2) -- (0.5-4+2,-2) -- (0.5-4+2,0) -- cycle;
\node at (-2-.1,-2+.6) {{\tiny$\triangle_-$}};
\draw[fill=gray!15] (0.5-4+4+8,-2) -- (0.5-4+4+8+2,-2) -- (0.5-4+4+8+2,0) -- cycle;
\node at (-2-.7+13,-2+.6) {{\tiny $\triangle_- +2\pi \vec{e}_1$}};
\draw[fill=gray!15] (6.5,0) -- (6.5,2) -- (8.5,2) -- cycle;
\draw[fill=gray!15] (2.5,0) -- (2.5,2) -- (4.5,2) -- cycle;
\node at (3.3,1+.3) {{\tiny $\triangle_+$}};
\node at (3.5+4,1+.3) {{\tiny $\triangle_+ -2\vec{e}_1$}};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1608.00208 | arxiv | 2016-08-02T02:07:47 |
|
The graph of =794526813 S_9. Here, M=\{(1,7), (3,4), (5,2),(8,1)\}% and M\,=\, 95683. | \documentclass[11pt]{article}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture}[scale=0.5]
\draw (0,0) rectangle (9,9);
\draw [fill,red] (1,7) circle (0.15);
\draw [fill] (2,9) circle (0.1);
\draw [fill,red] (3,4) circle (0.15);
\draw [fill] (4,5) circle (0.1);
\draw [fill,red] (5,2) circle (0.15);
\draw [fill] (6,6) circle (0.1);
\draw [fill] (7,8) circle (0.1);
\draw [fill,red] (8,1) circle (0.15);
\draw [fill] (9,3) circle (0.1);
\draw [dashed] (1,0) -- (1,7);
\draw [dashed] (2,0) -- (2,9);
\draw [dashed] (3,0) -- (3,4);
\draw [dashed] (4,0) -- (4,5);
\draw [dashed] (5,0) -- (5,2);
\draw [dashed] (6,0) -- (6,6);
\draw [dashed] (7,0) -- (7,8);
\draw [dashed] (8,0) -- (8,1);
\draw [dashed] (9,0) -- (9,3);
%
\draw [dashed] (0,8) -- (7,8);
\draw [dashed] (0,7) -- (1,7);
\draw [dashed] (0,6) -- (6,6);
\draw [dashed] (0,4) -- (3,4);
\draw [dashed] (0,3) -- (9,3);
\draw [dashed] (0,5) -- (4,5);
%
\draw [dashed] (0,2) -- (5,2);
\draw [dashed] (0,1) -- (8,1);
\node [below] at (0,0) {$0$};
\node [below] at (1,0) {$1$};
\node [below] at (2,0) {$2$};
\node [below] at (3,0) {$3$};
\node [below] at (4,0) {$4$};
\node [below] at (5,0) {$5$};
\node [below] at (6,0) {$6$};
\node [below] at (7,0) {$7$};
\node [below] at (8,0) {$8$};
\node [below] at (9,0) {$9$};
\node [left] at (0,1) {$1$};
\node [left] at (0,2) {$2$};
\node [left] at (0,3) {$3$};
\node [left] at (0,4) {$4$};
\node [left] at (0,5) {$5$};
\node [left] at (0,6) {$6$};
\node [left] at (0,7) {$7$};
\node [left] at (0,8) {$8$};
\node [left] at (0,9) {$9$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1606.07906 | arxiv | 2016-06-28T02:05:35 |
|
An example of the permutation constructed in the proof of Proposition prop-constr, in which N=41, w_1=3, w_2=2, w=6, and A=3, and the permutation is the decreasing permutation of length N-w. The circled black dot is at (I,J). The dashed blue line is the diagonal of [1,N]^2. The two red rectangles enclose B_1+(0,J) and B_2+(I,0). The sloped red line segment within each red rectangle is drawn A units above the diagonal of the rectangle. No point of is above a sloped red line segment. The solid blue line is the line y=N-x-A, which partitions the graph of as described in the Key Claim in the proof. The two sloped red line segments lie below the solid blue line. Observe that I=x(w_1+1) and J=y(w_1+1). | \documentclass[11pt]{article}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture}[scale=0.23]
\draw (0,0) rectangle (40,40);
\draw [red] (0,34) rectangle (16,11);
\draw [red] (34,0) rectangle (18,9);
%
\draw [dashed,blue] (0,40) -- (40,0);
\draw [very thin, blue] (0,37) -- (37,0);
\draw [very thin, red] (16,14) -- (2.1,34);
\draw [very thin, red] (20.5,9) -- (34,3);
%
\draw [fill] (3,28) circle (0.3);
\draw [fill] (9,21) circle (0.3);
\draw [fill] (12,15) circle (0.3);
\draw [fill] (17,10) circle (0.3); %
\draw (17,10) circle (0.8);
\draw [fill] (23,7) circle (0.3);
\draw [fill] (30,3) circle (0.3);
%
\draw [fill] (0,40) circle (0.3);
\draw [fill] (1,39) circle (0.3);
\draw [fill] (2,38) circle (0.3);
\draw [fill] (4,37) circle (0.3);
\draw [fill] (5,36) circle (0.3);
\draw [fill] (6,35) circle (0.3);
\draw [fill] (7,34) circle (0.3);
\draw [fill] (8,33) circle (0.3);
\draw [fill] (10,32) circle (0.3);
\draw [fill] (11,31) circle (0.3);
\draw [fill] (13,30) circle (0.3);
\draw [fill] (14,29) circle (0.3);
\draw [fill] (15,27) circle (0.3);
\draw [fill] (16,26) circle (0.3);
\draw [fill] (18,25) circle (0.3);
\draw [fill] (19,24) circle (0.3);
\draw [fill] (20,23) circle (0.3);
\draw [fill] (21,22) circle (0.3);
\draw [fill] (22,20) circle (0.3);
\draw [fill] (24,19) circle (0.3);
\draw [fill] (25,18) circle (0.3);
\draw [fill] (26,17) circle (0.3);
\draw [fill] (27,16) circle (0.3);
\draw [fill] (28,14) circle (0.3);
\draw [fill] (29,13) circle (0.3);
\draw [fill] (31,12) circle (0.3);
\draw [fill] (32,11) circle (0.3);
\draw [fill] (33,9) circle (0.3);
\draw [fill] (34,8) circle (0.3);
\draw [fill] (35,6) circle (0.3);
\draw [fill] (36,5) circle (0.3);
\draw [fill] (37,4) circle (0.3);
\draw [fill] (38,2) circle (0.3);
\draw [fill] (39,1) circle (0.3);
\draw [fill] (40,0) circle (0.3);
%
\draw [dashed] (3,40) -- (3,28) -- (40,28);
\draw [dashed] (9,40) -- (9,21) -- (40,21);
\draw [dashed] (12,40) -- (12,15) -- (40,15);
\draw [dashed] (17,40) -- (17,10) -- (40,10);
\draw [dashed] (23,40) -- (23,7) -- (40,7);
\draw [dashed] (30,40) -- (30,3) -- (40,3);
%
\node [below] at (0,0) {$1$};
\node [below] at (40,0) {$N$};
\node [below] at (34,0) {$N{-}2A$};
\node [left] at (0,40) {$N$};
\node [left] at (0,34) {$N{-}2A$};
\node [above] at (3,40) {$x(1)$};
\node [above] at (30,40) {$x(w)$};
\node [above] at (17,40) {$I$};
\node [right] at (40,28) {$y(1)$};
\node [right] at (40,3) {$y(w)$};
\node [right] at (40,10) {$J$};
%
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1606.07906 | arxiv | 2016-06-28T02:05:35 |
|
In this system, there are five processors p_1, p_2, p_3, p_4 and p_5; all communication links are bi-directional; and at most one processor can be adversarial, i.e., f=1. | \documentclass[letterpaper, 11pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes}
\begin{document}
\begin{tikzpicture}[auto, scale=1.2]
\node[draw,circle,minimum size=0.7cm,inner sep=0pt] (A) at (0,0) {$p_1$ };
\node [draw,circle,minimum size=0.7cm,inner sep=0pt] (D) at (0,-2) {$p_4$};
\node [draw,circle,minimum size=0.7cm,inner sep=0pt] (B) at (3,0) {$p_2$};
\node [draw,circle,minimum size=0.7cm,inner sep=0pt] (C) at (3,-2) {$p_3$};
\node [draw,circle,minimum size=0.7cm,inner sep=0pt] (E) at (1.5,-1) {$p_5$};
\draw[<->, thick] (A)--(B);
\draw[<->, thick] (B) -- (C);
\draw[<->, thick] (D) -- (C);
\draw[<->, thick] (A) -- (D);
\draw[<->, thick] (A) -- (E);
\draw[<->, thick] (B) -- (E);
\draw[<->, thick] (C) -- (E);
\draw[<->, thick] (D) -- (E);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1411.5282 | arxiv | 2015-04-17T02:04:09 |
|
In this system, there are n processors p_1, , p_n; all communication links are bi-directional; and at most one processor can be adversarial, i.e., f=1. Nodes p_2, , p_n form a cycle of length n-1 and these nodes are all connected to node p_1. | \documentclass[letterpaper, 11pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes}
\begin{document}
\begin{tikzpicture}[auto, scale=1.2]
\node[draw,circle,minimum size=0.7cm,inner sep=0pt] (A) at (0,0) {$p_2$ };
\node [draw,circle,minimum size=0.7cm,inner sep=0pt] (B) at (-1,-1) {$p_n$};
\node [draw,circle,minimum size=0.7cm,inner sep=0pt] (C) at (0,-2) {$p_6$};
\node [draw,circle,minimum size=0.7cm,inner sep=0pt] (D) at (2,-2) {$p_5$};
\node [draw,circle,minimum size=0.7cm,inner sep=0pt] (E) at (3,-1) {$p_4$};
\node[draw,circle,minimum size=0.7cm,inner sep=0pt] (F) at (2,0) {$p_3$ };
\node [draw,circle,minimum size=0.7cm,inner sep=0pt] (G) at (1,-1) {$p_1$};
\draw[<->, thick] (A)--(B);
\draw[-, dashed, thick] (B) -- (C);
\draw[<->, thick] (D) -- (C);
\draw[<->, thick] (D) -- (E);
\draw[<->, thick] (E) -- (F);
\draw[<->, thick] (F) -- (A);
\draw[<->, thick] (A) -- (G);
\draw[<->, thick] (B) -- (G);
\draw[<->, thick] (C) -- (G);
\draw[<->, thick] (D) -- (G);
\draw[<->, thick] (E) -- (G);
\draw[<->, thick] (F) -- (G);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1411.5282 | arxiv | 2015-04-17T02:04:09 |
|
Outline of the proposed method | \documentclass{llncs}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning,shapes.geometric}
\begin{document}
\begin{tikzpicture}[>=latex']
\tikzset{block/.style= {draw, rectangle, align=center,minimum width=2cm,minimum height=1cm}}
\node (input_img) {Input};
\node [block, right =5mm of input_img] (start) {Pre Processing};
\node [block, right =5mm of start] (acquire) {Canidate \\ seletion};
\node [block, right =5mm of acquire] (rgb2gray) {False\\ positive\\ rejection};
\node [right =5mm of rgb2gray](Segmented) {Cyst regions};
%% paths
\path[draw,->] (input_img) edge (start)
(start) edge (acquire)
(acquire) edge (rgb2gray)
(rgb2gray) edge (Segmented)
;
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1612.02675 | arxiv | 2016-12-09T02:05:54 |
|
A <-cycle of three elements and an ``incomparable triple-u'', where dashed lines are -edges. | \documentclass[envcountsame,reqno]{llncs}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{calc,positioning}
\begin{document}
\begin{tikzpicture}
[rotate = 0, transform shape, scale=1 ] %Change this to scale picture
\begin{scope}
[
node distance = 1 and 0.5,
on grid,
basickonf/.style={ %rotate = -90, %For reversing the rotation of labels
circle, draw, solid, thin, minimum size = 5, inner sep =0
},
konf/.style={ basickonf },
less/.style= { <- },
greater/.style= { -> },
inc/.style= { dashed, bend right=35 },
]
\begin{scope}
\node[konf] (left) {};
\node[konf, below right = of left] (down) {}
edge[less] (left)
;
\node[konf, above right = of down] {}
edge[less] (down)
edge[greater] (left)
;
\end{scope}
\begin{scope}[xshift = 100]
\foreach \pref in {0, ..., 0}
\foreach \row in {0, ..., 0}
{
\node [konf,] (\pref-\row-l) at ($(5*\pref, 4*\row)$) {};
\node [konf, below right = of \pref-\row-l] (\pref-\row-b_1) {}
edge [less] (\pref-\row-l)
;
\node [konf, above right = of \pref-\row-b_1] (\pref-\row-a_0) {}
edge [greater] (\pref-\row-b_1)
;
\node [konf, below right = of \pref-\row-a_0] (\pref-\row-b_2) {}
edge [less] (\pref-\row-a_0)
;
\node [konf, above right = of \pref-\row-b_2] (\pref-\row-c_0) {}
edge [greater] (\pref-\row-b_2)
edge[inc] (\pref-\row-l)
;
\node [konf, below right = of \pref-\row-c_0] (\pref-\row-b_3) {}
edge [less] (\pref-\row-c_0)
;
\node [konf, above right = of \pref-\row-b_3] (\pref-\row-r) {}
edge [greater] (\pref-\row-b_3)
edge [inc] (\pref-\row-a_0)
;
}
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1412.2905 | arxiv | 2015-02-25T02:10:20 |
|
The standard (5,3)-triple-u, where we only draw the Hasse diagram for <^D, and where dashed edges are -edges. | \documentclass[envcountsame,reqno]{llncs}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{calc,positioning}
\begin{document}
\begin{tikzpicture}
[rotate = 90, transform shape, scale =0.8 ] %Change this to scale picture
\begin{scope}
[
node distance = 1.2 and 0.5,
on grid,
basickonf/.style={ rotate= -90,% To get labels turned right way again
circle, draw, solid, thin, minimum size = 15, inner sep = 0
},
konf/.style={ basickonf },
less/.style= { <- },
greater/.style= { -> },
inc/.style= { dashed, bend right=35 },
]
\foreach \pref in {0, ..., 0}
\foreach \row in {0, ..., 0}
{
\node [konf] (\pref-\row-l) at ($(5*\pref, 4*\row)$) {$l$};
\node [konf, below right = of \pref-\row-l] (\pref-\row-b_1) {$b_1$}
edge [less] (\pref-\row-l)
;
\node [konf, above right = of \pref-\row-b_1] (\pref-\row-a_0) {$a_1$}
edge [greater] (\pref-\row-b_1)
;
\node [konf, below right = of \pref-\row-a_0] (\pref-\row-b_2) {$b_2$}
edge [less] (\pref-\row-a_0)
;
\node [konf, above right = of \pref-\row-b_2] (\pref-\row-c_0) {$a_2$}
edge [greater] (\pref-\row-b_2)
;
\node [konf, below right = of \pref-\row-c_0] (\pref-\row-b_3) {$b_3$}
edge [less] (\pref-\row-c_0)
;
\node [konf, above right = of \pref-\row-b_3] (\pref-\row-r) {$r$}
edge [greater] (\pref-\row-b_3)
edge [inc] (\pref-\row-l)
;
\foreach \knoten / \lang in {a/5,c/3} {
\foreach \i in {1, ..., \lang}
{
\pgfmathtruncatemacro{\minusOne}{\i-1}; %% sets an integer
%% macro! with set instead of
%% truncate we get rational numbers
\node [konf, above = of \pref-\row-\knoten_\minusOne] (\pref-\row-\knoten_\i) {}
edge [greater] (\pref-\row-\knoten_\minusOne)
;
}
}
}
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1412.2905 | arxiv | 2015-02-25T02:10:20 |
|
The classification tree T(h) for a hospital h. | \documentclass{llncs}
\usepackage{amsmath}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{fit, shapes, positioning}
\begin{document}
\begin{tikzpicture}{h}
% root
\draw[dotted, black, thick] (3.5, 4) -- (2, 2);
\draw[black, thick] (3.5, 4) -- (5.8, 1.5);
% left subtree
\draw[dotted, black, thick] (1, 1) -- (2, 2);
\draw[dotted, black, thick] (3, 1) -- (2, 2);
\draw[dotted, black, thick] (2, 0) -- (2, 2);
\draw[dotted, black, thick] (0, 0) -- (1, 1);
\draw[dotted, black, thick] (4, 0) -- (3, 1);
% right subtree
\node[draw,
fill=white,
shape border rotate=120,
regular polygon,
regular polygon sides=3,
node distance=2cm,
minimum height=6em] at (5.4, 1.5) {};
% root
\fill[white] (3.5, 4) ellipse (0.5 and 0.25);
% left subtree
\fill[white] (2, 2) ellipse (0.5 and 0.25);
\fill[white] (2, 0) ellipse (0.5 and 0.25);
\fill[white] (1, 1) ellipse (0.5 and 0.25);
\fill[white] (0, 0) ellipse (0.5 and 0.25);
\fill[white] (3, 1) ellipse (0.5 and 0.25);
\fill[white] (4, 0) ellipse (0.5 and 0.25);
% root
\draw[black, thick] (3.5, 4) ellipse (0.5 and 0.25) node[right, xshift=0.5cm] {$C^h_*$};
% left subtree
\draw[black, thick] (2, 2) ellipse (0.5 and 0.25) node[right, xshift=0.5cm] {$C^h_k$};
\draw[black, thick] (2, 0) ellipse (0.5 and 0.25);
\draw[black, thick] (1, 1) ellipse (0.5 and 0.25);
\draw[black, thick] (0, 0) ellipse (0.5 and 0.25) node[below, yshift=0.2cm] {$.., r, ..$};
\draw[black, thick] (0, 0) ellipse (0.5 and 0.25) node[below, yshift=-0.3cm] {$C^h_i$};
\draw[black, thick] (3, 1) ellipse (0.5 and 0.25) node[right, xshift=0.5cm] {$C^h_t$};
\draw[black, thick] (4, 0) ellipse (0.5 and 0.25) node[below, yshift=0.3cm] {$.., r', ..$};
\draw[black, thick] (4, 0) ellipse (0.5 and 0.25) node[below, yshift=-0.3cm] {$C^h_j$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.07650 | arxiv | 2016-12-20T02:05:54 |
|
(a) Resident preferences, (b) Hospital preferences, (c) T(h_1). The matchings M = \{(r_1, h_1), (r_2, h_2), (r_3, h_1)\}, M' = \{(r_2, h_1), (r_3, h_2), (r_4, h_1)\}, and M'' = \{(r_1, h_1), (r_2, h_3), (r_3, h_2), (r_4, h_1) \} are all feasible in the instance. | \documentclass{llncs}
\usepackage{amsmath}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{fit, shapes, positioning}
\begin{document}
\begin{tikzpicture}{h}
\node (A) [draw, ellipse] at (1.5, 2) {$ r_1, r_2, r_3, r_4 $};
\node (B) [draw, ellipse] at (0, 1) {$ r_1, r_2 $};
\node (C) [draw, ellipse] at (3, 1) {$ r_3, r_4 $};
\node [right=0.1cm of A] {$C^{h_1}_*$};
\node [right=0.1cm of B] {$C^{h_1}_1$};
\node [right=0.1cm of C] {$C^{h_1}_2$};
\draw[black, thick] (A) -- (B);
\draw[black, thick] (A) -- (C);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.07650 | arxiv | 2016-12-20T02:05:54 |
|
The edges (r_a^j_a, h) and (r_b^j_b, h) belong to , while the edge (r_a^j'_a, h) does not belong to . | \documentclass{llncs}
\usepackage{amsmath}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{fit, shapes, positioning}
\begin{document}
\begin{tikzpicture}[every node/.style={circle, draw, thick, inner sep=0pt, minimum width=5pt}]
\node (r_aa)[label=left:$r_a^{j_a}$] at (0, 4) {};
\node (r_bb)[label=left:$r_b^{j_b}$] at (0, 3) {};
\node (r_ac)[label=left:$r_a^{j'_a}$] at (0, 0) {};
\node (h)[label=right:$h$] at (2, 4) {};
\draw[thick, dotted] (r_aa) -- (h);
\draw[thick] (r_bb) -- (h);
\draw[thick, dotted] (r_ac) -- (h);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.07650 | arxiv | 2016-12-20T02:05:54 |
|
For a fixed kernel reduction f_n running in time p_n, the image of a string of length n + 1 can only be a string of length at most p_n(n + 1). The number of equivalence classes in R for strings of length n + 1 is greater than the number of equivalence classes in S for strings of length p_n(n + 1) for each polynomial p_n. | \documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[yscale=0.5]
\begin{scope}[shift={(0, 5)}]
\node at (0, 1) {$R$};
\draw (2, 0)
++(0, 1) node[anchor=east] {$\dotsb$} ++(0, -1)
rectangle ++(1, 2)
++(0.2, -2)
rectangle ++(1, 2)
++(0.2, -2)
rectangle ++(1, 2)
++(0, -1)
node[anchor=west] {$\dotsb$}
;
\path
(2.5, 1) node {$R_n$}
++(1.2, 0) node {$R_{n + 1}$}
++(1.2, 0) node {$R_{n + 2}$}
;
\end{scope}
\begin{scope}[shift={(0, 1)}]
\draw
(4.5, 1) node[shape=circle, fill=black, inner sep=1pt] (source) {}
++(-0.8, 3.2) node[shape=circle, fill=black, inner sep=1pt] (target) {};
\path[<-, >=stealth] (source) edge node[anchor=south west] {$f_n$} (target);
\end{scope}
\begin{scope}[shift={(0, 1)}]
\node at (0, 1) {$S$};
\draw (2, 0)
++(0, 1) node[anchor=east] {$\dotsb$} ++(0, -1)
rectangle ++(3, 2)
++(0.2, -2)
rectangle ++(4, 2)
++(0, -1)
node[anchor=west] {$\dotsb$}
;
\path
(3.5, 1) node {$S_n$}
++(3.8, 0) node {$S_{n + 1}$}
;
\end{scope}
\begin{scope}
\draw[shorten >=1pt]
(2, 0) node[anchor=north] (pn) {$p_n(n) + 1$}
-- ++(0, 1);
\draw[thick, color=gray] (4.5, 3.5)
-- ++(0, -5)
node[anchor=north, color=black] (pnplus1) {$p_n(n + 1)$}
;
\draw[shorten >=1pt]
(5.2, 0) node[anchor=north west, color=black] (pnplus1nplus1) {$p_{n + 1}(n + 1)$}
-- ++(-0.2, 1);
;
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.08558 | arxiv | 2016-04-29T02:11:59 |
|
The diagram illustrates the idea how we obtain the upper and the lower bound (in terms of the coefficients) for the function L_m(z). Starting point is denoted by a blue node, the finish nodes are red. | \documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,positioning,fit,petri,chains, matrix,scopes}
\begin{document}
\begin{tikzpicture}
[point/.style={coordinate},
>=stealth',thick,draw=black!50,
tip/.style={->,shorten >= 1pt},
every join/.style={rounded corners},
skip loop/.style={to path={-- ++(0,#1) -| (\tikztotarget)}},
fin/.style={
% The shape:
rectangle,
% The size:
minimum size=6mm,
% The border:
very thick,
draw=red!50!black!50,
% The filling:
top color=white,
bottom color=red!50!black!20,
% The font:
font=\ttfamily
},
aux/.style={
% The shape:
rectangle, minimum size=6mm, rounded corners=3mm,
% The border:
very thick, draw=black!50,
% The filling:
top color=white,
bottom color=black!20,
% The font:
font=\ttfamily
},
start/.style={
% The shape:
rectangle, minimum size=6mm, rounded corners=3mm,
% The border:
very thick, draw=blue!50!black!50,
% The filling:
top color=white,
bottom color=blue!50!black!20,
% The font:
font=\ttfamily
}
]
\matrix[column sep=3mm, row sep=3mm] {
% first row
\node (LhH) [aux] {$L_{m}^{(h,H)}(z) \succeq L _{m}(z)$}; &
\node (p4) [label=above:$4$] {}; &
\node (KhH) [aux] {$K_{m}^{(h,H)}(z) \succeq K_{m}(z)$}; &
\node (p5) [label=above:$5$] {}; &
\node (uL) [fin] {$\overline{L_m}(z) \succeq L_{m}(z)$}; &
\node (x) [point] {}; \\
% second row
&
\node (p3) [label=above right:$3$] {}; & &
\node (p2) [label=below:$2$] {}; & & \\
%third row
\node (Lh) [start] {$L_{m}^{(h)}(z) \preceq L_{m}(z)$}; &
\node (p1) [label=below:$1$] {}; &
\node (Kh) [aux] {$K_{m}^{(h)}(z) \preceq K_{m}(z)$}; & &
\node (lL) [fin] {$\underline{L_m}(z) \preceq L_{m}(z)$}; & \\
};
{ [start chain]
\chainin (Lh);
\chainin (Kh) [join=by tip];
{ [start branch=uL]
\chainin (uL) [join=by tip];
}
\chainin (LhH) [join=by tip];
\chainin (KhH) [join=by tip];
\chainin (x) [join=by {skip loop=7mm}];
\chainin (lL) [join=by {skip loop=-8mm,tip}];
}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1509.06139 | arxiv | 2015-09-22T02:14:24 |
|
Naming of the random variables in the general case. The columns X_i are distributed i.i.d according to P. Each X_i^(j) is distributed according to . The overall distribution of X is P. | \documentclass[11pt,notitlepage,onecolumn]{article}
\usepackage[utf8]{inputenc}
\usepackage[OT4]{fontenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{xcolor}
\begin{document}
\begin{tikzpicture}[yscale=-0.7]
\node(X__) at (0,0) {$\underline{\overline{X}}$};
\node(X1_) at (1,0) {$\overline{X}_1$};
\node(X2_) at (2,0) {$\overline{X}_2$};
\node(X3_) at (3,0) {$\dots$};
\node(X4_) at (4,0) {$\overline{X}_i$};
\node(X5_) at (5,0) {$\dots$};
\node(X6_) at (6,0) {$\overline{X}_n$};
\node(X_1) at (0,1) {$\underline{X}^{(1)}$};
\node(X11) at (1,1) {$X_1^{(1)}$};
\node(X21) at (2,1) {$X_2^{(1)}$};
\node(X31) at (3,1) {$\cdots$};
\node(X41) at (4,1) {$X_i^{(1)}$};
\node(X51) at (5,1) {$\cdots$};
\node(X51) at (6,1) {$X_n^{(1)}$};
\node(X_2) at (0,2) {$\underline{X}^{(2)}$};
\node(X12) at (1,2) {$X_1^{(2)}$};
\node(X22) at (2,2) {$X_2^{(2)}$};
\node(X32) at (3,2) {$\cdots$};
\node(X42) at (4,2) {$X_i^{(2)}$};
\node(X52) at (5,2) {$\cdots$};
\node(X52) at (6,2) {$X_n^{(2)}$};
\node(X_3) at (0,3) {$\vdots$};
\node(X13) at (1,3) {$\vdots$};
\node(X23) at (2,3) {$\vdots$};
\node(X43) at (4,3) {$\vdots$};
\node(X63) at (6,3) {$\vdots$};
\node(X_4) at (0,4) {$\underline{X}^{(j)}$};
\node(X14) at (1,4) {$X_1^{(j)}$};
\node(X24) at (2,4) {$X_2^{(j)}$};
\node(X34) at (3,4) {$\cdots$};
\node(X44) at (4,4) {$X_i^{(j)}$};
\node(X54) at (5,4) {$\cdots$};
\node(X64) at (6,4) {$X_n^{(j)}$};
\node(X_5) at (0,5) {$\vdots$};
\node(X15) at (1,5) {$\vdots$};
\node(X25) at (2,5) {$\vdots$};
\node(X45) at (4,5) {$\vdots$};
\node(X65) at (6,5) {$\vdots$};
\node(X_6) at (0,6) {$\underline{X}^{(\ell)}$};
\node(X16) at (1,6) {$X_1^{(\ell)}$};
\node(X26) at (2,6) {$X_2^{(\ell)}$};
\node(X36) at (3,6) {$\cdots$};
\node(X46) at (4,6) {$X_i^{(\ell)}$};
\node(X56) at (5,6) {$\cdots$};
\node(X66) at (6,6) {$X_n^{(\ell)}$};
\draw[-] (0.5,-.5) to (0.5,6.5);
\draw[-] (-.5,0.5) to (6.5,0.5);
\node(iid) at (4,-3) {\begin{minipage}{4.2cm}\raggedright
Tuples $\overline{X}_{i}$ are
i.i.d.~according to $\mathcal{P}$.
Each of the $\ell$ marginals of $\mathcal{P}$ is~$\pi$.\end{minipage}};
\draw[->] (iid) to (X1_.north);
\draw[->] (iid) to (X2_.north);
\draw[->] (iid) to (X4_.north);
\draw[->] (iid) to (X6_.north);
\node[rotate=0](rowdistr) at (-2.5, 4)
{\begin{minipage}{3cm}\raggedright Vectors $\underline{X}^{(j)}$
are distributed (dependently) according to $\underline{\pi} := \pi^n$.
\end{minipage}};
\draw[->] (rowdistr) to (X_1.west);
\draw[->] (rowdistr) to (X_2.west);
\draw[->] (rowdistr) to (X_4.west);
\draw[->] (rowdistr) to (X_6.west);
\node(commonDist) at (-1, -3)
{\begin{minipage}{3.2cm}\raggedright Distributed according to
$\underline{\mathcal{P}}:=\mathcal{P}^n$.\end{minipage}};
\draw[->] (commonDist) to (X__.north west);
\node(propertiesofP) at (0,9) {\begin{minipage}{5cm}\begin{align*}
\alpha(\mathcal{P}) &:= \min_{x \in \Omega} \mathcal{P}(x,x,\ldots,x)\\
\rho(\mathcal{P}) &: \text{See Definition~\ref{def:correlation}}
\end{align*}\end{minipage}};
\node(domainsofxij) at (6,10) {\begin{minipage}{4cm}\begin{align*}
X_{i}^{(j)} &\in \Omega\\
\underline{X}^{(j)} &\in \underline{\Omega} := \Omega^{n}\\
\overline{X}_{i} & \in \overline{\Omega} := \Omega^{\ell}\\
\underline{\overline{X}} & \in \underline{\overline{\Omega}}
:= \Omega^{n\cdot \ell}\\
S &\subseteq \underline{\Omega}
\end{align*}\end{minipage}};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1509.06191 | arxiv | 2017-06-06T02:01:10 |
|
Proper 8-edge-coloring of K_7-e with def( v_0,)=def(K_7-e)=2. | \documentclass[fleqn,12pt,twoside]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{shapes}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[style=thick]
\coordinate (V3) at (-120:4.8cm);
\coordinate (V2) at (-170:4.8cm);
\coordinate (V1) at (140:4.8cm);
\coordinate (V0) at (90:4.8cm);
\coordinate (V4) at (-60:4.8cm);
\coordinate (V5) at (-10:4.8cm);
\coordinate (V6) at (40:4.8cm);
\draw (V0) -- node [sloped,above,pos=0.4] {$1$} node [sloped,above,pos=0.6] {$1$} (V1);
\draw (V0) -- node [sloped,above,pos=0.2] {$7$} node [sloped,above,pos=0.8] {$7$} (V2);
\draw (V0) -- node [sloped,left,rotate=-90,pos=0.15] {$2$} node [sloped,left,rotate=-90,pos=0.85] {$2$} (V3);
\draw (V0) -- node [sloped,right,rotate=90,pos=0.15] {$8$} node [sloped,right,rotate=90,pos=0.85] {$8$} (V4);
\draw (V0) -- node [sloped,above,pos=0.2] {$3$} node [sloped,above,pos=0.8] {$3$} (V5);
\draw (V0) -- node [sloped,above,pos=0.37] {$6$} node [sloped,above,pos=0.63] {$6$} (V6);
\draw (V1) -- node [sloped,left,rotate=-90,pos=0.37] {$2$} node [sloped,left,rotate=-90,pos=0.63] {$2$} (V2);
\draw (V1) -- node [sloped,left,rotate=90,pos=0.2] {$3$} node [sloped,left,rotate=90,pos=0.8] {$3$} (V3);
\draw (V1) -- node [sloped,above,pos=0.15] {$4$} node [sloped,above,pos=0.85] {$4$} (V4);
\draw (V1) -- node [sloped,above,pos=0.15] {$5$} node [sloped,above,pos=0.85] {$5$} (V5);
\draw (V2) -- node [sloped,left,rotate=90,pos=0.37] {$6$} node [sloped,left,rotate=90,pos=0.63] {$6$} (V3);
\draw (V2) -- node [sloped,above,pos=0.2] {$3$} node [sloped,above,pos=0.8] {$3$} (V4);
\draw (V2) -- node [sloped,above,pos=0.15] {$4$} node [sloped,above,pos=0.85] {$4$} (V5);
\draw (V2) -- node [sloped,above,pos=0.15] {$5$} node [sloped,above,pos=0.85] {$5$} (V6);
\draw (V3) -- node [sloped,above,pos=0.37] {$5$} node [sloped,above,pos=0.63] {$5$} (V4);
\draw (V3) -- node [sloped,above,pos=0.2] {$7$} node [sloped,above,pos=0.8] {$7$} (V5);
\draw (V3) -- node [sloped,above,pos=0.15] {$4$} node [sloped,above,pos=0.85] {$4$} (V6);
\draw (V4) -- node [sloped,right,rotate=-90,pos=0.37] {$6$} node [sloped,right,rotate=-90,pos=0.63] {$6$} (V5);
\draw (V4) -- node [sloped,right,rotate=-90,pos=0.2] {$7$} node [sloped,right,rotate=-90,pos=0.8] {$7$} (V6);
\draw (V5) -- node [sloped,right,rotate=90,pos=0.37] {$8$} node [sloped,right,rotate=90,pos=0.63] {$8$} (V6);
\draw[fill=white,style=ultra thick] (V0) circle (3pt) node [above] {$v_0$};
\draw[fill=black] (V1) circle (2pt) node [left] {$v_1$};
\draw[fill=black] (V2) circle (2pt) node [left] {$v_2$};
\draw[fill=black] (V3) circle (2pt) node [left] {$v_3$};
\draw[fill=black] (V4) circle (2pt) node [right] {$v_4$};
\draw[fill=black] (V5) circle (2pt) node [right] {$v_5$};
\draw[fill=black] (V6) circle (2pt) node [right] {$v_6$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1608.00904 | arxiv | 2017-01-31T02:05:19 |
|
A circle divided into five segments by five randomly placed hash code points, and the search for the next hash code point from the key | \documentclass[runningheads,a4paper]{llncs}
\usepackage{color}
\usepackage[utf8]{inputenc}
\usepackage{
amsmath,
amsfonts,
amssymb,
amsxtra,
amsopn}
\usepackage{tikz}
\newcommand{\slice}[3]{
\draw (0,0) -- (#1:1) arc (#1:#2:1);
\draw (0,0) -- (#1:1.1);
\node at (#1:1.3) {#3};
}
\begin{document}
\begin{tikzpicture}[scale=1.2]
\newcounter{a}
\newcounter{b}
\foreach \t/\l in
{
30/$\delta$,
90/$\gamma$,
45/$\beta$,
135/$\epsilon$,
60/$\alpha$
}
{
\setcounter{a}{\value{b}}
\addtocounter{b}{\t}
\slice{\thea} {\theb} {\l}
}
\draw[dashed] (0,0) -- (325:1.6);
\node at (325:1.7) {$\kappa$};
\draw[->] (0,0) (325:1.3) arc (325:305:1.3);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1503.04988 | arxiv | 2015-03-19T01:06:43 |
|
Contour C^- | \documentclass[reqno]{amsart}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[decoration={markings,
mark=at position 1.5cm with {\arrow[line width=1pt]{>}},
mark=at position 3.2cm with {\arrow[line width=1pt]{>}},
mark=at position 5cm with {\arrow[line width=1pt]{>}},
mark=at position 6.5cm with {\arrow[line width=1pt]{>}},
mark=at position 8cm with {\arrow[line width=1pt]{>}},
mark=at position 9.8cm with {\arrow[line width=1pt]{>}},
mark=at position 11.7cm with {\arrow[line width=1pt]{>}}
}
]
% The axes
\draw[help lines,->] (-4,0) -- (4,0) coordinate (xaxis);
\draw[help lines,->] (0,-1) -- (0,1) coordinate (yaxis);
% The path
\path[draw,line width=1pt,postaction=decorate] (-4,-0.5) -- (2,-0.5) -- (2,0.5) -- (-4, 0.5);
% The labels
\node[below] at (xaxis) {$\Re z$};
\node[left] at (yaxis) {$\Im z$};
\node[below left] {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.02429 | arxiv | 2017-04-11T02:03:00 |
|
Contour C^+ | \documentclass[reqno]{amsart}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[decoration={markings,
mark=at position 1.5cm with {\arrow[line width=1pt]{>}},
mark=at position 3.2cm with {\arrow[line width=1pt]{>}},
mark=at position 4.7cm with {\arrow[line width=1pt]{>}},
mark=at position 6.5cm with {\arrow[line width=1pt]{>}},
mark=at position 8.3cm with {\arrow[line width=1pt]{>}},
mark=at position 10cm with {\arrow[line width=1pt]{>}},
mark=at position 11.8cm with {\arrow[line width=1pt]{>}}
}
]
% The axes
\draw[help lines,->] (-4,0) -- (4,0) coordinate (xaxis);
\draw[help lines,->] (0,-1) -- (0,1) coordinate (yaxis);
% The path
\path[draw,line width=1pt,postaction=decorate] (4,0.5) -- (-2,0.5) -- (-2,-0.5) -- (4,-0.5);
% The labels
\node[below] at (xaxis) {$\Re z$};
\node[left] at (yaxis) {$\Im z$};
\node[below left] {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.02429 | arxiv | 2017-04-11T02:03:00 |
|
Contour C' | \documentclass[reqno]{amsart}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[decoration={markings,
mark=at position 1.1cm with {\arrow[line width=1pt]{>}},
mark=at position 2.6cm with {\arrow[line width=1pt]{>}},
mark=at position 5cm with {\arrow[line width=1pt]{>}},
mark=at position 6.4cm with {\arrow[line width=1pt]{>}},
mark=at position 8.5cm with {\arrow[line width=1pt]{>}},
mark=at position 10cm with {\arrow[line width=1pt]{>}}
}
]
% The axes
\draw[help lines,->] (-4,0) -- (4,0) coordinate (xaxis);
\draw[help lines,->] (0,-3.5) -- (0,3.5) coordinate (yaxis);
% The path
\path[draw,line width=1pt,postaction=decorate] (-3,-3) -- (-0.707,-0.707) arc (-135:135:1) -- (-3,3);
% The labels
\node[below] at (xaxis) {$\Re z$};
\node[left] at (yaxis) {$\Im z$};
\node[below left] {$O$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1704.02429 | arxiv | 2017-04-11T02:03:00 |
|
Each row corresponds to one sequence of our data-set. It is composed of six gray-scale images of size 64 64: the ``grasping point image'', followed by five frames. In each sequence, the rectangle originally containing the grasping point is pulled upward and moves accordingly. It may collide with and push other rectangles. We show several frames of each sequence for clarity here, but use only the two leftmost images (S_n, G_n) and the rightmost one R_n from each sequence in our experiments, in which we try to predict the latter from the former. | \documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[colorlinks=true,linkcolor=blue,urlcolor=blue,citecolor=blue]{hyperref}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\node (n1) at (1, 0) {${{G_n}}$};
\node (n1) at (3, 0) {${{S_n}}$};
\node (n1) at (11, 0) {${{R_n}}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.04032 | arxiv | 2016-11-28T02:04:16 |
|
Some illustrative prediction results. Each column corresponds to an example. The first row shows the starting configuration S_n, the second row the ``grasping point'' image G_n, the third row the true resulting configuration R_n, and the last row the predicted resulting configuration (S_n, G_n). For clarity, we highlight the pixels in the two bottom rows proportionally to the difference with the starting configuration.%% On (a) and (b), a single rectangle moves. On (c)%% and (d), there are collisions between the pulled rectangle and%% others, and in (e) the network models the collision with the top%% border of the containing area, with an incorrect deformation. See ~sec:prediction for discussion. | \documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[colorlinks=true,linkcolor=blue,urlcolor=blue,citecolor=blue]{hyperref}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.93]
\draw[draw=none] (0,0) -- (0.5,0) -- (0.5,8) -- (0,8) -- (0,0);
\node (n1) at (0.25, 7) {${{G_n}}$};
\node (n1) at (0.25, 5) {${{S_n}}$};
\node (n1) at (0.25, 3) {${{R_n}}$};
\node (n1) at (0.25, 1) {${\Psi({{S_n}}, {{G_n}})}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1610.04032 | arxiv | 2016-11-28T02:04:16 |
|
The automaton computing the maximal difference between the lengths of blocks of a's at odd and the following even positions. | \documentclass[a4paper]{article}
\usepackage{amssymb,amsmath,color,verbatim,bm}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,shapes}
\usepackage[color=light gray]{todonotes}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\tikzstyle{state}=[draw,circle,minimum size=0.8cm]
\tikzstyle{Astate}=[draw,circle,minimum size=0.70cm]
\newcommand{\x}{1.9}
\node[state] (q1) at (0,0) {$q_0$};
\node[Astate] at (0,0) {};
\node[state] (q2) at (\x,0) {$q_1$};
\node[state] (q5) at (2*\x,0) {$q_2$};
\node[state] (q6) at (3*\x,0) {$q_3$};
\node (null) at (-1.0,0.3) {};
\draw[->] (q1) to node[above] {(\#,s,0)} (q2);
\draw[->] (q2) to node[above] {(\#,0,s)} (q5);
\draw[->, loop above] (q5) to node[left] {(a,1,-1)} (q5);
\draw[->] (q5) to node[above] {(\#,0,0)} (q6);
\draw[->, loop above] (q6) to node[left] {(a,-1,1)} (q6);
\draw[->, bend left] (q6) to node[above] {(\#,t,t)} (q1);
\draw[->] (null) to (q1);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.06764 | arxiv | 2016-04-25T02:11:06 |
|
An example of non-deterministic automaton, in which non-deterministic choices has to ``depend on the future'' in order to obtain the infimum. | \documentclass[a4paper]{article}
\usepackage{amssymb,amsmath,color,verbatim,bm}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,shapes}
\usepackage[color=light gray]{todonotes}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\tikzstyle{state}=[draw,circle,minimum size=0.8cm]
\tikzstyle{Astate}=[draw,circle,minimum size=0.70cm]
\node[state] (Q0) at (0,0) {$q_0$};
\node[Astate] at (0,0) {};
\node[state] (Q1) at (3,0) {$q_1$};
\node[Astate] at (3,0) {};
\draw[->,loop left] (Q0) to node[left]{$(\#,0)$} (Q0);
\draw[->,loop above] (Q0) to node[left]{$(a,1)$} (Q0);
\draw[->,loop below] (Q0) to node[left]{$(b,-1)$} (Q0);
\draw[->,loop right] (Q1) to node[right]{$(\#,0)$} (Q1);
\draw[->,loop above] (Q1) to node[right]{$(a,-1)$} (Q1);
\draw[->,loop below] (Q1) to node[right]{$(b,1)$} (Q1);
\draw[->,bend left] (Q0) to node[above]{$(\#,0)$} (Q1);
\draw[->,bend left] (Q1) to node[below]{$(\#,0)$} (Q0);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.06764 | arxiv | 2016-04-25T02:11:06 |
|
The (reduced) result of translation of the automaton A from Example~ex:NWA to an automaton with monitor counters. Vector 0(resp., t) denotes the k-dimensional vector whose all components equal 0(resp., t). Vector s_i denotes the k-dimensional vector whose i-th component is s and other components are 0. | \documentclass[a4paper]{article}
\usepackage{amssymb,amsmath,color,verbatim,bm}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,shapes}
\usepackage[color=light gray]{todonotes}
\usetikzlibrary{calc}
\newcommand{\aut}{{\cal A}}
\newcommand{\nestedA}{\mathbb{A}}
\begin{document}
\begin{tikzpicture}
\tikzstyle{state}=[draw,circle,minimum size=0.8cm]
\tikzstyle{Astate}=[draw,circle,minimum size=0.7cm]
\newcommand{\x}{2.0}
\node[state] (q0) at (-1,0) {$q_0$};
\node[Astate] at (-1,0) {$q_0$};
\node[state] (q1) at (\x,0) {$q_1$};
\node[state, inner sep =1pt] (q2) at (2*\x,0) {$q_{k-1}$};
\node[state] (q3) at (3*\x,0) {$q_k$};
\node at (1.5*\x,0) {$\ldots$};
\draw[->, loop above] (q1) to node[left] (e2) {$(\#,\vec{0})$} (q1);
\draw[->, loop above] (q2) to node[left] (e3) {$(\#,\vec{0})$} (q2);
\draw[->, loop above] (q3) to node[left] (e4) {$(\#,\vec{0})$} (q3);
\draw[->,bend left=10] (q1) to node[below] (e5) {$(g,\vec{t})$} (q0);
\draw[->,bend left=45] (q2) to node[below] (e6) {$(g,\vec{t})$} (q0);
\draw[->,bend left=65] (q3) to node[below] (e7) {$(g,\vec{t})$} (q0);
\draw[->] (q0) to node[above] (e8) {$(r,\vec{s_1})$} (q1);
\draw[->] (q2) to node[above] (e9) {$(r,\vec{s}_k)$} (q3);
\node at (5.5,-1.5) {$\aut_{\nestedA}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.06764 | arxiv | 2016-04-25T02:11:06 |
|
The (LimAvg;Sum)-automaton computing the average response time over words with infinite number of requests and grants such that between any two grants there are at most k requests. | \documentclass[a4paper]{article}
\usepackage{amssymb,amsmath,color,verbatim,bm}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,shapes}
\usepackage[color=light gray]{todonotes}
\usetikzlibrary{calc}
\newcommand{\masterA}{{\cal A}_{mas}}
\newcommand{\slaveA}{{\mathfrak{B}}}
\begin{document}
\begin{tikzpicture}
\tikzstyle{state}=[draw,circle,minimum size=0.8cm]
\tikzstyle{Astate}=[draw,circle,minimum size=0.7cm]
\newcommand{\x}{2.0}
\node[state] (q0) at (-1,0) {$q_0$};
\node[Astate] at (-1,0) {$q_0$};
\node[state] (q1) at (\x,0) {$q_1$};
\node[state, inner sep =1pt] (q2) at (2*\x,0) {$q_{k-1}$};
\node[state] (q3) at (3*\x,0) {$q_k$};
\node at (1.5*\x,0) {$\ldots$};
\draw[->, loop above] (q1) to node[left] (e2) {$(\#,1)$} (q1);
\draw[->, loop above] (q2) to node[left] (e3) {$(\#,1)$} (q2);
\draw[->, loop above] (q3) to node[left] (e4) {$(\#,1)$} (q3);
\draw[->,bend left=10] (q1) to node[below] (e5) {$(g,1)$} (q0);
\draw[->,bend left=45] (q2) to node[below] (e6) {$(g,1)$} (q0);
\draw[->,bend left=65] (q3) to node[below] (e7) {$(g,1)$} (q0);
\draw[->] (q0) to node[above] (e8) {$(r,2)$} (q1);
\draw[->] (q2) to node[above] (e9) {$(r,2)$} (q3);
\node at (5.5,-1.5) {$\masterA$};
\begin{scope}[yshift=3cm]
\node[state] (q00) at (0,0) {$q_0^1$};
\node[Astate] at (0,0) {};
\node (A1) at (0,-0.8) {$\slaveA_1$};
\node[state] (q10) at (4,0) {$q_0^2$};
\node[state] (q11) at (6,0) {$q_1^2$};
\node[Astate] at (6,0) {};
\node (A2) at (5,-0.8) {$\slaveA_2$};
\draw[->] (q10) to node[above] {$(g,0)$} (q11);
\draw[->, loop above] (q10) to node[left] {$(\#,1)$} (q10);
\draw[->, loop left] (q10) to node[left] {$(r,1)$} (q10);
\end{scope}
\draw[->, dashed] (e2) to (A1);
\draw[->, dashed] (e3) to (A1);
\draw[->, dashed] (e4) to (A1);
\draw[->, dashed, bend left = 15] (e5) to (A1);
\draw[->, dashed, bend left = 45] (e6) to (A1);
\draw[->, dashed, bend left = 60] (e7) to (A1);
\draw[->, dotted] (e8) to (A2);
\draw[->, dotted, bend left = 10] (e9) to (A2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.06764 | arxiv | 2016-04-25T02:11:06 |
|
A nested weighted automaton resulting from translation of the automaton from Example~ex:AMC. | \documentclass[a4paper]{article}
\usepackage{amssymb,amsmath,color,verbatim,bm}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,shapes}
\usepackage[color=light gray]{todonotes}
\usetikzlibrary{calc}
\newcommand{\slaveA}{{\mathfrak{B}}}
\begin{document}
\begin{tikzpicture}
\tikzstyle{state}=[draw,circle,minimum size=0.8cm]
\tikzstyle{Astate}=[draw,circle,minimum size=0.70cm]
\newcommand{\x}{0.8}
\begin{scope}[yshift=4cm,xshift=-2cm]
\node[state] (q11) at (0,-0.5) {$q_3$};
\node[Astate] at (0,-0.5) {};
\node[state] (q12) at (2*\x,-0.5) {$q_0$};
\node[state] (q15) at (2*\x,-2) {$q_1$};
\node[state] (q16) at (0,-2) {$q_2$};
\node (null) at (0.8,0.0) {};
\draw[->] (q12) to node[right] {(\#,0)} (q15);
\draw[->, loop right] (q15) to node[above] {(a,1)} (q15);
\draw[->] (q15) to node[above] {(\#,0)} (q16);
\draw[->, loop left] (q16) to node[above] {(a,-1)} (q16);
\draw[->] (null) to (q12);
\draw[->] (q16) to node[left] {(\#,0)} (q11);
\node (A1) at (1,-2.7) {$\slaveA_1$};
\end{scope}
\begin{scope}[yshift=3.8cm,xshift=1.8cm]
\node[state] (q21) at (0,-0.5) {$q_2$};
\node[Astate] at (0,-0.5) {};
\node[state] (q25) at (2*\x,-2) {$q_0$};
\node[state] (q26) at (0,-2) {$q_1$};
\node (null) at (1.0,-1.0) {};
\draw[->, loop right] (q25) to node[below] {(a,1)} (q25);
\draw[->] (q25) to node[below] {(\#,0)} (q26);
\draw[->, loop left] (q26) to node[below] {(a,-1)} (q26);
\draw[->] (null) to (q25);
\draw[->] (q26) to node[left] {(\#,0)} (q21);
\node (A2) at (1,-2.7) {$\slaveA_2$};
\end{scope}
\node[state] at (-2,0) {$q_0$};
\node[Astate] at (-2,0) {};
\node (A3) at (-2,-0.8) {$\slaveA_3$};
\node[state] (q1) at (0,0) {$q_0$};
\node[Astate] at (0,0) {};
\node[state] (q2) at (2*\x,0) {$q_1$};
\node[state] (q5) at (2*\x,-2) {$q_2$};
\node[state] (q6) at (0,-2) {$q_3$};
\node (null) at (-1.0,0.3) {};
\draw[->] (q1) to node[above] (e1) {(\#,1)} (q2);
\draw[->] (q2) to node[right] (e2) {(\#,2)} (q5);
\draw[->, loop right] (q5) to node[right] (e3) {(a,3)} (q5);
\draw[->] (q5) to node[above] (e4) {(\#,3)} (q6);
\draw[->, loop left] (q6) to node[left] (e5) {(a,3)} (q6);
\draw[->] (q6) to node[left] (e6) {(\#,3)} (q1);
\draw[->] (null) to (q1);
\draw[->,dotted] (e1) to (A1);
\draw[->,dotted] (e2) to (A2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1604.06764 | arxiv | 2016-04-25T02:11:06 |
|
One-dimensional digraph | \documentclass[12pt,a4paper,twoside]{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.4, >=stealth,shorten >=2pt,node distance=2.5cm, thick,main node/.style={circle,draw}]
\node [main node] (v1) {$v_{1}$};
\node [main node] (v2) [right of=v1]{$v_{2}$};
\node [main node] (v3) [right of=v2]{$v_{3}$};
\node [main node] (s1) [left of=v1]{$s_{1}$};
\node [main node] (s2) [right of=v3]{$s_{2}$};
\path [->] (v1) edge node {} (v2) %OK
(v2) edge node {} (v3) %OK
(v3) edge [bend right] node {} (v1) %OK
(s1) edge node {} (v1) %OK
(s2) edge node {} (v3) %OK
(v1) edge [out=145, in=65 , looseness=1.0, loop , distance=2cm] node {} (v1) %OK
(v1) edge [bend left=50] node {} (v3) %OK
(v3) edge [bend left] node {} (v2); %OK
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.7803 | arxiv | 2014-09-30T02:07:04 |
|
Realisation of the characteristic polynomial (eq:ExampleCharacteristicPolynomial) | \documentclass[12pt,a4paper,twoside]{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.25, >=stealth,shorten >=1pt,node distance=2.5cm, thick,main node/.style={circle,draw}]
\node [main node] (0) {$0$};
\node [main node] (1) [right of=0]{$1$};
\node [main node] (2) [right of=1]{$2$};
\path [->] (0) edge node {} (1)
(1) edge node [below, yshift=-0.4cm] {\small $w(1,2)(z-c_{\alpha})^{-1}$} (2)
(2) edge [bend right=40] node [above, xshift=-0.5cm] {\small $w(2,1)(z-c_{\alpha})^{-1}$} (1)
(2) edge [out=125, in=45 , looseness=1.5, loop , distance=4cm] node [above, xshift=1.5cm] {\small $w(2,2)(z-c_{\alpha})^{-1}$} (2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.7803 | arxiv | 2014-09-30T02:07:04 |
|
One-dimensional digraphs | \documentclass[12pt,a4paper,twoside]{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.25, >=stealth,shorten >=1pt,node distance=2.5cm, thick,main node/.style={circle,draw}]
\node [main node] (0) {$0$};
\node [main node] (1) [right of=0]{$1$};
\node [main node] (2) [right of=1]{$2$};
\path [->] (0) edge [in=100,out=80, distance=2.0cm] node [below]{\small $V[1,1]$} (1)
(0) edge [in=100,out=85, distance=3.5cm] node [pos=0.72, below] {\small $V[1,2]$} (2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.7803 | arxiv | 2014-09-30T02:07:04 |
|
Realisation of the characteristic polynomial (eq:ExampleCharacteristicPolynomial) | \documentclass[12pt,a4paper,twoside]{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.25, >=stealth,shorten >=1pt,node distance=2.5cm, thick,main node/.style={circle,draw}]
\node [main node] (0) {$0$};
\node [main node] (1) [right of=0]{$1$};
\node [main node] (2) [right of=1]{$2$};
\path [->] (0) edge node {} (1)
(1) edge node [below, yshift=-0.4cm] {\small $w(1,2)(z-c_{\alpha})^{-1}$} (2)
(2) edge [bend right=40] node [above, xshift=1.0cm] {\small $w(2,1)(z-c_{\alpha})^{-1}$} (1)
(1) edge [out=145, in=65 , looseness=1.5, loop , distance=4cm] node [above, xshift=-1.0cm] {\small $w(1,1)(z-c_{\alpha})^{-1}$} (1);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.7803 | arxiv | 2014-09-30T02:07:04 |
|
One-dimensional digraph with all possible realisation of the monomial M_2 | \documentclass[12pt,a4paper,twoside]{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.25, >=stealth,shorten >=1pt,node distance=2.5cm, thick,main node/.style={circle,draw}]
\node [main node] (0) {$0$};
\node [main node] (1) [right of=0]{$1$};
\node [main node] (2) [right of=1]{$2$};
\path [->] (0) edge node {} (1)
(1) edge node [below, yshift=-0.4cm] {\small $w(1,2)(z-c_{\alpha})^{-1}$} (2)
(2) edge [bend right=40] node [above] {\small $w(2,1)(z-c_{\alpha})^{-1}$} (1);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1409.7803 | arxiv | 2014-09-30T02:07:04 |
|
The widget graph W used to represent each variable | \documentclass[11pt]{article}
\usepackage{geometry,amssymb,latexsym,amsmath,graphicx, enumerate}
\usepackage[utf8]{inputenc}
\usepackage{tikz,ifthen}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
[thick,scale=1,
vertex/.style={circle,draw,inner sep=0pt,minimum
size=1.5mm,fill=white!100},
blackvertex/.style={circle,draw,inner sep=0pt,minimum
size=1.5mm,fill=black!100},
clause/.style={circle,draw,inner sep=0pt,minimum
size=3mm,fill=white!100}]
% positions
\coordinate (d1) at (0,0);
\coordinate (d2) at (0,3.5);
\coordinate (s1) at (-2,1);
\coordinate (s2) at (2,1);
\coordinate (x0) at (0,1);
\coordinate (x11) at (-1,1.5);
\coordinate (x12) at (-1,2.5);
\coordinate (x21) at (1,1.5);
\coordinate (x22) at (1,2.5);
%edges
\draw (d1)--(s1)--(x12)--(d2)--(x22)--(s2)--(d1);
\draw (d1)--(x0);
\draw (s2)--(x21)--(x0)--(x11)--(s1);
\draw
(x12)--(x0)--(x11)--(x22)--(x12)--(x21)--(d2)--(x11)--(x21)--(x0)--(x22);
%vertices
\draw (d1) node[blackvertex] {};
\draw (d2) node[blackvertex] {};
\draw (s1) node[vertex] {};
\draw (s2) node[vertex] {};
\draw (x0) node[vertex] {};
\draw (x11) node[vertex] {};
\draw (x12) node[vertex] {};
\draw (x21) node[vertex] {};
\draw (x22) node[vertex] {};
%labels
\draw (d1) node[below right] {$a_1$};
\draw (d2) node[above right] {$a_2$};
\draw (s1) node[left] {$b_1$};
\draw (s2) node[right] {$b_2$};
\draw (x0) node[below right] {$z$};
\draw (x11) node[below] {$x$};
\draw (x12) node[left] {$x'$};
\draw (x21) node[below] {$y$};
\draw (x22) node[right] {$y'$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1510.00140 | arxiv | 2016-06-20T02:12:33 |
|
The graph H|\{c_1,c_2,c_4\} for n=4 | \documentclass[11pt]{article}
\usepackage{geometry,amssymb,latexsym,amsmath,graphicx, enumerate}
\usepackage[utf8]{inputenc}
\usepackage{tikz,ifthen}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
[thick,scale=0.7,
vertex/.style={circle,draw,inner sep=0pt,minimum
size=1.5mm,fill=white!100},
blackvertex/.style={circle,draw,inner sep=0pt,minimum
size=1.5mm,fill=black!100},
clause/.style={circle,draw,inner sep=0pt,minimum
size=1.5mm,fill=white!100}]
\def\k {4};
\def\l {5};
% positions
\foreach \i in {0,1,...,\k}{
\coordinate (c\i) at (-90+\i*360/\l:2); }
\path (c0) ++(-0.5,-0.7) coordinate (x2) +(120:1) coordinate (x1);
\path (c0) ++(0.5,-0.7) coordinate (x3) +(60:1) coordinate (x4);
%edges
\draw (x1)--(x2)--(x3)--(x4);
\foreach \i in {1,2,...,\k}{
\foreach \j in {1,2,...,\i}{
\draw (c\i)--(c\j);
}}
\foreach \i in {1,2,...,\k}{
\draw (x1)--(c\i)--(x4);
% % partial edges
}
%vertices
\foreach \i in {1,2,...,\k}{
\draw (c\i) node[clause] {};}
\draw (c1) node[blackvertex] {};
\draw (c2) node[blackvertex] {};
\draw (c4) node[blackvertex] {};
\draw (x1) node[vertex] {};
\draw (x2) node[vertex] {};
\draw (x3) node[vertex] {};
\draw (x4) node[vertex] {};
%labels
\draw (c1) node[right] {$c_1$};
\draw (c2) node[right] {$c_2$};
\draw (c3) node[left] {$c_3$};
\draw (c4) node[left] {$c_4$};
\draw (x1) node[left] {$p_1$};
\draw (x2) node[left] {$p_2$};
\draw (x3) node[right] {$p_3$};
\draw (x4) node[right] {$p_4$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1510.00140 | arxiv | 2016-06-20T02:12:33 |
|
Example of the graph for formula X_1 (X_2 X_3)(X_3 X_4) | \documentclass[11pt]{article}
\usepackage{geometry,amssymb,latexsym,amsmath,graphicx, enumerate}
\usepackage[utf8]{inputenc}
\usepackage{tikz,ifthen}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
[thick,scale=0.45,
vertex/.style={circle,draw,inner sep=0pt,minimum
size=1.5mm,fill=white!100},
blackvertex/.style={circle,draw,inner sep=0pt,minimum
size=1.5mm,fill=black!100},
clause/.style={circle,draw,inner sep=0pt,minimum
size=2.2mm,fill=white!100}]
\def\k {3};
\def\l {4};
%%%% Variables
\foreach \i in {1,2,3,4}{
\coordinate (A\i) at (-20+8*\i,6);
\begin{scope}[shift=(A\i)]
% positions
\coordinate (d1\i) at (0,0);
\coordinate (d2\i) at (0,3.5);
\coordinate (s1) at (-2,1);
\coordinate (s2) at (2,1);
\coordinate (x0) at (0,1);
\coordinate (x11) at (-1,1.5);
\coordinate (x12) at (-1,2.5);
\coordinate (x21) at (1,1.5);
\coordinate (x22) at (1,2.5);
%edges
\draw (d1\i)--(s1)--(x12)--(d2\i)--(x22)--(s2)--(d1\i);
\draw (d1\i)--(x0);
\draw (s2)--(x21)--(x0)--(x11)--(s1);
\draw
(x12)--(x0)--(x11)--(x22)--(x12)--(x21)--(d2\i)--(x11)--(x21)--(x0)--(x22);
%vertices
\draw (d1\i) node[blackvertex] {};
\draw (d2\i) node[blackvertex] {};
\draw (s1) node[vertex] {};
\draw (s2) node[vertex] {};
\draw (x0) node[vertex] {};
\draw (x11) node[vertex] {};
\draw (x12) node[vertex] {};
\draw (x21) node[vertex] {};
\draw (x22) node[vertex] {};
%labels
\end{scope}
}
%%%% CLAUSES
% positions
\foreach \i in {0,1,...,\k}{
\coordinate (c\i) at (-90+\i*360/\l:3); }
\path (c0) ++(-0.5,-0.5) coordinate (x2) +(120:1) coordinate (x1);
\path (c0) ++(0.5,-0.5) coordinate (x3) +(60:1) coordinate (x4);
%edges
\draw (x1)--(x2)--(x3)--(x4);
\foreach \i in {1,2,...,\k}{
\foreach \j in {1,2,...,\i}{
\draw (c\i)--(c\j);
}};
\foreach \i in {1,2,...,\k}{
\draw (x1)--(c\i)--(x4);
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FORMULA %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\draw (c3)--(d11) (d21) .. controls +(+2,-0.5) .. (c3);
\draw (c2)--(d12) (d22) .. controls +(+2,-0.5) .. (c2);
\draw (c2)--(d13) (d23) .. controls +(-2,-0.5) .. (c2);
\draw (c1)--(d13) (d23) .. controls +(2,-0.5) and +(5.5,8) .. (c1);
\draw (c1)--(d14) (d24) .. controls +(-2,-0.5) .. (c1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%vertices
\foreach \i in {1,2,...,\k}{
\draw (c\i) node[clause] {};}
\draw (x1) node[vertex] {};
\draw (x2) node[vertex] {};
\draw (x3) node[vertex] {};
\draw (x4) node[vertex] {};
%labels
\draw (x4) node[below right] {$P$};
\draw (c1) node[below right] {$c_3$};
\draw (c2) node[right] {$c_2$};
\draw (c3) node[below left] {$c_1$};
\foreach \i in {1,2,3,4}{
\draw (d2\i) node[above] {$X_\i$};
}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1510.00140 | arxiv | 2016-06-20T02:12:33 |
|
Our feature extraction algorithm involves tracking the location of the patient's active wrist, segmenting the location signal, and then computing motion features. | \documentclass[letterpaper]{article}
\usepackage{amssymb}
\usepackage[usenames]{color}
\usepackage{tikz}
\usetikzlibrary{fit, positioning, shapes, arrows, intersections}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\tikzset{
smallblock/.style= {draw, rectangle, align=center,text width=3.2cm, inner sep=1mm, minimum height=1cm, node distance=0.7cm},
block/.style= {draw, rectangle, align=center,text width=4.5cm, inner sep=1mm, minimum height=1cm, node distance=0.7cm},
largeblock/.style= {draw, rectangle, align=center,text width=5.2cm, inner sep=1mm, minimum height=1cm, node distance=1cm},
line/.style = {draw, -latex'}
}
\node(poseest)[smallblock]{Run pose estimator\\ on each frame};
\node (A) [above right=0.4cm and -3.4cm of poseest] {\textbf{Track patient's head and active wrist}};
\node(optflow)[block, right=0.5cm of poseest]{Compute dense optical flow\\ between all adjacent frames};
\node(tempreg)[largeblock, below right=0.6cm and -2cm of poseest]{Enforce temporal continuity\\ of pose estimates\\ using optical flow};
\node[fit=(A)(poseest)(optflow)(tempreg), dashed,draw,inner sep=0.2cm] (Box) {};
\node(relloc)[largeblock, below=0.8cm of tempreg]{Compute wrist location relative to head location};
\node(seg)[largeblock, below=0.6cm of relloc]{Segment wrist location signal\\ into cycles};
\node(compfeat)[largeblock, below=0.6cm of seg]{Compute motion features};
\path[line](poseest)--(tempreg);
\path[line](optflow)--(tempreg);
\path[line](tempreg)--(relloc);
\path[line](relloc)--(seg);
\path[line](seg)--(compfeat);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1612.04007 | arxiv | 2017-01-23T02:02:42 |
|
% The gadget H_ of Provan and Ball~provan1983complexity as used in the proof of Theorem~thm:bishard. It corresponds to an -fattening of the edge~u,v, followed by a 4-stretch of each of the parallel edges. | \documentclass[a4paper,english]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{shapes}
\begin{document}
\begin{tikzpicture}[-, scale = 0.7]
\node[draw,circle](1) at (0,0) {$u$};
\node[draw,circle](2) at (1.5,1.5) {$~~$};
\node[draw,circle](3) at (1.5,-1.5) {$~~$};
\node[draw,circle](4) at (3,1.5) {$~~$};
\node[draw,circle](5) at (3,-1.5) {$~~$};
\node[draw,circle](6) at (4.5,1.5) {$~~$};
\node[draw,circle](7) at (4.5,-1.5) {$~~$};
\node[draw,circle](8) at (6,0) {$v$};
\draw(1) -- (2);
\draw(1) -- (3);
\draw(2) -- (4);
\draw(3) -- (5);
\draw(4) -- (6);
\draw(5) -- (7);
\draw(6) -- (8);
\draw(7) -- (8);
\node(10) at (4.25,0) {$\ell$ copies};
\node[circle,inner sep=1pt,fill](42) at (3,0.75) {};
\node[circle,inner sep=1pt,fill](43) at (3,0) {};
\node[circle,inner sep=1pt,fill](44) at (3,-0.75) {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1606.06581 | arxiv | 2016-06-22T02:12:08 |
|
Network architecture | \documentclass[11pt]{article}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\draw[->] (2.5, 0) node[below] {$x_{t-2}$} -- (2.5, 1);
\draw[->] (6.5, 0) node[below] {$x_{t-1}$} -- (6.5, 1);
\draw[->] (10.5, 0) node[below] {$x_t$} -- (10.5, 1);
\draw (1, 1) rectangle (4, 2);
\draw (2.5, 1.5) node {LSTM Layers};
\draw (5, 1) rectangle (8, 2);
\draw (6.5, 1.5) node {LSTM Layers};
\draw (9, 1) rectangle (12, 2);
\draw (10.5, 1.5) node {LSTM Layers};
\draw[->] (0, 1.5) -- (1, 1.5);
\draw[->] (4, 1.5) -- (5, 1.5);
\draw[->] (8, 1.5) -- (9, 1.5);
\draw[->] (12, 1.5) -- (13, 1.5);
\draw[->] (2.5, 2) -- (2.5, 3);
\draw[->] (6.5, 2) -- (6.5, 3);
\draw[->] (10.5, 2) -- (10.5, 3);
\draw (1, 3) rectangle (4, 4);
\draw (2.5, 3.5) node {Dense Layer};
\draw (5, 3) rectangle (8, 4);
\draw (6.5, 3.5) node {Dense Layer};
\draw (9, 3) rectangle (12, 4);
\draw (10.5, 3.5) node {Dense Layer};
\draw[->] (2.5, 4) -- (2.5, 5);
\draw[->] (6.5, 4) -- (6.5, 5);
\draw[->] (10.5, 4) -- (10.5, 5);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.07893 | arxiv | 2016-08-30T02:03:44 |
|
The number of ``blue'' regions is equal to the number of folds m. The number of total regions is t. For each observed c_j, instead of checking all the t regions, we only assign vote to the these ``blue'' regions. Since only these m ``blue'' regions can be the candidate region that contains frequency f. | \documentclass[11pt,documentclass,onecolumn]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}
\def\dx{8}
\draw (-\dx,0) -- (\dx,0) ;
\draw (\dx,0) -- (\dx,0.2);
\node at (-\dx,-0.5) {$l_j -\frac{\Delta l}{2}$};
\node at (\dx,-0.5) {$l_j + \frac{\Delta l}{2}$};
\node at (0,-0.5) {$l_j$};
\node at (3,0.5) {$l_j - \frac{\Delta l}{2} + (q'-1)\frac{\Delta l}{t}$};
\draw [red,thick] (2.5,0) -- (2.5,0.3);
\draw [red,thick] (3.0,0) -- (3.0,0.3);
\node at (4,-0.5) {$l_j - \frac{\Delta l}{2} + q'\frac{\Delta l}{t}$};
\draw (-\dx+1,0) -- (-\dx+1,0.2);
\draw (-\dx+2,0) -- (-\dx+2,0.2);
\draw (-\dx+3,0) -- (-\dx+3,0.2);
%%%%%%%%%%%
\draw (-\dx,-2) -- (\dx,-2) ;
\draw (-\dx,-3) -- (\dx,-3) ;
\foreach \i in {-\dx,...,7}
{
\draw (\i,0) -- (\i,0.2);
\draw (\i+0.5,0) -- (\i+0.5,0.2);
\draw (\i,-2) -- (\i,-3);
\draw (\i+0.5,-2) -- (\i+0.5,-3);
}
\draw (\dx,-2) -- (\dx,-3);
\foreach \i in {1,...,8}
{
\draw [fill=green,ultra thick,blue!50] (-\dx-2+0.5+\i*4*0.5,-3) rectangle (-\dx-2+0.5+0.5+\i*4*0.5,-2);
}
\draw [->,thick] (\dx-0.25,-3.5) -- (\dx-0.25,-3);
\node at (\dx-0.25,-3.8) {$\text{region}(j,t)$};
\node at (\dx-0.25,-2.5) {$v_{j,t}$};
\draw [->,thick] (-\dx+0.25,-3.5) -- (-\dx+0.25,-3);
\node at (-\dx+0.25,-3.8) {$\text{region}(j,1)$};
\node at (-\dx+0.25,-2.5) {$v_{j,1}$};
\node at (-\dx+0.25+0.5,-2.5) {$v_{j,2}$};
\draw [->,thick] (2.5+0.25,-3.5) -- (2.5+0.25,-3);
\node at (2.5+0.25,-3.8) {$\text{region}(j,q')$};
\node at (2.5+0.25,-2.5) {$v_{j,q'}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.00896 | arxiv | 2016-09-06T02:03:32 |
|
Diagram of the structure of a single LSTM cell | \documentclass[11pt]{article}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\draw[-] (4, 0) node[below] {$x_t$} -- (4, 1);
\draw[-] (6, 0) node[below] {$y_{t-1}$} -- (6, 1);
\draw[-] (4, 1) -- (6, 1);
\draw[-] (5, 1) -- (5, 1.5);
\draw (4.5, 1.5) rectangle (5.5, 2.5);
\draw (4.5, 1.5) .. controls (5, 1.5) and (5, 2.5) .. (5.5, 2.5);
\draw (4.5, 2) node[left] {Nonlinear Transformation};
\draw (5, 3) node[left] {$c_t$};
\draw[-] (5, 2.5) -- (5, 4);
\draw[-] (5, 4) node[circle,fill,inner sep=1pt,label=left:Input Gate]{} node[above right] {$i_t$} -- (6, 4);
\draw (6, 3.5) rectangle (7, 4.5);
\draw (6, 3.5) .. controls (6.5, 3.5) and (6.5, 4.5) .. (7, 4.5);
\draw[-] (7, 4) -- (8, 4);
\draw[-] (8, 5) -- (8, 3);
\draw[-] (8, 3) -- (9, 3) node[right] {$x_t$};
\draw[-] (8, 5) -- (9, 5) node[right] {$y_{t-1}$};
\draw[-] (5, 4) -- (5, 6);
\draw (4.5, 6) rectangle (5.5, 7);
\draw[-] (4.5, 6) -- (5.5, 7);
\draw (4.5, 6.5) node[above left] {Internal State};
\draw (4.5, 6.5) node[below left] {$S_t = i_t \odot c_t + f_t \odot S_{t-1}$};
\draw [-] (5, 7) .. controls (5, 7.5) and (6, 7.5) .. (6, 7);
\draw [-] (6, 7) -- (6, 6);
\draw [<-] (5, 6) .. controls (5, 5.5) and (6, 5.5) .. (6, 6);
\draw[-] (6, 6.5) node[circle,fill,inner sep=1pt,label=below right:Forget Gate](Forget Gate){} node[above right] {$f_t$} -- (8.5, 6.5);
\draw (8.5, 6) rectangle (9.5, 7);
\draw (8.5, 6) .. controls (9, 6) and (9, 7) .. (9.5, 7);
\draw[-] (9.5, 6.5) -- (10, 6.5);
\draw[-] (10, 5.5) -- (10, 7.5);
\draw[-] (10, 5.5) -- (10.5, 5.5) node[right] {$x_t$};
\draw[-] (10, 7.5) -- (10.5, 7.5) node[right] {$y_{t-1}$};
\draw (5, 7) -- (5, 8);
\draw (4.5, 8) rectangle (5.5, 9);
\draw (4.5, 8.5) node[left] {Nonlinear Transformation};
\draw (4.5, 8) .. controls (5, 8) and (5, 9) .. (5.5, 9);
\draw[->] (5, 9) -- (5, 11);
\draw[-] (5, 10) node[circle,fill,inner sep=1pt,label=left:Output Gate](Output Gate){} node[above right] {$o_t$} -- (6, 10);
\draw (6, 9.5) rectangle (7, 10.5);
\draw (6, 9.5) .. controls (6.5, 9.5) and (6.5, 10.5) .. (7, 10.5);
\draw[-] (7, 10) -- (8, 10);
\draw[-] (8, 9) -- (8, 11);
\draw[-] (8, 9) -- (9, 9) node[right] {$x_t$};
\draw[-] (8, 11) -- (9, 11) node[right] {$y_{t-1}$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1603.07893 | arxiv | 2016-08-30T02:03:44 |
|
We demonstrate the algorithm for merging various stages(R=O( k)) on 2-dimensional data. Note that the true data should be 3-dimensional, since for each tone (v_i,f_i), v_i C and f_i R. The x-axis represents the frequency and the y-axis represents the real part of magnitude. | \documentclass[11pt,documentclass,onecolumn]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=3cm,
thick,red node/.style={scale=.4,circle,fill=red,draw,font=\sffamily\bfseries},blue node/.style={scale=.4,circle,fill=blue,draw,font=\sffamily\bfseries},green node/.style={scale=.4,circle,fill=green,draw,font=\sffamily\bfseries},yellow node/.style={scale=.4,circle,fill=yellow,draw,font=\sffamily\bfseries},gray node/.style={scale=.4,circle,fill=gray,draw,font=\sffamily\bfseries}]
[scale=.8,auto=left,every node/.style={thick,->,>=stealth',auto,circle,fill=blue!20}]
\def\x{8.2}
\draw [->] (0,0) -- (7,0);
\draw [->] (0,0) -- (0,3);
\node at (0,-0.5) {$0$};
\node at (7,-0.5) {$F$};
\node[gray node] (gray1) at (0.20,1.30) {};
\node[gray node] (gray1) at (0.50,0.40) {};
\node[gray node] (gray1) at (0.70,2.60) {};
\node[gray node] (gray1) at (2.30,0.70) {};
\node[gray node] (gray1) at (2.40,1.60) {};
\node[gray node] (gray1) at (2.50,2.30) {};
\node[gray node] (gray1) at (4.80,1.10) {};
\node[gray node] (gray1) at (4.95,0.20) {};
\node[gray node] (gray1) at (5.20,2.40) {};
\node[gray node] (gray1) at (6.50,1.10) {};
\node[gray node] (gray1) at (6.60,0.20) {};
%%red node
\node[red node] (red1) at (1.05,1.10) {};
\node[red node] (red2) at (1.20,1.05) {};
\node[red node] (red3) at (1.15,1.35) {};
\node[red node] (red4) at (1.40,1.15) {};
\node[red node] (red5) at (1.35,1.00) {};
\node[red node] (red6) at (1.10,0.95) {};
\node[red node] (red7) at (0.90,1.20){};
\node[red node] (red8) at (1.60,1.10){};
%%green node
\node[green node] (green1) at (3.05,0.50) {};
\node[green node] (green2) at (3.20,0.65) {};
\node[green node] (green3) at (3.15,0.85) {};
\node[green node] (green4) at (3.40,0.75) {};
\node[green node] (green5) at (3.35,0.70) {};
\node[green node] (green6) at (3.10,0.85) {};
\node[green node] (green6) at (2.90,0.60){};
\node[green node] (green6) at (2.75,0.80){};
\node[green node] (green6) at (3.55,0.70){};
\node[green node] (green6) at (3.55,0.90){};
%%blue node
\node[blue node] (blue1) at (4.05,2.60) {};
\node[blue node] (blue2) at (4.20,2.55) {};
\node[blue node] (blue3) at (4.15,2.35) {};
\node[blue node] (blue4) at (4.40,2.55) {};
\node[blue node] (blue5) at (4.35,2.40) {};
\node[blue node] (blue6) at (4.10,2.85) {};
\node[blue node] (blue7) at (4.50,2.60) {};
\node[blue node] (blue8) at (4.60,2.20) {};
\node[blue node] (blue9) at (3.95,2.40) {};
%%yellow node
\node[yellow node] (yellow1) at (5.55,1.60) {};
\node[yellow node] (yellow2) at (5.70,1.45) {};
\node[yellow node] (yellow3) at (5.65,1.95) {};
\node[yellow node] (yellow4) at (5.90,1.55) {};
\node[yellow node] (yellow5) at (5.95,1.80) {};
\node[yellow node] (yellow6) at (5.60,1.85) {};
\node[yellow node] (yellow7) at (5.45,1.80) {};
\node[yellow node] (yellow8) at (5.40,1.85) {};
\node[yellow node] (yellow9) at (6.10,1.90) {};
\node[yellow node] (yellow10) at (6.05,1.55) {};
\node[] at (7.3,2.5) {$\mathsf{OneStage}$};
\draw [->] (6.5,2) -- (8.5,2);
\draw [->] (\x+0,0) -- (\x+7,0);
\draw [->] (\x+0,0) -- (\x+0,3);
\node at (\x+0,-0.5) {$0$};
\node at (\x+7,-0.5) {$F$};
\node[gray node] (gray1) at (\x+0.20,1.30) {};
\node[gray node] (gray1) at (\x+0.50,0.40) {};
\node[gray node] (gray1) at (\x+0.70,2.60) {};
\node[gray node] (gray1) at (\x+2.30,0.70) {};
\node[gray node] (gray1) at (\x+2.40,1.60) {};
\node[gray node] (gray1) at (\x+2.50,2.30) {};
\node[gray node] (gray1) at (\x+4.80,1.10) {};
\node[gray node] (gray1) at (\x+4.95,0.20) {};
\node[gray node] (gray1) at (\x+5.20,2.40) {};
\node[gray node] (gray1) at (\x+6.50,1.10) {};
\node[gray node] (gray1) at (\x+6.60,0.20) {};
%%red node
\node[red node] (red1) at (\x+1.05,1.10) {};
\node[red node] (red2) at (\x+1.20,1.05) {};
\node[red node] (red3) at (\x+1.15,1.35) {};
\node[red node] (red4) at (\x+1.40,1.15) {};
\node[red node] (red5) at (\x+1.35,1.00) {};
\node[red node] (red6) at (\x+1.10,0.95) {};
\node[red node] (red7) at (\x+0.90,1.20){};
\node[red node] (red8) at (\x+1.60,1.10){};
%%green node
\node[green node] (green1) at (\x+3.05,0.50) {};
\node[green node] (green2) at (\x+3.20,0.65) {};
\node[green node] (green3) at (\x+3.15,0.85) {};
\node[green node] (green4) at (\x+3.40,0.75) {};
\node[green node] (green5) at (\x+3.35,0.70) {};
\node[green node] (green6) at (\x+3.10,0.85) {};
\node[green node] (green6) at (\x+2.90,0.60){};
\node[green node] (green6) at (\x+2.75,0.80){};
\node[green node] (green6) at (\x+3.55,0.70){};
\node[green node] (green6) at (\x+3.55,0.90){};
%%blue node
\node[blue node] (blue1) at (\x+4.05,2.60) {};
\node[blue node] (blue2) at (\x+4.20,2.55) {};
\node[blue node] (blue3) at (\x+4.15,2.35) {};
\node[blue node] (blue4) at (\x+4.40,2.55) {};
\node[blue node] (blue5) at (\x+4.35,2.40) {};
\node[blue node] (blue6) at (\x+4.10,2.85) {};
\node[blue node] (blue7) at (\x+4.50,2.60) {};
\node[blue node] (blue8) at (\x+4.60,2.20) {};
\node[blue node] (blue9) at (\x+3.95,2.40) {};
%%yellow node
\node[yellow node] (yellow1) at (\x+5.55,1.60) {};
\node[yellow node] (yellow2) at (\x+5.70,1.45) {};
\node[yellow node] (yellow3) at (\x+5.65,1.95) {};
\node[yellow node] (yellow4) at (\x+5.90,1.55) {};
\node[yellow node] (yellow5) at (\x+5.95,1.80) {};
\node[yellow node] (yellow6) at (\x+5.60,1.85) {};
\node[yellow node] (yellow7) at (\x+5.45,1.80) {};
\node[yellow node] (yellow8) at (\x+5.40,1.85) {};
\node[yellow node] (yellow9) at (\x+6.10,1.90) {};
\node[yellow node] (yellow10) at (\x+6.05,1.55) {};
\draw [dashed] (\x+1.0,2) -- (\x+1.0,-0.2);
\draw [dashed] (\x+1.5,2) -- (\x+1.5,-0.2);
\node[] at (\x+1.2,-0.5) {$c\eta$};
\node[] at (\x+2.3,-0.5) {$\gtrsim \eta$};
\draw [dashed] (\x+3.0,2) -- (\x+3.0,-0.2);
\draw [dashed] (\x+3.5,2) -- (\x+3.5,-0.2);
\node [] at (\x+3.2,-0.5) {$c\eta$};
\draw [dashed] (\x+4.0,2.5) -- (\x+4.0,-0.2);
\draw [dashed] (\x+4.5,2.5) -- (\x+4.5,-0.2);
\node [] at (\x+4.2,-0.5) {$c\eta$};
\node [] at (\x+5.1,-0.5) {$\gtrsim \eta$};
\draw [dashed] (\x+5.5,2) -- (\x+5.5,-0.2);
\draw [dashed] (\x+6.0,2) -- (\x+6.0,-0.2);
\node [] at (\x+5.7,-0.5) {$c\eta$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.00896 | arxiv | 2016-09-06T02:03:32 |
|
_-^+(T,1|-f_i|) (T,1|-f_j|) d | \documentclass[11pt,documentclass,onecolumn]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}
\def\PI{2*3.14159265359}
\def\T{4}
\def\freqi{4}
\def\freqj{9}
\draw [domain=\freqi+1/\T:\freqj+3,variable=\t,smooth,samples=100]
plot (\t,{ 1/(\t-\freqi)/\T });
\draw [domain=\freqi-1/\T:\freqi-3,variable=\t,smooth,samples=100]
plot (\t,{ 1/(-\t+\freqi)/\T });
\draw (\freqi-1/\T,1) --(\freqi+1/\T,1);
\draw [domain=\freqj-1/\T:\freqi-3,variable=\t,smooth,samples=100]
plot (\t,{ 1/(-\t+\freqj)/\T });
\draw [domain=\freqj+1/\T:\freqj+3,variable=\t,smooth,samples=100]
plot (\t,{ 1/(\t-\freqj)/\T });
\draw (\freqj-1/\T,1) --(\freqj+1/\T,1);
\node at (1,-0.5) {$-\infty$};
\node at (12,-0.5) {$+\infty$};
\draw [blue] (1,0) -- (12,0);
\draw (\freqi,0) -- (\freqi,-0.2);
\node at (\freqi,-0.5) {$f_i$};
\draw (\freqj,0) -- (\freqj,-0.2);
\node at (\freqj,-0.5) {$f_j$};
\draw (\freqj+1/\T,0) -- (\freqj+1/\T,-0.2);
\node at (\freqj+1/\T+0.5,-0.8) {$f_j+\frac{1}{T}$};
\draw (\freqj-1/\T,0) -- (\freqj-1/\T,-0.2);
\node at (\freqj-1/\T-0.5,-0.8) {$f_j-\frac{1}{T}$};
\draw (\freqi+1/\T,0) -- (\freqi+1/\T,-0.2);
\node at (\freqi+1/\T+0.5,-0.8) {$f_i+\frac{1}{T}$};
\draw (\freqi-1/\T,0) -- (\freqi-1/\T,-0.2);
\node at (\freqi-1/\T-0.5,-0.8) {$f_i-\frac{1}{T}$};
\node at (\freqi, 1.5) {$\min(T,\frac{1}{|\theta-f_i|})$};
\node at (\freqj, 1.5) {$\min(T,\frac{1}{|\theta-f_j|})$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.00896 | arxiv | 2016-09-06T02:03:32 |
|
For an arbitrary frequency interval [ l_j - l2, l_j+ l2], we scale it by 2 to get a longer interval [2(l_j + l2) , 2(l_j - l2)]. Then, we wrap the longer interval on a circle [0,2). The number of folds after wrapping is l. For any random sample, the observation c_j is close to the true answer within 1/ with some ``good'' probability. | \documentclass[11pt,documentclass,onecolumn]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 1.0]
\def\PI{3.1415926}
\node at (-10,0) {$[-F,F] \supseteq$};
%%right value
\draw [->] (0,-2.5) -- (0,-0.9);
\draw [->] (2,-2) -- (2,-0.1);
\node at (0,-3) {$2\pi\sigma\beta(l_j-\frac{\Delta l}{2})$};
\node at (2,-2.5) {$2\pi\sigma\beta(l_j+\frac{\Delta l}{2})$};
\draw [thick] (-9,0) -- (-7,0);
\node at (-9,2) {$l_j - \frac{\Delta l}{2}$};
\draw [->](-9,1.8) -- (-9, 0.4);
\node at (-7,2) {$l_j + \frac{\Delta l}{2}$};
\draw [->](-7,1.8) -- (-7, 0.4);
\node at (-8,1) {$l_j$};
\draw [->] (-8,0.8) -- (-8,0.4);
\draw [thick] (-9,0) -- (-9,0.2);
\draw [thick] (-8,0) -- (-8,0.2);
\draw [thick] (-7,0) -- (-7,0.2);
%%% rightarrow
\node at (-4.5,0.5) {scaling by $2\pi \sigma \beta$};
\node at (-4.5,-0.5) {wrapping on a circle};
\draw[thick,->] (-6,0) -- (-3,0);
%%circle wrapping
%http://tex.stackexchange.com/questions/142814/how-can-i-draw-a-spiral-that-gets-arbitrary-close-to-a-unit-circle
\node at (0,2.4) {$\#$folds};
\draw [blue] (-0.2,0.8) -- (0.2,0.8);
\draw [blue] (-0.2,2.1) -- (0.2,2.1);
\draw [blue] (0,0.8) --(0,2.1);
\draw [domain=0:80,variable=\t,smooth,samples=500]
plot ({\t r}: {0.01+2*exp(-0.01*\t)});
\draw [->,thick,blue] (0,0) -- (2.5,2.5) ;
\draw [->] (0,0) -- (3,0) ;
\draw [->,thick,red] (0,0) -- ( { 3*0.76604 }, { 3*0.62478 } );
\draw [->,thick,red] (0,0) -- ( { 3*0.62478 }, { 3*0.76604 } );
\node at (1.5,3) {$c_j \approx$ {\color{blue} $2\pi\beta \sigma \theta$ } $\pm$ {\color{red} $\frac{1}{\rho}$} };
\node at (0.5,0.2) {{\color{blue} $\theta$ } };
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.00896 | arxiv | 2016-09-06T02:03:32 |
|
F() is a function and has derivate function F'(). | \documentclass[11pt,documentclass,onecolumn]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}
\def\PI{2*3.14159265359}
\def\s{2}
\def\dy{4}
\node at (2,1) {$F(\theta)$};
\node at (-8,-0.5) {$-\infty$};
\node at (8,-0.5) {$+\infty$};
\draw [domain=-0.05:-8,variable=\t,smooth,samples=500]
plot (\t,{sin(\s*\t r)/\t});
\draw [domain=0.05:8,variable=\t,smooth,samples=500]
plot (\t,{sin(\s*\t r)/\t});
\draw [blue] (-8,0) -- (8,0);
\draw [blue] (0,-1.5) -- (0,2.5);
\node at (2,1-\dy) {$F'(\theta)$};
\node at (-8,-0.5-\dy) {$-\infty$};
\node at (8,-0.5-\dy) {$+\infty$};
\draw [domain=-0.05:-8,variable=\t,smooth,samples=500]
plot (\t,{-\dy+(\s*\t*cos(\s*\t r) - sin(\s*\t r))/(\t*\t) });
\draw [domain=0.05:8,variable=\t,smooth,samples=500]
plot (\t,{-\dy+(\s*\t*cos(\s*\t r) - sin(\s*\t r))/(\t*\t) });
\draw [blue] (-8,0-\dy) -- (8,0-\dy);
\draw [blue] (0,-1.5-\dy) -- (0,2-\dy);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.00896 | arxiv | 2016-09-06T02:03:32 |
|
Filter G'(f) | \documentclass[11pt,documentclass,onecolumn]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}
\def\PI{3.1415926}
\def\s{3}
\def\height{0.8}
\def\rh{\height*sin(\s* 0.05 r)/0.05 }
\def\rc{1}
\def\rightposition{0.05+\rc+ 2*\PI/40}
\def\leftposition{ -0.05-\rc- 2*\PI/40}
\draw [blue] (-4.25,0) --(4,0);
\draw [dashed] (\leftposition-0.02 , -0.4) -- (\leftposition-0.02 , 2.6);
\draw [dashed] (\rightposition-0.22 , -0.4) -- (\rightposition-0.22 , 2.6);
\draw [dashed] (\leftposition-0.02 -1.0 , -0.4) -- (\leftposition-0.02 -1.0, 2.6);
\draw [dashed] (\rightposition-0.22 +0.95 , -0.4) -- (\rightposition-0.22 +0.95, 2.6);
\node at (\leftposition-0.02,-0.7) {$-\frac{(1-\alpha)\pi}{B}$};
\node at (\rightposition-0.22,-0.7) {$\frac{(1-\alpha)\pi}{B}$};
\node at (\leftposition-0.02-\rc-0.3,-0.7) {$-\frac{\pi}{B}$};
\node at (\rightposition-0.22+\rc,-0.7) {$\frac{\pi}{B}$};
\draw [domain={\leftposition-0.04}:{\rightposition-0.2},variable=\t,smooth,samples=500]
plot ( {\t },{\rh + 0.02* sin( 10* \t r)});
\draw [domain=-0.05:{-\PI/\s},variable=\t,smooth,samples=500]
plot ( {\t - \leftposition-0.07},{\height*sin(\s* \t r)/\t});
\draw [domain=0.05:{\PI/\s},variable=\t,smooth,samples=500]
plot ( {\t + \rightposition-0.3},{\height*sin(\s* \t r)/\t});
\draw [domain={-\PI/\s-\leftposition-1.7}:{-\PI/\s-\leftposition+0.3},variable=\t,smooth,samples=500]
plot ( {\t-0.37 },{ 0.02* sin( 10* \t r)});
\draw [domain={\PI/\s+\rightposition+2}:{\PI/\s+\rightposition-0.08},variable=\t,smooth,samples=500]
plot ( {\t -0.25 },{ 0.02* sin( 10* \t r)});
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1609.00896 | arxiv | 2016-09-06T02:03:32 |
|
Vertex Subset Relationships | \documentclass[12pt]{article}
\usepackage{amsfonts,amssymb,amscd,amsmath,enumerate,verbatim,calc,graphicx}
\usepackage[colorlinks,breaklinks,backref]{hyperref}
\usepackage[]{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=3cm,
thick,main node/.style={rectangle,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) {Identifying Code};
\node[main node] (1) [below left of=0] {Dominating Set};
\node[main node] (2) [below right of=0] {Determining Set};
\node[main node] (3) [above right of=2] {Resolving Set};
\path[every node/.style={font=\sffamily\small}]
(0) edge node [left] {} (1)
edge node [left] {} (2)
(3) edge node [left] {} (2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1412.5842 | arxiv | 2015-08-27T02:11:42 |
|
A 1-identifying code in the graph B(2,3)(black vertices). A 2-identifying code in this graph requires all vertices but one of \{000,111\}, and there are no t-identifying codes for t 3. | \documentclass[12pt]{article}
\usepackage{amsfonts,amssymb,amscd,amsmath,enumerate,verbatim,calc,graphicx}
\usepackage[colorlinks,breaklinks,backref]{hyperref}
\usepackage[]{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,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[new node] (1) [above right of=0] {001};
\node[main node] (2) [below right of=1] {010};
\node[new node] (4) [below right of=0] {100};
\node[main node] (5) [right of=2] {101};
\node[new 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/1412.5842 | arxiv | 2015-08-27T02:11:42 |
|
A minimum size determining set for B(2,3)(black vertex). | \documentclass[12pt]{article}
\usepackage{amsfonts,amssymb,amscd,amsmath,enumerate,verbatim,calc,graphicx}
\usepackage[colorlinks,breaklinks,backref]{hyperref}
\usepackage[]{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,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[new 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[main 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/1412.5842 | arxiv | 2015-08-27T02:11:42 |
|
A directed resolving set in the graph B(2,3)(black vertices). | \documentclass[12pt]{article}
\usepackage{amsfonts,amssymb,amscd,amsmath,enumerate,verbatim,calc,graphicx}
\usepackage[colorlinks,breaklinks,backref]{hyperref}
\usepackage[]{color}
\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,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[new node] (1) [above right of=0] {001};
\node[new node] (2) [below right of=1] {010};
\node[main node] (4) [below right of=0] {100};
\node[new node] (5) [right of=2] {101};
\node[new node] (6) [below right of=5] {110};
\node[main 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/1412.5842 | arxiv | 2015-08-27T02:11:42 |
|
Examples of popular concave penalization functions, that are closer to _0 than _1. In this work, we focus on MCP. | \documentclass[journal,a4paper, 10pt, twocolumn]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{intersections}
\usepackage[latin1]{inputenc}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\begin{axis}[xmin=-1.8,xmax=1.8,ymin=-0.02, ymax=1.1, xtick={0}, ytick={0}, ylabel={Penalization},axis lines=left, legend entries={\small{$\ell_1$}, \small{$\ell_0$} , ,\small{$\log$}, \small{MCP }},legend pos= south east]
\addplot[name path = funone, draw=black, mark=none, semithick] {abs(x)};
\addplot[draw=red, mark=none, semithick, domain=-1.8:-0.05,-(,shorten >=-1pt]
{1};
\addplot[ draw=red, mark=none, semithick, domain=1.8:0.05,-(,shorten >=-1pt]
{1};
\draw[color=red, fill] (axis cs:0,0) circle (2pt);
\addplot[draw=green, mark=none, semithick,samples=1500] {0.2*ln( 100*abs(x)+1)};
\addplot[draw=blue, mark=none,thick,domain=-sqrt(2):sqrt(2)]{abs(x)*sqrt(2)-0.5*x^2} ;
\addplot[ draw=blue, mark=none, thick, domain=-1.8:-sqrt(2)] {1};
\addplot[ draw=blue, mark=none, thick, domain=1.8:sqrt(2)] {1} ;
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1611.02431 | arxiv | 2016-11-09T02:04:12 |
|
T^i_k has 4 components. | \documentclass[reqno,12pt,twoside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amssymb}
\usepackage{amsmath,amsfonts,epsfig}
\usepackage{tikz}
\usetikzlibrary{arrows,patterns}
\usepackage{amssymb,latexsym}
\usetikzlibrary{arrows,patterns}
\usepackage{color}
\usepackage[final,linkcolor = blue,citecolor = blue,colorlinks=true]{hyperref}
\begin{document}
\begin{tikzpicture}[>=latex',scale=0.8]
%cycek -2
\shadedraw[shift={(11,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=205] (12,-1.515) arc [start angle=-90,end angle=90, x radius=0.4, y radius =1.08] to [out=205,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
%cycek
\shadedraw[top color=black!15!white, bottom color = black!25!white] (12,-1.515) to [out=25, in=-180] (13,-1.2) to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=25] (12,0.645) arc [start angle=90,end angle=270, x radius=0.4, y radius =1.08];
\filldraw[very thin,color=black,fill=white!80!gray] (12,0.565) arc [start angle=90,end angle=450, x radius=0.36, y radius =1];
%tentacle z alfy
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines]
(12,4.22) to [out=-4,in=180] (15,4) to [out=0,in=90](16,3.7) to [out=-90,in=0] (15,3.4) to [out=180,in=-4] (12,3.66) arc [start angle=270,end angle=90, x radius=0.1, y radius =0.28];
%wewn?trzna dziura - cie? -2
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -2
\draw (15,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (15,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -2
\draw[help lines] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%denko w alfie -2
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(11,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -2
\draw[color=white!20!gray,shift={(11,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 2
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=40] (1,-1) arc [start angle=270,end angle=90, x radius=0.095, y radius =0.27] to [out=40,in=190] (4.5,1) to [out=10, in=-90] (6.3,1.84);
%tentacle 2 cd
\shadedraw[color=darkgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}]
(1,2) to [out=25,in=190] (5,3) to [out=10,in=185] (12,3.89) arc [start angle=90,end angle=-90, x radius=0.09, y radius =0.25] to [out=185,in=10] (5,2.5) to [out=190,in=25] (1,1.6) arc [start angle=270,end angle=90, x radius=0.074, y radius =0.2];
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}]
(-4.55,-0.61) to [out=60,in=210]
(0,1.5) to [out=30,in=205] (1,2) arc [start angle=90,end angle=-90, x radius=0.074, y radius =0.2] to [out=205,in=30] (0,1) to [out=210,in=50] (-4,-0.58);
\begin{scope}
\draw[very thin,color=gray] (12,4.22) arc [start angle=90,end angle=-90, x radius=0.1, y radius =0.28];
\filldraw[very thin, color=gray, fill=white!90!gray] (12,4.19) arc [start angle=90, end angle=450, x radius =0.08, y radius=0.252];
\draw[very thin,color=gray] (12,2) arc [start angle=90,end angle=-90, x radius=0.074, y radius =0.2];
\draw[very thin,color=gray] (12,2) arc [start angle=90,end angle=270, x radius=0.074, y radius =0.2];
\filldraw[very thin, color=gray, fill=white!90!gray] (12,1.97) arc [start angle=90,end angle=450, x radius=0.058, y radius =0.17];
\draw[thin,color=black] (12,0.645) arc [start angle=90,end angle=-90, x radius=0.4, y radius =1.08];
\draw[very thin,color=gray, opacity=0.4] (12,0.565) arc [start angle=90,end angle=-90, x radius=0.37, y radius =1];
\draw[very thin,color=black] (12,0.565) arc [start angle=90,end angle=450, x radius=0.36, y radius =1];
\draw[very thin,color=gray] (12,-1) arc [start angle=-90,end angle=90, x radius=0.095, y radius =0.27];
\filldraw[very thin,color=gray,fill=white!90!gray] (12,-0.97) arc [start angle=-90,end angle=270, x radius=0.08, y radius =0.24];
\end{scope}
\begin{scope}[shift={(11,0)}]
\draw[very thin,color=gray] (12,3.89) arc [start angle=90,end angle=-90, x radius=0.09, y radius =0.25];
\draw[very thin,color=gray!90!white] (12,3.89) arc [start angle=90,end angle=270, x radius=0.09, y radius =0.25];
\draw[very thin,color=gray!90!white] (12,3.86) arc [start angle=90,end angle=450, x radius=0.07, y radius =0.22];
\draw[very thin, color=gray,opacity=0.5] (12,1.97) arc [start angle=90,end angle=450, x radius=0.058, y radius =0.17];
\draw[very thin,color=gray, opacity=0.5] (12,2) arc [start angle=90,end angle=270, x radius=0.074, y radius =0.2];
\draw[very thin,color=gray, opacity=0.5] (12,0.645) arc [start angle=90,end angle=-90, x radius=0.4, y radius =1.08];
\draw[very thin,color=gray, opacity=0.4] (12,0.565) arc [start angle=90,end angle=-90, x radius=0.37, y radius =1];
\draw[very thin,color=gray,opacity=0.4] (12,0.645) arc [start angle=90,end angle=270, x radius=0.4, y radius =1.08];
\draw[very thin,color=gray,opacity=0.4] (12,0.565) arc [start angle=90,end angle=270, x radius=0.37, y radius =1];
\end{scope}
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}]
(1,-1) to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45, in=-145] (1,-0.45) arc [start angle=90,end angle=-90, x radius=0.095, y radius =0.275] -- cycle;
\draw[very thin,color=gray, opacity=0.4] (23,-0.48) arc [start angle=90,end angle=-270, x radius=0.08, y radius =0.24];
\draw[very thin,color=gray, opacity=0.4] (23,-0.45) arc [start angle=90,end angle=270, x radius=0.095, y radius =0.27];
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1710.02050 | arxiv | 2017-10-06T02:07:59 |
|
A 3-trumpet and its loop. | \documentclass[reqno,12pt,twoside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amssymb}
\usepackage{amsmath,amsfonts,epsfig}
\usepackage{tikz}
\usetikzlibrary{arrows,patterns}
\usepackage{amssymb,latexsym}
\usetikzlibrary{arrows,patterns}
\usepackage{color}
\usepackage[final,linkcolor = blue,citecolor = blue,colorlinks=true]{hyperref}
\begin{document}
\begin{tikzpicture}[scale=0.25,>=latex']
%cycek -3
\shadedraw[shift={(22,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
%cycek -2
\shadedraw[shift={(11,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
%cycek
\shadedraw[top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=120,in=-60] (8,0) --cycle;
% ca?y torus
\shadedraw[top color=black!15!white, bottom color = black!25!white](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%denko w alfie
\shadedraw[color=lightgray,help lines,top color=black!30!white, bottom color=black!15!white] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi
\draw[color=white!20!gray,thick] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%lewe denko - ?rodek
\shadedraw[color=black,thick,top color=black!30!white, bottom color = black!5!white, opacity=0.5](1.2,1.1) arc [start angle=90, end angle=450, x radius=0.45, y radius=1.11];
%lewe denko - otok
\shadedraw[top color=black!60!white, bottom color = black!40!white, opacity=0.5](1.2,1.2) arc [start angle=90, end angle=450, x radius=0.5, y radius=1.2];
\draw[very thin,->] (-0.5,-2) -- (1.2,-1);
\node[below left] at (-0.5,-2) {$\gamma$};
%tentacle z alfy
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=20] (3,-0.1) to [out=200, in=-70] (0,0) to [out=110, in=-110] (0,2) to [out=70,in=180] (15,4) to [out=0,in=90](16,3.7) to [out=-90,in=0] (15,3.4) to [out=180,in=70] (0.45,1.6) to [out=-110,in=110] (0.45,0.4) to [out=-70,in=200] (3,0.5) to [out=30, in =190] (5.8,1.35) to [out=10, in=-90] (6.3,1.84);
\draw[color=gray,thick](1.2,1.1) arc [start angle=90, end angle=-90, x radius=0.45, y radius=1.11];
%ca?y torus raz jeszcze
\shadedraw[top color=black!5!white, bottom color = black!25!white, opacity=0.5](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%wewn?trzna dziura - cie?
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy
\draw (4,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (4,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury
\draw[help lines] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%alfa
%denko w alfie - pogrubienie
%alfa - brzeg
%wewn?trzna dziura - cie? -2
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -2
\draw (15,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (15,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -2
\draw[help lines] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%denko w alfie -2
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(11,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -2
\draw[color=white!20!gray,shift={(11,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 2
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 2 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1710.02050 | arxiv | 2017-10-06T02:07:59 |
|
Vertical planes intersecting a trumpet. | \documentclass[reqno,12pt,twoside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amssymb}
\usepackage{amsmath,amsfonts,epsfig}
\usepackage{tikz}
\usetikzlibrary{arrows,patterns}
\usepackage{amssymb,latexsym}
\usetikzlibrary{arrows,patterns}
\usepackage{color}
\usepackage[final,linkcolor = blue,citecolor = blue,colorlinks=true]{hyperref}
\begin{document}
\begin{tikzpicture}[scale=0.25,>=latex']
\filldraw[color=lightgray,fill=black!5!white,dashed] (10,8) -- (14,4)--(14,-8) --(10,-4)--(10,6);
\filldraw[color=lightgray,fill=black!5!white,dashed,shift={(11,0)}] (10,8) -- (14,4)--(14,-8) --(10,-4)--(10,6);
\filldraw[color=lightgray,fill=black!5!white,dashed,shift={(22,0)}] (10,8) -- (14,4)--(14,-8) --(10,-4)--(10,6);
%cycek -4
\shadedraw[shift={(33,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
%cycek -3
\shadedraw[shift={(22,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
%cycek -2
\shadedraw[shift={(11,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
%cycek
\shadedraw[top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=120,in=-60] (8,0) --cycle;
% ca?y torus
\shadedraw[top color=black!15!white, bottom color = black!25!white](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%denko w alfie
\shadedraw[color=lightgray,help lines,top color=black!30!white, bottom color=black!15!white] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi
\draw[color=white!20!gray,thick] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%lewe denko - ?rodek
\shadedraw[color=black,thick,top color=black!30!white, bottom color = black!5!white, opacity=0.5](1.2,1.1) arc [start angle=90, end angle=450, x radius=0.45, y radius=1.11];
%lewe denko - otok
\shadedraw[top color=black!60!white, bottom color = black!40!white, opacity=0.5](1.2,1.2) arc [start angle=90, end angle=450, x radius=0.5, y radius=1.2];
%tentacle z alfy
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=20] (3,-0.1) to [out=200, in=-70] (0,0) to [out=110, in=-110] (0,2) to [out=70,in=180] (15,4) to [out=0,in=90](16,3.7) to [out=-90,in=0] (15,3.4) to [out=180,in=70] (0.45,1.6) to [out=-110,in=110] (0.45,0.4) to [out=-70,in=200] (3,0.5) to [out=30, in =190] (5.8,1.35) to [out=10, in=-90] (6.3,1.84);
\draw[color=gray,thick](1.2,1.1) arc [start angle=90, end angle=-90, x radius=0.45, y radius=1.11];
%ca?y torus raz jeszcze
\shadedraw[top color=black!5!white, bottom color = black!25!white, opacity=0.5](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%wewn?trzna dziura - cie?
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy
\draw (4,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (4,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury
\draw[help lines] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%alfa
%denko w alfie - pogrubienie
%alfa - brzeg
%wewn?trzna dziura - cie? -2
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -2
\draw (15,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (15,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -2
\draw[help lines] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\begin{scope}
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\end{scope}
\begin{scope}[shift={(11,0)}]
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\end{scope}
%denko w alfie -2
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(11,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -2
\draw[color=white!20!gray,shift={(11,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 2
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 2 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\begin{scope}
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\end{scope}
\begin{scope}[shift={(11,0)}]
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\end{scope}
\draw (-1,-6) -- (56,-6);
\draw (1,-5.9) -- (1,-6.1);
\draw (12,-5.9) -- (12,-6.1);
\draw (23,-5.9) -- (23,-6.1);
\draw (34,-5.9) -- (34,-6.1);
\draw (45,-5.9) -- (45,-6.1);
\begin{scope}
\filldraw[color=lightgray,fill=black!5!white,dashed, opacity=0.35] (12,6) -- (14,4)--(14,-8) --(12,-6);
\filldraw[very thin,color=gray,fill=white!70!black] (12,4.22) arc [start angle=90,end angle=-90, x radius=0.1, y radius =0.27];
\draw[very thin,color=gray!80!white] (12,4.22) arc [start angle=90,end angle=270, x radius=0.1, y radius =0.27];
\filldraw[very thin,color=gray,fill=white!85!black] (12,2) arc [start angle=90,end angle=-90, x radius=0.074, y radius =0.2];
\draw[very thin,color=gray!70!white] (12,2) arc [start angle=90,end angle=270, x radius=0.074, y radius =0.2];
\draw[very thin,color=gray, opacity=0.5] (12,0.645) arc [start angle=90,end angle=-90, x radius=0.4, y radius =1.08];
\draw[very thin,color=gray, opacity=0.4] (12,0.565) arc [start angle=90,end angle=-90, x radius=0.37, y radius =1];
\draw[very thin,color=gray,opacity=0.4] (12,0.645) arc [start angle=90,end angle=270, x radius=0.4, y radius =1.08];
\draw[very thin,color=white!95!black] (12,0.645) arc [start angle=90,end angle=123, x radius=0.4, y radius =1.08];
\draw[very thin,color=gray,opacity=0.4] (12,0.565) arc [start angle=90,end angle=270, x radius=0.37, y radius =1];
\draw[very thin,color=gray, opacity=0.7] (12,-0.45) arc [start angle=90,end angle=-90, x radius=0.095, y radius =0.27];
\draw[very thin,color=gray, opacity=0.4] (12,-0.45) arc [start angle=90,end angle=270, x radius=0.095, y radius =0.27];
\end{scope}
\begin{scope}[shift={(11,0)}]
\filldraw[color=lightgray,fill=black!5!white,dashed, opacity=0.35] (12,6) -- (14,4)--(14,-8) --(12,-6);
\filldraw[very thin,color=gray,fill=white!70!black] (12,3.89) arc [start angle=90,end angle=-90, x radius=0.09, y radius =0.25];
\draw[very thin,color=gray!80!white] (12,3.89) arc [start angle=90,end angle=270, x radius=0.09, y radius =0.25];
\filldraw[very thin,color=gray,fill=white!85!black] (12,2) arc [start angle=90,end angle=-90, x radius=0.074, y radius =0.2];
\draw[very thin,color=gray!70!white] (12,2) arc [start angle=90,end angle=270, x radius=0.074, y radius =0.2];
\draw[very thin,color=gray, opacity=0.5] (12,0.645) arc [start angle=90,end angle=-90, x radius=0.4, y radius =1.08];
\draw[very thin,color=gray, opacity=0.4] (12,0.565) arc [start angle=90,end angle=-90, x radius=0.37, y radius =1];
\draw[very thin,color=gray,opacity=0.4] (12,0.645) arc [start angle=90,end angle=270, x radius=0.4, y radius =1.08];
\draw[very thin,color=white!95!black] (12,0.645) arc [start angle=90,end angle=123, x radius=0.4, y radius =1.08];
\draw[very thin,color=gray,opacity=0.4] (12,0.565) arc [start angle=90,end angle=270, x radius=0.37, y radius =1];
\draw[very thin,color=gray, opacity=0.7] (12,-0.45) arc [start angle=90,end angle=-90, x radius=0.095, y radius =0.27];
\draw[very thin,color=gray, opacity=0.4] (12,-0.45) arc [start angle=90,end angle=270, x radius=0.095, y radius =0.27];
\end{scope}
\begin{scope}[shift={(22,0)}]
\filldraw[color=lightgray,fill=black!5!white,dashed, opacity=0.35] (12,6) -- (14,4)--(14,-8) --(12,-6);
\filldraw[very thin,color=gray,fill=white!70!black] (12,3.89) arc [start angle=90,end angle=-90, x radius=0.09, y radius =0.25];
\draw[very thin,color=gray!80!white] (12,3.89) arc [start angle=90,end angle=270, x radius=0.09, y radius =0.25];
\filldraw[very thin,color=gray,fill=white!85!black] (12,2) arc [start angle=90,end angle=-90, x radius=0.074, y radius =0.2];
\draw[very thin,color=gray!70!white] (12,2) arc [start angle=90,end angle=270, x radius=0.074, y radius =0.2];
\draw[very thin,color=gray, opacity=0.5] (12,0.645) arc [start angle=90,end angle=-90, x radius=0.4, y radius =1.08];
\draw[very thin,color=gray, opacity=0.4] (12,0.565) arc [start angle=90,end angle=-90, x radius=0.37, y radius =1];
\draw[very thin,color=gray,opacity=0.4] (12,0.645) arc [start angle=90,end angle=270, x radius=0.4, y radius =1.08];
\draw[very thin,color=white!95!black] (12,0.645) arc [start angle=90,end angle=123, x radius=0.4, y radius =1.08];
\draw[very thin,color=gray,opacity=0.4] (12,0.565) arc [start angle=90,end angle=270, x radius=0.37, y radius =1];
\draw[very thin,color=gray, opacity=0.7] (12,-0.45) arc [start angle=90,end angle=-90, x radius=0.095, y radius =0.27];
\draw[very thin,color=gray, opacity=0.4] (12,-0.45) arc [start angle=90,end angle=270, x radius=0.095, y radius =0.27];
\end{scope}
\node[below] at (1,-6) {$-5$};
\node[below] at (12,-6) {$-4$};
\node[below] at (23,-6) {$-3$};
\node[below] at (34,-6) {$-2$};
\node[below] at (45,-6) {$-1$};
\node[below] at (56,-6) {$0$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1710.02050 | arxiv | 2017-10-06T02:07:59 |
|
Loop _1 is a commutator of _2 and _2. | \documentclass[reqno,12pt,twoside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amssymb}
\usepackage{amsmath,amsfonts,epsfig}
\usepackage{tikz}
\usetikzlibrary{arrows,patterns}
\usepackage{amssymb,latexsym}
\usetikzlibrary{arrows,patterns}
\usepackage{color}
\usepackage[final,linkcolor = blue,citecolor = blue,colorlinks=true]{hyperref}
\begin{document}
\begin{tikzpicture}[>=latex']
\node at (-0.3,0) {};
\node at (6,-9.7) {};
%seicycek
\begin{scope}[shift={(6.17,-8.95)}, scale=0.05]
\shadedraw[top color=white!20!gray, bottom color=lightgray!40!white] (5.4,-6) to [out=-80, in=75] (5.8,-7) to [out=-120,in=90] (5.5,-7.5) to [out=-90,in=180] (6.4,-8.1) to [out=0,in=-90] (7.3,-7.5) to[out=90,in=-60] (7,-7) to [out=105,in=-100] (7.4,-6);
\shadedraw[help lines, color=gray!10!lightgray, top color=white!35!lightgray, bottom color=black!10!lightgray] (5.97,-7.6) arc [start angle=-140, end angle=-40, x radius=0.62, y radius =0.35] arc [start angle=40, end angle=140, x radius=0.62, y radius =0.2];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-30, x radius=0.62, y radius =0.35];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-150, x radius=0.62, y radius =0.35];
\end{scope}
%tentacle z seicycka
\begin{scope}[shift={(6.17,-8.95)}, scale=0.05]
\filldraw[help lines,color=white!40!gray,fill=white!35!gray] (6.1,-7.56) arc [start angle=0, end angle=75, x radius=0.48, y radius=0.48];
\filldraw[very thin,fill=white!35!gray] (6.1,-7.56) arc [start angle=270-15, end angle=180, x radius=0.48, y radius=0.48];
\shadedraw[help lines, color=darkgray!20!lightgray,bottom color=darkgray!10!lightgray, top color= darkgray!30!lightgray] (6.1,-7.56) to [out=135,in=255] (6.3,-7) to [out=75,in=-75] (6.2,-6)--(6,-6) to[out=-75,in=75] (6.07,-7) to [out=255,in=-55] (5.75,-7.1);
\end{scope}
%quincycek
\begin{scope}[shift={(5.85,-8.46)}, scale=0.1]
\shadedraw[top color=white!20!gray, bottom color=lightgray!40!white] (5.4,-6) to [out=-80, in=75] (5.8,-7) to [out=-120,in=90] (5.5,-7.5) to [out=-90,in=180] (6.4,-8.1) to [out=0,in=-90] (7.3,-7.5) to[out=90,in=-60] (7,-7) to [out=105,in=-100] (7.4,-6);
\shadedraw[help lines, color=gray!10!lightgray, top color=white!35!lightgray, bottom color=black!10!lightgray] (5.97,-7.6) arc [start angle=-140, end angle=-40, x radius=0.62, y radius =0.35] arc [start angle=40, end angle=140, x radius=0.62, y radius =0.2];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-30, x radius=0.62, y radius =0.35];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-150, x radius=0.62, y radius =0.35];
\end{scope}
%tentacle z quincycka
\begin{scope}[shift={(6.22,-9.02)},scale=0.04]
\filldraw[color=lightgray!50!gray,fill=gray] (7,-4.71) arc [start angle=-97, end angle=14, x radius=0.9, y radius=0.9] -- (8.05,-3.64) arc [start angle=15, end angle=-89,x radius=0.9, y radius=0.9] --cycle;
\filldraw[help lines,fill=gray!40!lightgray,opacity=0.4] (7,-4.71) arc [start angle=-97, end angle=20, x radius=0.9, y radius=0.9] arc [start angle=83, end angle=200, x radius =0.9, y radius =0.9];
\draw[color=black] (7,-4.71) arc [start angle=-97, end angle=20, x radius=0.9, y radius=0.9];
\shadedraw[help lines, color=darkgray!20!lightgray,bottom color=lightgray, top color= darkgray!30!lightgray] (7,-4.71) to [out=55, in=-60] (6.22,-3) to [out=120,in=-100] (6.2,-2)-- (6.7,-2) to [out=-100,in=120] (6.8,-3) to [out=-60,in=-135] (7.95,-3.5) arc [start angle=20, end angle=-97, x radius=0.9, y radius=0.9];
\end{scope}
%quadcycek
\begin{scope}[shift={(5.2,-7.5)}, scale=0.2]
\shadedraw[top color=white!20!gray, bottom color=lightgray!40!white] (5.4,-6) to [out=-80, in=75] (5.8,-7) to [out=-120,in=90] (5.5,-7.5) to [out=-90,in=180] (6.4,-8.1) to [out=0,in=-90] (7.3,-7.5) to[out=90,in=-60] (7,-7) to [out=105,in=-100] (7.4,-6);
\shadedraw[help lines, color=gray!10!lightgray, top color=white!35!lightgray, bottom color=black!10!lightgray] (5.97,-7.6) arc [start angle=-140, end angle=-40, x radius=0.62, y radius =0.35] arc [start angle=40, end angle=140, x radius=0.62, y radius =0.2];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-30, x radius=0.62, y radius =0.35];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-150, x radius=0.62, y radius =0.35];
\end{scope}
%tentacle z quadcycka
\begin{scope}[shift={(5.2,-7.5)}, scale=0.2]
\filldraw[help lines,color=white!40!gray,fill=white!35!gray] (6.1,-7.56) arc [start angle=0, end angle=75, x radius=0.48, y radius=0.48];
\filldraw[very thin,fill=white!35!gray] (6.1,-7.56) arc [start angle=270-15, end angle=180, x radius=0.48, y radius=0.48];
\shadedraw[help lines, color=darkgray!20!lightgray,bottom color=darkgray!10!lightgray, top color= darkgray!30!lightgray] (6.1,-7.56) to [out=135,in=255] (6.3,-7) to [out=75,in=-75] (6.2,-6)--(6,-6) to[out=-75,in=75] (6.07,-7) to [out=255,in=-55] (5.75,-7.1);
\end{scope}
%tricycek
\begin{scope}[shift={(3.58,-5.15)}, scale=0.45]
\shadedraw[top color=white!20!gray, bottom color=lightgray!40!white] (5.4,-6) to [out=-80, in=75] (5.8,-7) to [out=-120,in=90] (5.5,-7.5) to [out=-90,in=180] (6.4,-8.1) to [out=0,in=-90] (7.3,-7.5) to[out=90,in=-60] (7,-7) to [out=105,in=-100] (7.4,-6);
\shadedraw[help lines, color=gray!10!lightgray, top color=white!35!lightgray, bottom color=black!10!lightgray] (5.97,-7.6) arc [start angle=-140, end angle=-40, x radius=0.62, y radius =0.35] arc [start angle=40, end angle=140, x radius=0.62, y radius =0.2];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-30, x radius=0.62, y radius =0.35];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-150, x radius=0.62, y radius =0.35];
\end{scope}
%tentacle z tricycka
\begin{scope}[shift={(5.2,-7.63)},scale=0.19]
\filldraw[color=lightgray!50!gray,fill=gray] (7,-4.71) arc [start angle=-97, end angle=16, x radius=0.9, y radius=0.9] -- (8.05,-3.64) arc [start angle=15, end angle=-89,x radius=0.9, y radius=0.9] --cycle;
\filldraw[help lines,fill=gray!40!lightgray,opacity=0.4] (7,-4.71) arc [start angle=-97, end angle=20, x radius=0.9, y radius=0.9] arc [start angle=83, end angle=200, x radius =0.9, y radius =0.9];
\draw[color=black] (7,-4.71) arc [start angle=-97, end angle=20, x radius=0.9, y radius=0.9];
\shadedraw[help lines, color=darkgray!20!lightgray,bottom color=lightgray, top color= darkgray!30!lightgray] (7,-4.71) to [out=55, in=-60] (6.22,-3) to [out=120,in=-100] (6.2,-2)-- (6.7,-2) to [out=-100,in=120] (6.8,-3) to [out=-60,in=-135] (7.95,-3.5) arc [start angle=20, end angle=-97, x radius=0.9, y radius=0.9];
\end{scope}
%bicycek
\shadedraw[top color=white!20!gray, bottom color=lightgray!40!white] (5.4,-6) to [out=-80, in=75] (5.8,-7) to [out=-120,in=90] (5.5,-7.5) to [out=-90,in=180] (6.4,-8.1) to [out=0,in=-90] (7.3,-7.5) to[out=90,in=-60] (7,-7) to [out=105,in=-100] (7.4,-6);
\shadedraw[help lines, color=gray!10!lightgray, top color=white!35!lightgray, bottom color=black!10!lightgray] (5.97,-7.6) arc [start angle=-140, end angle=-40, x radius=0.62, y radius =0.35] arc [start angle=40, end angle=140, x radius=0.62, y radius =0.2];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-30, x radius=0.62, y radius =0.35];
\draw (5.97,-7.6) arc [start angle=-140, end angle=-150, x radius=0.62, y radius =0.35];
%tentacle z bicycka
\filldraw[help lines,color=white!40!gray,fill=white!35!gray] (6.1,-7.56) arc [start angle=0, end angle=75, x radius=0.48, y radius=0.48];
\filldraw[fill=white!35!gray] (6.1,-7.56) arc [start angle=270-15, end angle=180, x radius=0.48, y radius=0.48];
\shadedraw[help lines, color=darkgray!20!lightgray,bottom color=darkgray!10!lightgray, top color= darkgray!30!lightgray] (6.1,-7.56) to [out=135,in=255] (6.3,-7) to [out=75,in=-75] (6.2,-6)--(6,-6) to[out=-75,in=75] (6.07,-7) to [out=255,in=-55] (5.75,-7.1);
%cycek
\filldraw[fill=lightgray!70!white] (4.7,-2)
to [out=-45, in=70] (5,-3)
to [out=-110, in=90] (4,-5)
to [out=-90, in=180] (6.35,-6.5)
to [out=0, in=-90] (8.7,-5)
to [out=90, in=-70] (7.7,-3)
to [out=110, in=-135] (8,-2)--cycle;
%dziura w cycku
\filldraw[color=darkgray,help lines, fill=white] (5.2,-4.9) arc [start angle=-140, end angle=-40, x radius=1.51, y radius =1] arc [start angle=40, end angle=140, x radius=1.5, y radius =0.7];
\draw[color=black] (5.2,-4.9) arc [start angle=-140, end angle=-30, x radius=1.5, y radius =1];
\draw[color=black] (5.2,-4.9) arc [start angle=-140, end angle=-150, x radius=1.5, y radius =1];
\draw[color=black] (5.2,-4.9) arc [start angle=140, end angle=40, x radius=1.5, y radius =0.7];
%wype?nienie dziury w cycku
\shadedraw[color=lightgray,top color=white!40!lightgray, bottom color=black!10!lightgray] (5.2,-4.9) arc [start angle=-140, end angle=-40, x radius=1.5, y radius =1] arc [start angle=40, end angle=140, x radius=1.5, y radius =0.7];
%wklejone denko w cycku
\filldraw[color=lightgray,fill=white!15!gray] (7,-4.71) arc [start angle=-97, end angle=19, x radius=0.9, y radius=0.9] -- (8.05,-3.64) arc [start angle=15, end angle=-89,x radius=0.9, y radius=0.9] --cycle;
\draw[color=black] (5.2,-4.9) arc [start angle=-140, end angle=-30, x radius=1.5, y radius =1];
\draw[color=black] (5.2,-4.9) arc [start angle=-140, end angle=-150, x radius=1.5, y radius =1];
\filldraw[help lines,fill=lightgray,opacity=0.4] (7,-4.71) arc [start angle=-97, end angle=20, x radius=0.9, y radius=0.9] arc [start angle=83, end angle=200, x radius =0.9, y radius =0.9];
\draw[color=black] (7,-4.71) arc [start angle=-97, end angle=20, x radius=0.9, y radius=0.9];
%tentacle z denka
\shadedraw[help lines, color=darkgray!20!lightgray,bottom color=white!7!lightgray, top color= darkgray!10!lightgray] (7,-4.71) to [out=55, in=-60] (6.22,-3) to [out=120,in=-100] (6.2,-2)-- (6.7,-2) to [out=-100,in=120] (6.8,-3) to [out=-60,in=-135] (7.95,-3.5) arc [start angle=20, end angle=-97, x radius=0.9, y radius=0.9];
% ca?y torus
\shadedraw[top color=black!5!white, bottom color = black!10!white](2,1) arc [start angle=145, end angle=-145, x radius=5, y radius=2] arc [start angle=-90, end angle=90, x radius=0.5, y radius=1.15] -- cycle;
%denko w alfie
\shadedraw[color=lightgray,help lines,top color=black!30!white, bottom color=black!15!white] (6.3,0.245) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.8];
%wklejone denko w alfie - brzegi
\draw[color=white!20!gray,thick] (6.3,0.245) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.8];
%tentacle z alfy
\shadedraw[color=lightgray,top color=black!30!white, bottom color = black!5!white,help lines] (6.3,0.245) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=20] (3,0.1) to [out=200, in=-90] (1.6,-0.1) to [out=90, in=210] (2,0.5)
to [out=30, in =180] (5.5,1.35) to [out=0, in=-90] (6.3,1.845);
\draw[color=darkgray,thick] (6.35,-4.85) ellipse [x radius=1.6, y radius=0.7];
\node at (7,-5.75) {$\beta_2$};
%lewe denko - otok
\shadedraw[top color=black!70!white, bottom color = black!50!white, opacity=0.5](2,1) arc [start angle=90, end angle=450, x radius=0.5, y radius=1.15];
%lewe denko - ?rodek
\shadedraw[color=darkgray,thick,top color=black!30!white, bottom color = black!5!white, opacity=1](2,0.9) arc [start angle=90, end angle=450, x radius=0.45, y radius=1.035];
%tentacle z lewego denka
\shadedraw[color=black,top color=black!30!white, bottom color = black!5!white] (2.28,0.655) arc [start angle=50, end angle=-0, x radius=0.45, y radius=1.035]
to [out=210, in =60] (1.3,-1.1)
to [out=240, in=135] (2.2,-3.5)
to [out=-45,in=20] (3,-5)
to [out=200,in=-20] (2.8,-5)
to [out=160, in=-45] (1.5,-4)
to [out=135, in=-90] (0.5,-1.5)
to [out=90,in=210] (2.28,0.655);
%ca?y torus raz jeszcze
\shadedraw[top color=black!50!white, bottom color = black!20!white, opacity=0.5](2,1) arc [start angle=145, end angle=-145, x radius=5, y radius=2] arc [start angle=-90, end angle=90, x radius=0.5, y radius=1.15] -- cycle;
%wewn?trzna dziura - cie?
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy
\draw (4,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (4,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury
\draw[help lines] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%denko w alfie - pogrubienie
\filldraw[fill=lightgray,color=lightgray,help lines] (6.3,0.245) arc [ start angle=-90, end angle=90,x radius=0.3, y radius=0.8] -- (6.4,1.855) arc [start angle=90, end angle=-90,x radius=0.3, y radius=0.8]--cycle ;
%alfa - brzeg
\draw[color=darkgray,thick] (6.3,0.245) arc [start angle=-90, end angle=90,x radius=0.3, y radius=0.8];
\draw[color=black,thin,->] (7,2.5)--(6.55,1.5);
\node at (7.1,2.6) {$\alpha_1$};
\draw[thick,color=darkgray] (6.35,0) ellipse [x radius=2.8, y radius=1];
\node at (7,-1.3) {$\beta_1$};
%tentacle z cycka na zewn?trz
\shadedraw[bottom color=white!15!lightgray, top color= darkgray!10!lightgray] (6.5,-0.615) to [out=70, in=160] (9,1) to [out=-20,in=88] (10.4,-2) to [out=-92,in=75] (8.8,-7.7) to [out=-105,in=0] (8.6,-8) to [out=180, in=-105] (8.4,-7.7) to [out=75,in=-92] (9.9,-2) to [out=88,in=-3] (8.5,0.7) to [out=183,in=65] (6.98,-0.59);
\draw[thick,color=gray] (10.12,-2.5) ellipse [x radius=0.25, y radius=0.08];
\draw[thick,color=black] (9.87,-2.5) arc [start angle=-180, end angle=0,x radius=0.25, y radius=0.08];
\node at (10.12,-2.75) {$\alpha_2$};
%tentacle z bicycka na zewn?trz
\shadedraw[bottom color=white!15!lightgray, top color= darkgray!10!lightgray] (6,-5.225) to [out=110,in=30] (4.6,-4.4) to [out=210,in=85] (3.8,-6) to [out=265,in=120] (5.3,-8.5) to [out=-60,in=180] (5.55,-8.75)to [out=0,in=-60] (5.5,-8.5) to [out=120,in=265] (4.02,-5.95) to [out=85,in=195] (4.82,-4.48) to [out=15,in=120] (5.8,-5.18);
%tentacle z tricycka na zewn?trz
\shadedraw[bottom color=white!15!lightgray, top color= darkgray!10!lightgray,shift={(5.2,-7.605)},scale=0.19] (6.5,-0.615) to [out=70, in=160] (9,1) to [out=-20,in=88] (10.4,-2) to [out=-92,in=75] (8.8,-7.7) to [out=-105,in=0] (8.6,-8) to [out=180, in=-105] (8.4,-7.7) to [out=75,in=-92] (9.9,-2) to [out=88,in=-3] (8.5,0.7) to [out=183,in=65] (6.98,-0.59);
%tentacle z quadcycka na zewn?trz
\shadedraw[bottom color=white!15!lightgray, top color= darkgray!10!lightgray,shift={(5.21,-7.573)}, scale=0.2] (6,-5.225) to [out=110,in=30] (4.6,-4.4) to [out=210,in=85] (3.8,-6) to [out=265,in=120] (5.3,-8.5) to [out=-60,in=180] (5.55,-8.75)to [out=0,in=-60] (5.5,-8.5) to [out=120,in=265] (4.02,-5.95) to [out=85,in=195] (4.82,-4.48) to [out=15,in=120] (5.8,-5.18);
%tentacle z quincycka na zewn?trz
\shadedraw[very thin,bottom color=white!15!lightgray, top color= darkgray!10!lightgray,shift={(6.22,-9.02)},scale=0.04] (6.5,-0.615) to [out=70, in=160] (9,1) to [out=-20,in=88] (10.4,-2) to [out=-92,in=75] (8.8,-7.7) to [out=-105,in=0] (8.6,-8) to [out=180, in=-105] (8.4,-7.7) to [out=75,in=-92] (9.9,-2) to [out=88,in=-3] (8.5,0.7) to [out=183,in=65] (6.98,-0.59);
%tentacle z seicycka na zewn?trz
\shadedraw[color=black,very thin,bottom color=white!15!lightgray, top color= darkgray!10!lightgray,shift={(6.17,-8.96)}, scale=0.05] (6,-5.225) to [out=110,in=30] (4.6,-4.4) to [out=210,in=85] (3.8,-6) to [out=265,in=120] (5.3,-8.5) to [out=-60,in=180] (5.55,-8.75)to [out=0,in=-60] (5.5,-8.5) to [out=120,in=265] (4.02,-5.95) to [out=85,in=195] (4.82,-4.48) to [out=15,in=120] (5.8,-5.18);
\begin{scope}
\clip (0,-9.3) rectangle (12,2);
\clip (6.5,-2.4) ellipse (5.5 and 7);
\draw[thick,dotted] (6.5,-9.3) circle (6.5);
\draw[thick,dotted] (6.5,-9.3) circle (2.8 and 2.6);
\draw[thick,dotted] (6.5,-9.3) circle (1.3 and 1.1);
\draw[thick,dotted] (6.5,-9.3) circle (0.5 and 0.45);
\end{scope}
\node at (1.3,-5.4) {$r_1$};
\node at (3.7,-8.7) {$r_2$};
\node at (5.2,-9.35) {$r_3$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1710.02050 | arxiv | 2017-10-06T02:07:59 |
|
The rectangular parallelepiped C^i_k contains T^i+1_k and T^i+2_k. | \documentclass[reqno,12pt,twoside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amssymb}
\usepackage{amsmath,amsfonts,epsfig}
\usepackage{tikz}
\usetikzlibrary{arrows,patterns}
\usepackage{amssymb,latexsym}
\usetikzlibrary{arrows,patterns}
\usepackage{color}
\usepackage[final,linkcolor = blue,citecolor = blue,colorlinks=true]{hyperref}
\begin{document}
\begin{tikzpicture}[>=latex',scale=0.8]
%7-trumpet
\begin{scope}[shift={(15,4)},scale=0.2]
\filldraw[very thin, draw=lightgray, fill=lightgray,opacity=0.3] (19,-4.5)--(41,-4.5)--(41,12)--(19,12);
\filldraw[color=black!20!white, fill=black!20!white] (65,30) -- (85,15) -- (85,-30) -- (65,-15);
\filldraw[fill=lightgray,draw=lightgray,opacity=0.4] (24,-8.25)--(24,-1.2)--(24,8.25)--(19,12)--(19,-4.5)--cycle;
\draw[very thin, dashed] (19,12)--(19,-4.5);
\begin{scope}[shift={(22,0)}]
\filldraw[fill=lightgray,draw=lightgray,opacity=0.4] (24,-8.25)--(24,-1.2)--(24,8.25)--(19,12)--(19,-4.5)--cycle;
\draw[very thin, dashed] (19,12)--(19,-4.5);
\end{scope}
\foreach \i in {5,4,3,2,1,0}
{
%cycek
\shadedraw[shift={(\i*11,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
}
%cycek -3
%cycek -2
%cycek
% ca?y torus
\shadedraw[top color=black!15!white, bottom color = black!25!white](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%denko w alfie
\shadedraw[color=lightgray,help lines,top color=black!30!white, bottom color=black!15!white] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi
\draw[color=white!20!gray,thick] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%lewe denko - ?rodek
\shadedraw[color=black,thick,top color=black!30!white, bottom color = black!5!white, opacity=0.5](1.2,1.1) arc [start angle=90, end angle=450, x radius=0.45, y radius=1.11];
%lewe denko - otok
\shadedraw[top color=black!60!white, bottom color = black!40!white, opacity=0.5](1.2,1.2) arc [start angle=90, end angle=450, x radius=0.5, y radius=1.2];
%tentacle z alfy
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=20] (3,-0.1) to [out=200, in=-70] (0,0) to [out=110, in=-110] (0,2) to [out=70,in=180] (15,4) to [out=0,in=90](16,3.7) to [out=-90,in=0] (15,3.4) to [out=180,in=70] (0.45,1.6) to [out=-110,in=110] (0.45,0.4) to [out=-70,in=200] (3,0.5) to [out=30, in =190] (5.8,1.35) to [out=10, in=-90] (6.3,1.84);
\draw[color=gray,thick](1.2,1.1) arc [start angle=90, end angle=-90, x radius=0.45, y radius=1.11];
%ca?y torus raz jeszcze
\shadedraw[top color=black!5!white, bottom color = black!25!white, opacity=0.5](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%wewn?trzna dziura - cie?
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy
\draw (4,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (4,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury
\draw[help lines] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%wewn?trzna dziura - cie? -2
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -2
\draw (15,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (15,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -2
\draw[help lines] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\begin{scope}
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\end{scope}
\foreach \i in {1,2,3}
{
\begin{scope}[shift={(\i*11,0)}]
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\end{scope}
}
%denko w alfie -2
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(11,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -2
\draw[color=white!20!gray,shift={(11,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 2
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 2 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\begin{scope}
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\end{scope}
\foreach \i in {1,2,3}
{
\begin{scope}[shift={(11*\i,0)}]
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\end{scope}
}
%maskowanie ustnika
\filldraw[color=black!20!white, fill=black!20!white] (73,2)--(77,2)--(77,-2.2)--(73,-2.2) arc [start angle=-90, end angle=90, x radius=1, y radius=2.1];
\filldraw[very thin,fill=lightgray,draw=lightgray,opacity=0.4] (24,8.25)--(29,4.5)--(29,-12)--(24,-8.25)--(24,-1.2) arc [x radius=0.6,y radius=1.2, start angle=-90, end angle=90]--(24,1.95) arc [x radius=0.11,y radius=0.22, start angle=-90, end angle=90]--(24,3.42) arc [x radius=0.13,y radius=0.26, start angle=-90, end angle=90]--cycle;
\draw[thin, densely dotted, draw=gray] (24,-1.2) arc [x radius=0.6,y radius=1.2, start angle=-90, end angle=90];
\draw[thin, densely dotted, draw=gray] (24,1.95) arc [x radius=0.11,y radius=0.22, start angle=-90, end angle=90];
\draw[thin, densely dotted, draw=gray] (24,3.42) arc [x radius=0.13,y radius=0.26, start angle=-90, end angle=90];
\draw[thick,lightgray!40!white] (24,-8.25)--(24,-4.5);
\draw[thick,lightgray!60!white] (24,-4.5)--(24,-1.23);
\draw[thick,lightgray!60!white] (24,1.24)--(24,1.925);
\draw[thick,lightgray!60!white] (24,2.42)--(24,3.4);
\draw[thick,lightgray!60!white] (24,3.98)--(24,8.23);
\draw[very thin, dashed] (19,12)--(29,4.5)--(29,-12)--(19,-4.5);
\begin{scope}[shift={(22,0)}]
\filldraw[very thin,fill=lightgray,draw=lightgray,opacity=0.4] (24,8.25)--(29,4.5)--(29,-12)--(24,-8.25)--(24,-1.2) arc [x radius=0.6,y radius=1.2, start angle=-90, end angle=90]--(24,1.95) arc [x radius=0.11,y radius=0.22, start angle=-90, end angle=90]--(24,3.42) arc [x radius=0.13,y radius=0.26, start angle=-90, end angle=90]--cycle;
\draw[thin, densely dotted, draw=gray] (24,-1.2) arc [x radius=0.6,y radius=1.2, start angle=-90, end angle=90];
\draw[thin, densely dotted, draw=gray] (24,1.95) arc [x radius=0.11,y radius=0.22, start angle=-90, end angle=90];
\draw[thin, densely dotted, draw=gray] (24,3.42) arc [x radius=0.13,y radius=0.26, start angle=-90, end angle=90];
\draw[thick,lightgray!40!white] (24,-8.25)--(24,-1.23);
\draw[thick,lightgray!40!white] (24,1.24)--(24,1.925);
\draw[thick,lightgray!40!white] (24,2.42)--(24,3.4);
\draw[thick,lightgray!40!white] (24,3.98)--(24,8.23);
\draw[very thin, dashed] (19,12)--(29,4.5)--(29,-12)--(19,-4.5);
\end{scope}
\filldraw[very thin, draw=lightgray, fill=lightgray,opacity=0.3] (29,-12)--(51,-12)--(51,4.5)--(29,4.5);
\draw[very thin, dashed] (29,-12)--(51,-12)--(51,-20.25)--(29,-20.25) -- (29,-12);
\draw[very thin, dashed] (19,-4.5)--(41,-4.5)--(41,-12.75)--(19,-12.75) -- (19,-4.5);
\draw[very thin, dashed] (19,-12.75)--(29,-20.25);
\draw[very thin, dashed] (41,-12.75)--(51,-20.25);
\begin{scope}[shift={(0,24.75)}]
\draw[very thin, dashed] (29,-12)--(51,-12)--(51,-20.25)--(29,-20.25) -- (29,-12);
\draw[very thin, dashed] (19,-4.5)--(41,-4.5)--(41,-12.75)--(19,-12.75) -- (19,-4.5);
\draw[very thin, dashed] (19,-12.75)--(29,-20.25);
\draw[very thin, dashed] (41,-12.75)--(51,-20.25);
\draw[very thin, dashed] (19,-4.5)--(29,-12);
\draw[very thin, dashed] (41,-4.5)--(51,-12);
\end{scope}
\node at (39,-6.5) {$B^i_k$};
\node at (55.6,6.9) {$T^i_k$};
\draw[very thin,->] (55,6) -- (52,2);
\node at (34.5,7) {$T^{i+2}_k$};
\draw[very thin,->] (33,6) -- (30,2);
\node[scale=1.2] at (35,25) {$C^i_k$};
\draw[thin,->] (51,-20.25)--(47,-20.25);
\draw[thin,->] (51,-20.25)--(51,-16.25);
\draw[thin,->] (51,-20.25)--(48.14285,-18.10714);
\node[scale=0.8] at (52.1,-18.75) {$e_1$};
\node[scale=0.8] at (49.5,-21.25) {$e_2$};
\node[scale=0.8] at (49.7,-18) {$e_3$};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1710.02050 | arxiv | 2017-10-06T02:07:59 |
|
A piece of the trumpet wall. | \documentclass[reqno,12pt,twoside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amssymb}
\usepackage{amsmath,amsfonts,epsfig}
\usepackage{tikz}
\usetikzlibrary{arrows,patterns}
\usepackage{amssymb,latexsym}
\usetikzlibrary{arrows,patterns}
\usepackage{color}
\usepackage[final,linkcolor = blue,citecolor = blue,colorlinks=true]{hyperref}
\begin{document}
\begin{tikzpicture}[scale=0.2,>=latex']
%wall
\filldraw[very thin,fill=black!15!white,dashed] (30,26) -- (56,10)--(56,-26) --(30,-10)--(30,26);
\filldraw[very thin,fill=black!8!white,dotted] (34,26) -- (30,26) -- (56,10)--(60,10);
\filldraw[very thin,fill=black!8!white,dotted] (60,10) -- (56,10) -- (56,-26)--(60,-26);
%1-trumpet
\begin{scope}[shift={(50,8)},scale=0.25]
%cycek
\shadedraw[top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=120,in=-60] (8,0) --cycle;
% ca?y torus
\shadedraw[top color=black!15!white, bottom color = black!25!white](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%denko w alfie
\shadedraw[color=lightgray,help lines,top color=black!30!white, bottom color=black!15!white] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi
\draw[color=white!20!gray,thick] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%lewe denko - ?rodek
\shadedraw[color=black,thick,top color=black!30!white, bottom color = black!5!white, opacity=0.5](1.2,1.1) arc [start angle=90, end angle=450, x radius=0.45, y radius=1.11];
%lewe denko - otok
\shadedraw[top color=black!60!white, bottom color = black!40!white, opacity=0.5](1.2,1.2) arc [start angle=90, end angle=450, x radius=0.5, y radius=1.2];
%tentacle z alfy
\shadedraw[color=lightgray!60!black,right color=black!40!white, left color = black!15!white,help lines] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=20] (3,-0.1) to [out=200, in=-70] (0,0) to [out=110, in=-110] (0,2) to [out=70,in=180] (15,4) to [out=0,in=90](16,3.7) to [out=-90,in=0] (15,3.4) to [out=180,in=70] (0.45,1.6) to [out=-110,in=110] (0.45,0.4) to [out=-70,in=200] (3,0.5) to [out=30, in =190] (5.8,1.35) to [out=10, in=-90] (6.3,1.84);
\draw[color=gray,thick](1.2,1.1) arc [start angle=90, end angle=-90, x radius=0.45, y radius=1.11];
%ca?y torus raz jeszcze
\shadedraw[top color=black!5!white, bottom color = black!25!white, opacity=0.5](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%wewn?trzna dziura - cie?
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy
\draw (4,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (4,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury
\draw[help lines] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%maskowanie ustnika
\filldraw[color=black!15!white, fill=black!15!white] (20,0) circle [radius=3];
\end{scope}
%3-trumpet
\begin{scope}[shift={(43,-17)},scale=0.25]
%cycek -3
\shadedraw[shift={(22,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
%cycek -2
\shadedraw[shift={(11,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
%cycek
\shadedraw[top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=120,in=-60] (8,0) --cycle;
% ca?y torus
\shadedraw[top color=black!15!white, bottom color = black!25!white](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%denko w alfie
\shadedraw[color=lightgray,help lines,top color=black!30!white, bottom color=black!15!white] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi
\draw[color=white!20!gray,thick] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%lewe denko - ?rodek
\shadedraw[color=black,thick,top color=black!30!white, bottom color = black!5!white, opacity=0.5](1.2,1.1) arc [start angle=90, end angle=450, x radius=0.45, y radius=1.11];
%lewe denko - otok
\shadedraw[top color=black!60!white, bottom color = black!40!white, opacity=0.5](1.2,1.2) arc [start angle=90, end angle=450, x radius=0.5, y radius=1.2];
%tentacle z alfy
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=20] (3,-0.1) to [out=200, in=-70] (0,0) to [out=110, in=-110] (0,2) to [out=70,in=180] (15,4) to [out=0,in=90](16,3.7) to [out=-90,in=0] (15,3.4) to [out=180,in=70] (0.45,1.6) to [out=-110,in=110] (0.45,0.4) to [out=-70,in=200] (3,0.5) to [out=30, in =190] (5.8,1.35) to [out=10, in=-90] (6.3,1.84);
\draw[color=gray,thick](1.2,1.1) arc [start angle=90, end angle=-90, x radius=0.45, y radius=1.11];
%ca?y torus raz jeszcze
\shadedraw[top color=black!5!white, bottom color = black!25!white, opacity=0.5](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%wewn?trzna dziura - cie?
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy
\draw (4,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (4,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury
\draw[help lines] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%alfa
%denko w alfie - pogrubienie
%alfa - brzeg
%wewn?trzna dziura - cie? -2
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -2
\draw (15,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (15,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -2
\draw[help lines] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%denko w alfie -2
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(11,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -2
\draw[color=white!20!gray,shift={(11,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 2
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 2 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
%maskowanie ustnika
\filldraw[color=black!15!white, fill=black!15!white] (43,0) circle [radius=3];
\end{scope}
%7-trumpet
\begin{scope}[shift={(15,4)},scale=0.25]
\foreach \i in {5,4,3,2,1,0}
{
%cycek
\shadedraw[shift={(\i*11,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
}
%cycek -3
%cycek -2
%cycek
% ca?y torus
\shadedraw[top color=black!15!white, bottom color = black!25!white](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%denko w alfie
\shadedraw[color=lightgray,help lines,top color=black!30!white, bottom color=black!15!white] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi
\draw[color=white!20!gray,thick] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%lewe denko - ?rodek
\shadedraw[color=black,thick,top color=black!30!white, bottom color = black!5!white, opacity=0.5](1.2,1.1) arc [start angle=90, end angle=450, x radius=0.45, y radius=1.11];
%lewe denko - otok
\shadedraw[top color=black!60!white, bottom color = black!40!white, opacity=0.5](1.2,1.2) arc [start angle=90, end angle=450, x radius=0.5, y radius=1.2];
%tentacle z alfy
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=20] (3,-0.1) to [out=200, in=-70] (0,0) to [out=110, in=-110] (0,2) to [out=70,in=180] (15,4) to [out=0,in=90](16,3.7) to [out=-90,in=0] (15,3.4) to [out=180,in=70] (0.45,1.6) to [out=-110,in=110] (0.45,0.4) to [out=-70,in=200] (3,0.5) to [out=30, in =190] (5.8,1.35) to [out=10, in=-90] (6.3,1.84);
\draw[color=gray,thick](1.2,1.1) arc [start angle=90, end angle=-90, x radius=0.45, y radius=1.11];
%ca?y torus raz jeszcze
\shadedraw[top color=black!5!white, bottom color = black!25!white, opacity=0.5](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%wewn?trzna dziura - cie?
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy
\draw (4,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (4,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury
\draw[help lines] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%alfa
%denko w alfie - pogrubienie
%alfa - brzeg
%wewn?trzna dziura - cie? -2
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -2
\draw (15,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (15,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -2
\draw[help lines] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\begin{scope}
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\end{scope}
\foreach \i in {1,2,3}
{
\begin{scope}[shift={(\i*11,0)}]
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\end{scope}
}
%denko w alfie -2
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(11,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -2
\draw[color=white!20!gray,shift={(11,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 2
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 2 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\begin{scope}
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\end{scope}
\foreach \i in {1,2,3}
{
\begin{scope}[shift={(11*\i,0)}]
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\end{scope}
}
%maskowanie ustnika
\filldraw[color=black!15!white, fill=black!15!white] (75,0) circle [radius=3];
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1710.02050 | arxiv | 2017-10-06T02:07:59 |
|
Case 2. | \documentclass[reqno,12pt,twoside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amssymb}
\usepackage{amsmath,amsfonts,epsfig}
\usepackage{tikz}
\usetikzlibrary{arrows,patterns}
\usepackage{amssymb,latexsym}
\usetikzlibrary{arrows,patterns}
\usepackage{color}
\usepackage[final,linkcolor = blue,citecolor = blue,colorlinks=true]{hyperref}
\begin{document}
\begin{tikzpicture}
%7-trumpet
\begin{scope}[shift={(15,4)},scale=0.12]
%the Wall
\filldraw[color=black!20!white, fill=black!20!white,shift={(44,0)}] (65,30) -- (85,15) -- (85,-30) -- (65,-15);
\foreach \i in {0,1}
{
\begin{scope}[shift={(-11+\i*55,0)}]
\filldraw[very thin, draw=lightgray, fill=lightgray,opacity=0.3] (19,-4.5)--(41,-4.5)--(41,12)--(19,12);
\filldraw[fill=lightgray,draw=lightgray,opacity=0.4] (24,-8.25)--(24,-1.2)--(24,8.25)--(19,12)--(19,-4.5)--cycle;
\draw[very thin, dashed] (19,12)--(19,-4.5);
\begin{scope}[shift={(22,0)}]
\filldraw[fill=lightgray,draw=lightgray,opacity=0.4] (24,-8.25)--(24,-1.2)--(24,8.25)--(19,12)--(19,-4.5)--cycle;
\draw[very thin, dashed] (19,12)--(19,-4.5);
\end{scope}
\end{scope}
}
%outlines of trumpet stages
\foreach \i in {9,8,7,6,5,4,3,2,1,0}
{
%cycek
\shadedraw[shift={(\i*11,0)},top color=black!15!white, bottom color = black!25!white] (3,0) to [out=-30, in=160] (7,-3.7) to [out=-20,in=-160] (9.9,-3.7) to [out=20, in=-180] (13,-1.2)
to [out=0,in=180] (17,-2) to [out=0,in=-90] (21.5,0) to [out=90,in=0] (17,1.8) to [out=180,in=20] (13,1.2)
to [out=200,in=40] (9.9,-1.7) to [out=220,in=-100] (7.7,-2) to [out=80,in=-60] (8,0) --cycle;
}
%first stage
\shadedraw[top color=black!15!white, bottom color = black!25!white](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%denko w alfie
\shadedraw[color=lightgray,help lines,top color=black!30!white, bottom color=black!15!white] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi
\draw[color=white!20!gray,thick] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%lewe denko - ?rodek
\shadedraw[color=black,thick,top color=black!30!white, bottom color = black!5!white, opacity=0.5](1.2,1.1) arc [start angle=90, end angle=450, x radius=0.45, y radius=1.11];
%lewe denko - otok
\shadedraw[top color=black!60!white, bottom color = black!40!white, opacity=0.5](1.2,1.2) arc [start angle=90, end angle=450, x radius=0.5, y radius=1.2];
%tentacle z alfy
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=20] (3,-0.1) to [out=200, in=-70] (0,0) to [out=110, in=-110] (0,2) to [out=70,in=180] (15,4) to [out=0,in=90](16,3.7) to [out=-90,in=0] (15,3.4) to [out=180,in=70] (0.45,1.6) to [out=-110,in=110] (0.45,0.4) to [out=-70,in=200] (3,0.5) to [out=30, in =190] (5.8,1.35) to [out=10, in=-90] (6.3,1.84);
\draw[color=gray,thick](1.2,1.1) arc [start angle=90, end angle=-90, x radius=0.45, y radius=1.11];
%ca?y torus raz jeszcze
\shadedraw[top color=black!5!white, bottom color = black!25!white, opacity=0.5](1.2,1.2) to [out=-20,in=180] (6,1.8) to [out=0,in=90] (10.5,0) to [out=-90,in=0] (6,-2) to [out=180,in=20] (1.2,-1.2) arc [start angle=-90, end angle=90, x radius=0.5, y radius =1.2];
%wewn?trzna dziura - cie?
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy
\draw (4,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (4,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury
\draw[help lines] (4,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
%wewn?trzna dziura - cie? -2
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -2
\draw (15,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (15,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -2
\draw[help lines] (15,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\begin{scope}
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\end{scope}
\foreach \i in {1,2,3,4,5,6,7}
{
\begin{scope}[shift={(\i*11,0)}]
%wewn?trzna dziura - cie? -3
\shadedraw[top color=black!20!white, bottom color=gray, color=lightgray, opacity=0.6] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] --cycle;
%dolny ?uk ?rodkowej dziury - u?miechy -3
\draw (26,-0.2) arc [start angle=-145, end angle=-155, x radius=2.8, y radius=1];
\draw (26,-0.2) arc [start angle=-145, end angle=-25, x radius=2.8, y radius=1];
%g�rny ?uk ?rodkowej dziury -3
\draw[help lines] (26,-0.2) arc [start angle=-145, end angle=-35, x radius=2.8, y radius=1] arc [start angle=35, end angle=145, x radius=2.8, y radius=1];
\end{scope}
}
%denko w alfie -2
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(11,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -2
\draw[color=white!20!gray,shift={(11,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 2
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 2 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(11,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\begin{scope}
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\end{scope}
\foreach \i in {1,2,3,4,5,6,7}
{
\begin{scope}[shift={(11*\i,0)}]
%denko w alfie -3
\shadedraw[color=lightgray,help lines,left color=black!20!white, right color=black!45!white,shift={(22,0)}] (6.3,0.24) arc [start angle=-90, end angle=270,x radius=0.3, y radius=0.78];
%wklejone denko w alfie - brzegi -3
\draw[color=white!20!gray,shift={(22,0)}] (6.3,0.24) arc [color=lightgray, start angle=270, end angle=90,x radius=0.3, y radius=0.78];
%tentacle 3
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (6.3,0.24) to [out=90,in=0] (5.8,0.6) to [out=180, in=10] (4.5,0.5) to [out=190, in=45] (1,-1)to [out=-135, in=0] (-2.5,-3.5) to [out=180,in=-85] (-4.8,-2.02)to [out=0,in=180] (-4.3,-2.02) to [out=-85, in=180] (-2.5,-3) to [out=0,in=-135] (0.4,-1) to [out=45,in=190] (4.5,1)
to [out=10, in=-90] (6.3,1.84);
%tentacle 3 cd
\shadedraw[color=lightgray,right color=black!40!white, left color = black!5!white,help lines,shift={(22,0)}] (-4.55,-0.6) to [out=60,in=210] (0,1.5) to [out=30,in=190] (5,3) to [out=10,in=180] (16.5,4)to [out=0,in=90] (17,3.75) to [out=-90,in=0](16.5,3.5) to [out=180,in=10] (5,2.5) to [out=190,in=35] (0,1) to [out=215,in=50] (-4,-0.55);
\end{scope}
}
%maskowanie ustnika
\filldraw[color=black!20!white, fill=black!20!white,shift={(44,0)}] (73,2)--(77,2)--(77,-2.2)--(73,-2.2) arc [start angle=-90, end angle=90, x radius=1, y radius=2.1];
\foreach \i in {0,1}
{
\begin{scope}[shift={(-11+\i*55,0)}]
\filldraw[very thin,fill=lightgray,draw=lightgray,opacity=0.4] (24,8.25)--(29,4.5)--(29,-12)--(24,-8.25)--(24,-1.2) arc [x radius=0.6,y radius=1.2, start angle=-90, end angle=90]--(24,1.95) arc [x radius=0.11,y radius=0.22, start angle=-90, end angle=90]--(24,3.42) arc [x radius=0.13,y radius=0.26, start angle=-90, end angle=90]--cycle;
\draw[thin, densely dotted, draw=gray] (24,-1.2) arc [x radius=0.6,y radius=1.2, start angle=-90, end angle=90];
\draw[thin, densely dotted, draw=gray] (24,1.95) arc [x radius=0.11,y radius=0.22, start angle=-90, end angle=90];
\draw[thin, densely dotted, draw=gray] (24,3.42) arc [x radius=0.13,y radius=0.26, start angle=-90, end angle=90];
\draw[thick,lightgray!40!white] (24,-8.25)--(24,-4.5);
\draw[thick,lightgray!60!white] (24,-4.5)--(24,-1.23);
\draw[thick,lightgray!60!white] (24,1.24)--(24,1.925);
\draw[thick,lightgray!60!white] (24,2.42)--(24,3.4);
\draw[thick,lightgray!60!white] (24,3.98)--(24,8.23);
\draw[very thin, dashed] (19,12)--(29,4.5)--(29,-12)--(19,-4.5);
\begin{scope}[shift={(22,0)}]
\filldraw[very thin,fill=lightgray,draw=lightgray,opacity=0.4] (24,8.25)--(29,4.5)--(29,-12)--(24,-8.25)--(24,-1.2) arc [x radius=0.6,y radius=1.2, start angle=-90, end angle=90]--(24,1.95) arc [x radius=0.11,y radius=0.22, start angle=-90, end angle=90]--(24,3.42) arc [x radius=0.13,y radius=0.26, start angle=-90, end angle=90]--cycle;
\draw[thin, densely dotted, draw=gray] (24,-1.2) arc [x radius=0.6,y radius=1.2, start angle=-90, end angle=90];
\draw[thin, densely dotted, draw=gray] (24,1.95) arc [x radius=0.11,y radius=0.22, start angle=-90, end angle=90];
\draw[thin, densely dotted, draw=gray] (24,3.42) arc [x radius=0.13,y radius=0.26, start angle=-90, end angle=90];
\draw[thick,lightgray!40!white] (24,-8.25)--(24,-1.23);
\draw[thick,lightgray!40!white] (24,1.24)--(24,1.925);
\draw[thick,lightgray!40!white] (24,2.42)--(24,3.4);
\draw[thick,lightgray!40!white] (24,3.98)--(24,8.23);
\draw[very thin, dashed] (19,12)--(29,4.5)--(29,-12)--(19,-4.5);
\end{scope}
\filldraw[very thin, draw=lightgray, fill=lightgray,opacity=0.3] (29,-12)--(51,-12)--(51,4.5)--(29,4.5);
\draw[very thin, dashed] (29,-12)--(51,-12)--(51,-20.25)--(29,-20.25) -- (29,-12);
\draw[very thin, dashed] (19,-4.5)--(41,-4.5)--(41,-12.75)--(19,-12.75) -- (19,-4.5);
\draw[very thin, dashed] (19,-12.75)--(29,-20.25);
\draw[very thin, dashed] (41,-12.75)--(51,-20.25);
\begin{scope}[shift={(0,24.75)}]
\draw[very thin, dashed] (29,-12)--(51,-12)--(51,-20.25)--(29,-20.25) -- (29,-12);
\draw[very thin, dashed] (19,-4.5)--(41,-4.5)--(41,-12.75)--(19,-12.75) -- (19,-4.5);
\draw[very thin, dashed] (19,-12.75)--(29,-20.25);
\draw[very thin, dashed] (41,-12.75)--(51,-20.25);
\draw[very thin, dashed] (19,-4.5)--(29,-12);
\draw[very thin, dashed] (41,-4.5)--(51,-12);
\end{scope}
\end{scope}
}
\node at (33,-6.5) {$B^i_k$};
\node at (88,-6.5) {$B^j_k$};
\node[scale=1.2] at (17,25) {$C^i_k$};
\node[scale=1.2] at (84,25) {$C^j_k$};
\filldraw[draw=gray,fill=gray] (22,-7) circle [radius=0.4];
\node at (24,-8) {$x$};
\draw[gray] (22,-7) to [out=70,in=-90] (25,0) to [out=90,in=-80] (24,8);
\filldraw (23,16) circle [radius=0.4];
\node at (21,18) {$x'$};
\filldraw (24,8) circle [radius=0.4];
\node at (27,8.5) {$x''$};
\draw[gray!80!black] (24,8) to [out=100,in=-90] (23,16);
\draw (24,8) arc [start angle=180, end angle=120, x radius=30, y radius = 20];
\draw[loosely dotted] (41,26.1) arc [start angle=115, end angle=65, x radius=30, y radius = 20] ;
\filldraw[draw=gray,fill=gray] (84.5,5) circle [radius=0.4];
\node at (87,5) {$y$};
\draw[gray] (84.5,5) to [out=110,in=-80] (82,8.5);
\filldraw (79,16) circle [radius=0.4];
\node at (77,16) {$y'$};
\filldraw (82,8.5) circle [radius=0.4];
\draw[gray!80!black] (82,8.5) to [out=100,in=-90] (79,16);
\draw (82,8.5) arc [start angle=0, end angle=60, x radius=30, y radius = 20];
\node at (85,10) {$y''$};
\draw[thin,->] (35,-23)--(24.2,-3.2);
\node at (36.5,-25) {$\gamma_x$};
\draw[thin,->] (65,-18)--(83,6.8);
\node at (63,-19.5) {$\gamma_y$};
\node at (53.5,31.5) {$\gamma_{x'' y''}$};
\filldraw[very thin, fill=white,draw=white] (46,5)--(56,5) --(56,-5)--(46,-5) -- cycle;
\node[scale=2] at (51,0) {...};
\filldraw[very thin, fill=white,draw=white,shift={(55,0)}] (43,5)--(52,5) --(52,-5)--(43,-5) -- cycle;
\node[scale=2] at (103,0) {...};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1710.02050 | arxiv | 2017-10-06T02:07:59 |
|
Response time (seconds) for correct and incorrect player predictions. Distributions are not significantly different (p=0.419). | \documentclass[format=acmsmall, review=false, screen=true]{acmart}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}
\usetikzlibrary{pgfplots.groupplots}
\usetikzlibrary{shapes.geometric}
\pgfplotsset{
jitter/.style={
y filter/.code={\pgfmathparse{\pgfmathresult+rnd*#1}}
},
jitter/.default=0.05
}
\begin{document}
\begin{tikzpicture}
\sffamily
\begin{axis}[
title =,
legend style={font=\scriptsize, draw= none, fill = none},
every tick label/.append style={font=\scriptsize},
width = 3.4in, height = 1.5in,
xlabel = {\small Response Time},
enlarge y limits=0.00,
ylabel near ticks,
ymin=0, ymax =2000,
xlabel near ticks,
y label style={at={(axis description cs:-0.08,.5)}},
]
\addplot[blue, fill = blue!30!white, opacity=0.99] coordinates {
%correct
(0.0,9) (1.0,106) (2.0,698) (3.0,1319) (4.0,1904) (5.0,2012) (6.0,1887) (7.0,1634) (8.0,1528) (9.0,1231) (10.0,1074) (11.0,863) (12.0,741) (13.0,615) (14.0,539) (15.0,412) (16.0,403) (17.0,328) (18.0,262) (19.0,215) (20.0,185) (21.0,174) (22.0,128) (23.0,128) (24.0,117) (25.0,103) (26.0,82) (27.0,79) (28.0,67) (29.0,63)
};
\addplot[red, fill = red!30!white, opacity=0.99,] coordinates {
%incorrect
(0.0,6) (1.0,81) (2.0,399) (3.0,734) (4.0,972) (5.0,1152) (6.0,1168) (7.0,1083) (8.0,999) (9.0,782) (10.0,759) (11.0,662) (12.0,540) (13.0,432) (14.0,365) (15.0,288) (16.0,242) (17.0,216) (18.0,183) (19.0,192) (20.0,134) (21.0,124) (22.0,104) (23.0,93) (24.0,85) (25.0,74) (26.0,72) (27.0,65) (28.0,64) (29.0,75)
};
\legend{Correct,Incorrect}
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1809.00740 | arxiv | 2018-09-05T02:24:11 |
|
No Entropy | \documentclass[10pt,journal,transmag]{IEEEtran}
\usepackage{tikz}
\usepackage{tikzscale}
\usepackage{colortbl}
\usepackage{pgfplotstable}
\usepackage{pgfplots}
\usepackage{amsmath,amsfonts,amssymb,amsthm,bm}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xlabel={Epoch},
ylabel={Accuracy},
legend pos=north west,
ymajorgrids=true,
grid style=dashed,
]
\addplot[color=blue]
coordinates {
(1,44.4444444444)(2,50.0)(3,66.6666666667)(4,72.2222222222)(5,66.6666666667)(6,72.2222222222)(7,66.6666666667)(8,66.6666666667)(9,72.2222222222)(10,72.2222222222)(11,72.2222222222)(12,72.2222222222)(13,72.2222222222)(14,77.7777777778)(15,77.7777777778)(16,77.7777777778)(17,77.7777777778)(18,77.7777777778)(19,77.7777777778)(20,77.7777777778)(21,77.7777777778)(22,83.3333333333)(23,83.3333333333)(24,72.2222222222)(25,83.3333333333)(26,83.3333333333)(27,83.3333333333)(28,83.3333333333)(29,83.3333333333)(30,77.7777777778)(31,83.3333333333)(32,83.3333333333)(33,83.3333333333)(34,83.3333333333)(35,83.3333333333)(36,83.3333333333)(37,83.3333333333)(38,83.3333333333)(39,83.3333333333)(40,83.3333333333)(41,83.3333333333)(42,83.3333333333)(43,83.3333333333)(44,83.3333333333)(45,83.3333333333)(46,83.3333333333)(47,83.3333333333)(48,83.3333333333)(49,83.3333333333)(50,83.3333333333)(51,83.3333333333)(52,83.3333333333)(53,83.3333333333)(54,83.3333333333)(55,83.3333333333)(56,83.3333333333)(57,83.3333333333)(58,83.3333333333)(59,83.3333333333)(60,83.3333333333)(61,83.3333333333)(62,83.3333333333)(63,83.3333333333)(64,83.3333333333)(65,83.3333333333)(66,83.3333333333)(67,83.3333333333)(68,83.3333333333)(69,83.3333333333)(70,83.3333333333)(71,83.3333333333)(72,83.3333333333)(73,83.3333333333)(74,83.3333333333)(75,83.3333333333)(76,83.3333333333)(77,83.3333333333)(78,83.3333333333)(79,83.3333333333)(80,83.3333333333)(81,83.3333333333)(82,83.3333333333)(83,83.3333333333)(84,83.3333333333)(85,83.3333333333)(86,83.3333333333)(87,83.3333333333)(88,83.3333333333)(89,83.3333333333)(90,83.3333333333)(91,83.3333333333)(92,83.3333333333)(93,83.3333333333)(94,83.3333333333)(95,83.3333333333)(96,83.3333333333)(97,83.3333333333)(98,83.3333333333)(99,83.3333333333)(100,83.3333333333)(101,83.3333333333)(102,83.3333333333)(103,83.3333333333)(104,83.3333333333)(105,83.3333333333)(106,83.3333333333)(107,83.3333333333)(108,83.3333333333)(109,83.3333333333)(110,83.3333333333)(111,83.3333333333)(112,83.3333333333)(113,83.3333333333)(114,83.3333333333)(115,83.3333333333)(116,83.3333333333)(117,83.3333333333)(118,83.3333333333)(119,83.3333333333)(120,83.3333333333)(121,83.3333333333)(122,83.3333333333)(123,83.3333333333)(124,83.3333333333)(125,83.3333333333)(126,83.3333333333)(127,83.3333333333)(128,83.3333333333)(129,83.3333333333)(130,83.3333333333)(131,83.3333333333)(132,83.3333333333)(133,83.3333333333)(134,83.3333333333)(135,83.3333333333)(136,83.3333333333)(137,83.3333333333)(138,83.3333333333)(139,83.3333333333)(140,83.3333333333)(141,83.3333333333)(142,83.3333333333)(143,83.3333333333)(144,83.3333333333)(145,83.3333333333)(146,83.3333333333)(147,83.3333333333)(148,83.3333333333)(149,83.3333333333)(150,83.3333333333)(151,83.3333333333)(152,83.3333333333)(153,83.3333333333)(154,83.3333333333)(155,83.3333333333)(156,83.3333333333)(157,83.3333333333)(158,83.3333333333)(159,83.3333333333)(160,83.3333333333)(161,83.3333333333)(162,83.3333333333)(163,83.3333333333)(164,83.3333333333)(165,83.3333333333)(166,83.3333333333)(167,83.3333333333)(168,83.3333333333)(169,83.3333333333)(170,83.3333333333)(171,83.3333333333)(172,83.3333333333)(173,83.3333333333)(174,83.3333333333)(175,83.3333333333)(176,83.3333333333)(177,83.3333333333)(178,83.3333333333)(179,83.3333333333)(180,83.3333333333)(181,83.3333333333)(182,83.3333333333)(183,83.3333333333)(184,83.3333333333)(185,83.3333333333)(186,83.3333333333)(187,83.3333333333)(188,83.3333333333)(189,83.3333333333)(190,83.3333333333)(191,83.3333333333)(192,83.3333333333)(193,83.3333333333)(194,83.3333333333)(195,83.3333333333)(196,83.3333333333)(197,83.3333333333)(198,83.3333333333)(199,83.3333333333)(200,83.3333333333)
};
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1709.08385 | arxiv | 2017-09-26T02:12:53 |
|
Accuracy | \documentclass[10pt,journal,transmag]{IEEEtran}
\usepackage{tikz}
\usepackage{tikzscale}
\usepackage{colortbl}
\usepackage{pgfplotstable}
\usepackage{pgfplots}
\usepackage{amsmath,amsfonts,amssymb,amsthm,bm}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xlabel={Epoch},
ylabel={Accuracy},
legend pos=north west,
ymajorgrids=true,
grid style=dashed,
]
\addplot[color=blue]
coordinates {
(1,16.6666666667)(2,33.3333333333)(3,33.3333333333)(4,42.0)(5,58.0)(6,58.0)(7,64.6666666667)(8,74.0)(9,77.3333333333)(10,78.0)(11,78.6666666667)(12,78.6666666667)(13,78.6666666667)(14,78.6666666667)(15,78.6666666667)(16,78.6666666667)(17,78.6666666667)(18,78.6666666667)(19,79.3333333333)(20,79.3333333333)(21,79.3333333333)(22,79.3333333333)(23,79.3333333333)(24,79.3333333333)(25,79.3333333333)(26,79.3333333333)(27,79.3333333333)(28,79.3333333333)(29,79.3333333333)(30,79.3333333333)(31,79.3333333333)(32,79.3333333333)(33,84.6666666667)(34,87.3333333333)(35,87.3333333333)(36,87.3333333333)(37,87.3333333333)(38,87.3333333333)(39,92.0)(40,92.0)(41,92.0)(42,92.0)(43,92.0)(44,92.0)(45,92.0)(46,92.0)(47,92.0)(48,92.0)(49,92.0)(50,92.0)(51,91.3333333333)(52,91.3333333333)(53,91.3333333333)(54,91.3333333333)(55,91.3333333333)(56,91.3333333333)(57,91.3333333333)(58,91.3333333333)(59,91.3333333333)(60,91.3333333333)(61,91.3333333333)(62,91.3333333333)(63,91.3333333333)(64,91.3333333333)(65,91.3333333333)(66,91.3333333333)(67,91.3333333333)(68,91.3333333333)(69,91.3333333333)(70,91.3333333333)(71,91.3333333333)(72,91.3333333333)(73,91.3333333333)(74,91.3333333333)(75,91.3333333333)(76,91.3333333333)(77,91.3333333333)(78,91.3333333333)(79,91.3333333333)(80,91.3333333333)(81,91.3333333333)(82,91.3333333333)(83,91.3333333333)(84,91.3333333333)(85,91.3333333333)(86,91.3333333333)(87,91.3333333333)(88,91.3333333333)(89,91.3333333333)(90,91.3333333333)(91,91.3333333333)(92,91.3333333333)(93,91.3333333333)(94,91.3333333333)(95,91.3333333333)(96,91.3333333333)(97,91.3333333333)(98,91.3333333333)(99,91.3333333333)(100,91.3333333333)(101,91.3333333333)(102,91.3333333333)(103,91.3333333333)(104,91.3333333333)(105,91.3333333333)(106,91.3333333333)(107,91.3333333333)(108,91.3333333333)(109,91.3333333333)(110,91.3333333333)(111,91.3333333333)(112,91.3333333333)(113,91.3333333333)(114,91.3333333333)(115,91.3333333333)(116,91.3333333333)(117,91.3333333333)(118,91.3333333333)(119,91.3333333333)(120,91.3333333333)(121,91.3333333333)(122,91.3333333333)(123,91.3333333333)(124,91.3333333333)(125,91.3333333333)(126,91.3333333333)(127,91.3333333333)(128,91.3333333333)(129,91.3333333333)(130,91.3333333333)(131,91.3333333333)(132,91.3333333333)(133,91.3333333333)(134,91.3333333333)(135,91.3333333333)(136,91.3333333333)(137,91.3333333333)(138,91.3333333333)(139,91.3333333333)(140,91.3333333333)(141,91.3333333333)(142,91.3333333333)(143,91.3333333333)(144,91.3333333333)(145,91.3333333333)(146,91.3333333333)(147,91.3333333333)(148,91.3333333333)(149,91.3333333333)(150,91.3333333333)(151,91.3333333333)(152,91.3333333333)(153,91.3333333333)(154,91.3333333333)(155,91.3333333333)(156,91.3333333333)(157,91.3333333333)(158,91.3333333333)(159,91.3333333333)(160,91.3333333333)(161,91.3333333333)(162,91.3333333333)(163,91.3333333333)(164,91.3333333333)(165,91.3333333333)(166,91.3333333333)(167,91.3333333333)(168,91.3333333333)(169,91.3333333333)(170,91.3333333333)(171,91.3333333333)(172,91.3333333333)(173,91.3333333333)(174,91.3333333333)(175,91.3333333333)(176,91.3333333333)(177,91.3333333333)(178,91.3333333333)(179,91.3333333333)(180,91.3333333333)(181,91.3333333333)(182,91.3333333333)(183,91.3333333333)(184,91.3333333333)(185,91.3333333333)(186,91.3333333333)(187,91.3333333333)(188,91.3333333333)(189,91.3333333333)(190,91.3333333333)(191,91.3333333333)(192,91.3333333333)(193,91.3333333333)(194,91.3333333333)(195,91.3333333333)(196,91.3333333333)(197,91.3333333333)(198,91.3333333333)(199,91.3333333333)(200,91.3333333333)
};
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1709.08385 | arxiv | 2017-09-26T02:12:53 |
|
Loss | \documentclass[10pt,journal,transmag]{IEEEtran}
\usepackage{tikz}
\usepackage{tikzscale}
\usepackage{colortbl}
\usepackage{pgfplotstable}
\usepackage{pgfplots}
\usepackage{amsmath,amsfonts,amssymb,amsthm,bm}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xlabel={Epoch},
ylabel={Loss},
legend pos=north west,
ymajorgrids=true,
grid style=dashed,
]
\addplot[color=blue]
coordinates {
(1,10.4208867105)(2,3.54709836245)(3,2.49701992989)(4,1.82397160769)(5,1.43311875979)(6,1.19170774698)(7,1.04767643134)(8,0.928929870129)(9,0.849987079302)(10,0.783912360668)(11,0.737599990368)(12,0.694495043755)(13,0.663360946178)(14,0.634204741319)(15,0.607301534017)(16,0.581317017873)(17,0.562984978358)(18,0.543091324965)(19,0.526758409341)(20,0.511348976294)(21,0.49542066733)(22,0.48448233525)(23,0.471139218012)(24,0.46061521848)(25,0.449605449041)(26,0.441346580187)(27,0.432134724458)(28,0.424323595365)(29,0.416519887447)(30,0.409754830996)(31,0.403712936242)(32,0.398227467537)(33,0.393072562218)(34,0.387631996473)(35,0.382697094282)(36,0.379256293774)(37,0.374848823547)(38,0.371861948967)(39,0.367107718786)(40,0.36467404445)(41,0.361048485438)(42,0.358396440347)(43,0.356146982511)(44,0.353112214406)(45,0.350838128726)(46,0.348096529643)(47,0.346560227871)(48,0.344988881747)(49,0.342361463706)(50,0.340565017064)(51,0.339166916211)(52,0.337667791843)(53,0.337078268528)(54,0.334806743463)(55,0.333399202824)(56,0.331588227749)(57,0.33059271733)(58,0.329080308278)(59,0.328821618557)(60,0.327389864127)(61,0.325973951022)(62,0.325373023351)(63,0.324868667126)(64,0.323185049693)(65,0.323312126795)(66,0.322028078238)(67,0.321320043405)(68,0.320612010956)(69,0.320513776938)(70,0.319735908508)(71,0.319512310028)(72,0.318820685546)(73,0.317756039302)(74,0.316770845254)(75,0.315983622074)(76,0.315458637873)(77,0.314942479928)(78,0.314327776432)(79,0.314089023272)(80,0.314094823996)(81,0.314049825668)(82,0.313600503604)(83,0.312807788054)(84,0.312146238486)(85,0.311612041791)(86,0.310949191252)(87,0.310612769127)(88,0.310046453476)(89,0.309523847103)(90,0.308986432552)(91,0.308665304979)(92,0.308878088792)(93,0.308586746852)(94,0.308492782911)(95,0.308048229218)(96,0.30765969038)(97,0.307377621333)(98,0.306815571785)(99,0.306474717458)(100,0.306192189058)(101,0.305982268651)(102,0.305350179672)(103,0.305388417244)(104,0.305023016135)(105,0.305322937171)(106,0.304928580125)(107,0.304613521894)(108,0.304450887839)(109,0.304386614164)(110,0.303951394558)(111,0.303636771838)(112,0.303348594507)(113,0.303165516059)(114,0.302883589268)(115,0.302566858133)(116,0.302258486748)(117,0.301905886332)(118,0.301690202554)(119,0.301829241117)(120,0.301660993099)(121,0.301389846007)(122,0.301276929379)(123,0.300533151627)(124,0.300493408839)(125,0.300438973904)(126,0.30063801686)(127,0.300356249809)(128,0.300268266996)(129,0.299990942478)(130,0.299675424894)(131,0.299506925742)(132,0.299580977758)(133,0.299486906528)(134,0.299353706042)(135,0.299030293624)(136,0.299131000837)(137,0.299040827751)(138,0.298642200629)(139,0.298620378971)(140,0.298458778858)(141,0.298525598049)(142,0.298570979436)(143,0.298200043043)(144,0.298149270217)(145,0.297947038015)(146,0.297996121248)(147,0.297908996741)(148,0.297834521135)(149,0.297700354258)(150,0.297609206041)(151,0.297325871785)(152,0.297285206318)(153,0.297139006456)(154,0.297052094936)(155,0.297054817677)(156,0.296980622609)(157,0.296587167581)(158,0.29650414149)(159,0.296559971968)(160,0.296308396657)(161,0.296045589447)(162,0.296044406891)(163,0.295965127945)(164,0.296094043255)(165,0.296161585649)(166,0.29586378177)(167,0.295864402453)(168,0.295618231297)(169,0.295448635419)(170,0.295336367289)(171,0.295325770378)(172,0.295229818821)(173,0.295061469078)(174,0.294995590051)(175,0.294918276469)(176,0.294669408003)(177,0.294492212931)(178,0.294641476472)(179,0.294363030593)(180,0.2943019104)(181,0.294367969831)(182,0.294297254086)(183,0.294205362002)(184,0.294039355119)(185,0.294215842883)(186,0.294310154915)(187,0.294238858223)(188,0.29395762682)(189,0.293773727417)(190,0.293799756368)(191,0.293674414158)(192,0.293686238925)(193,0.293584829171)(194,0.293474515279)(195,0.293450963497)(196,0.293507437706)(197,0.293371779124)(198,0.293456209501)(199,0.293230075041)(200,0.293039073944)
};
\end{axis}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1709.08385 | arxiv | 2017-09-26T02:12:53 |
|
Unfolding of the original square trajectories for the ball which corresponds to straight lines. | \documentclass[english]{article}
\usepackage{amssymb,amsmath,amsfonts,amsthm,epsfig,pstricks,graphics,tikz}
\begin{document}
\begin{tikzpicture}
\fill[gray!20!white] (0,0)--(9,0)--(9,3)--(0,3)--(0,0);
\fill[white] (0,0)--(3,0)--(3,3)--(0,3)--(0,0);
\draw[ultra thick] (0,0)--(9,0)--(9,3)--(0,3)--(0,0);
\foreach \x in {3,6} \draw[ultra thick] (\x,0)--(\x,3);
\draw[->] (0,0)--(3,1)--(0,2)--(2.9,2.9);
\draw[dashed,->] (3,1)--(8.9,2.9);
\draw (1.5,0) arc (0:18.3:1.5) node[above] at (1.2,0) {$\alpha$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1906.01911 | arxiv | 2019-06-06T02:11:07 |
|
Distribution of all endpoints for words of fixed length. Red equals n=1, orange n=2, yellow n=3, green n=4, blue n=5 and violet n=6. | \documentclass[english]{article}
\usepackage{amssymb,amsmath,amsfonts,amsthm,epsfig,pstricks,graphics,tikz}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\draw (0,0) grid (10.5,7.5);
\draw(0,0)--(7.5,7.5);
\fill[red!40!black,draw=black] (1,1) circle (0.1); %n=0
\fill[red,draw=black] (2,1) circle (0.1); %n=1
\fill[orange,draw=black] (3,1) circle (0.1); %n=2
\fill[orange,draw=black] (1,2) circle (0.1); %n=2
\fill[yellow,draw=black] (4,1) circle (0.1); %n=3
\fill[yellow,draw=black] (1,3) circle (0.1); %n=3
\fill[yellow,draw=black] (3,2) circle (0.1); %n=3
\fill[green,draw=black] (5,1) circle (0.1); %n=4
\fill[green,draw=black] (5,2) circle (0.1); %n=4
\fill[green,draw=black] (4,3) circle (0.1); %n=4
\fill[green,draw=black] (2,3) circle (0.1); %n=4
\fill[green,draw=black] (1,4) circle (0.1); %n=4
\fill[blue,draw=black] (6,1) circle (0.1); %n=5
\fill[blue,draw=black] (7,2) circle (0.1); %n=5
\fill[blue,draw=black] (5,3) circle (0.1); %n=5
\fill[blue,draw=black] (7,3) circle (0.1); %n=5
\fill[blue,draw=black] (5,4) circle (0.1); %n=5
\fill[blue,draw=black] (1,5) circle (0.1); %n=5
\fill[blue,draw=black] (2,5) circle (0.1); %n=5
\fill[blue,draw=black] (3,4) circle (0.1); %n=5
\fill[violet,draw=black] (7,1) circle (0.1); %n=6
\fill[violet,draw=black] (9,2) circle (0.1); %n=6
\fill[violet,draw=black] (10,3) circle (0.1); %n=6
\fill[violet,draw=black] (9,4) circle (0.1); %n=6
\fill[violet,draw=black] (8,3) circle (0.1); %n=6
\fill[violet,draw=black] (6,5) circle (0.1); %n=6
\fill[violet,draw=black] (7,5) circle (0.1); %n=6
\fill[violet,draw=black] (7,4) circle (0.1); %n=6
\fill[violet,draw=black] (1,6) circle (0.1); %n=6
\fill[violet,draw=black] (2,7) circle (0.1); %n=6
\fill[violet,draw=black] (3,7) circle (0.1); %n=6
\fill[violet,draw=black] (4,5) circle (0.1); %n=6
\fill[violet,draw=black] (3,5) circle (0.1); %n=6
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1906.01911 | arxiv | 2019-06-06T02:11:07 |
|
Quadratic billiard table with four corners labelled as A,~B,~C and D. | \documentclass[english]{article}
\usepackage{amssymb,amsmath,amsfonts,amsthm,epsfig,pstricks,graphics,tikz}
\begin{document}
\begin{tikzpicture}
\draw[ultra thick] (0,0)--(2,0)--(2,2)--(0,2)--(0,0);
\node[left] at (0,0) {$A$};
\node[left] at (0,2) {$D$};
\node[right] at (2,0) {$B$};
\node[right] at (2,2) {$C$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1906.01911 | arxiv | 2019-06-06T02:11:07 |
|
Construction of the straight line with slope m= by action of fib^k on 11. In addition, the line with slope m=1 is shown. | \documentclass[english]{article}
\usepackage{amssymb,amsmath,amsfonts,amsthm,epsfig,pstricks,graphics,tikz}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\draw[ultra thick,blue,dashed] (0,0)--(31.717:11) node[right] {\textbf{$m=\frac{1}{\varphi}$}};
\draw[gray] (0,0) grid (10.5,9.5);
\fill[black] (1,1) circle (0.1);
\draw (2,1) circle (0.1);
\draw[->] (1,1) arc (240:290:1);
\draw[->] (2,1)--(1.1,1.9);
\node[above] at (0.7,2) {$fib^1$};
\fill[black] (1,2) circle (0.1);
\draw (3,2) circle (0.1);
\draw[->] (1,2) arc (240:290:2);
\draw[->] (3,2)--(2.1,2.9);
\node[above] at (1.65,3) {$fib^2$};
\fill[black] (2,3) circle (0.1);
\draw (5,3) circle (0.1);
\draw[->] (2,3) arc (240:290:3);
\draw[->] (5,3)--(3.1,4.9);
\node[above] at (2.65,5) {$fib^3$};
\fill[black] (3,5) circle (0.1);
\draw (8,5) circle (0.1);
\draw[->] (3,5) arc (240:290:5);
\draw[->] (8,5)--(5.1,7.9);
\node[above] at (4.65,8) {$fib^4$};
\fill[black] (5,8) circle (0.1);
\draw[->] (5,8) arc (240:290:6.5);
\draw[blue,ultra thick] (0,0)--(58.2825:11);
\node[right,blue] at (6,9.3) {\textbf{$m=\varphi$}};
\draw[dashed] (0,0)--(9.1,9.1);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1906.01911 | arxiv | 2019-06-06T02:11:07 |
|
Blue points correspond to the words ^n_2. Red points correspond to words of the form ^n_1^n_2 forming straight lines of slope m=1n_1 with respect to the starting point (1|0). | \documentclass[english]{article}
\usepackage{amssymb,amsmath,amsfonts,amsthm,epsfig,pstricks,graphics,tikz}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\draw[gray] (0,0) grid (9.5,9.5);
\draw[black,ultra thick, dashed] (1,0)--(1,9.5);
\draw[black,dashed] (1,0)--(9.5,8.5);
\draw[black,dashed] (1,0)--(9.5,4.25);
\draw[black,dashed] (1,0)--(9.5,2.8333);
\draw[black,dashed] (1,0)--(9.5,2.125);
\draw[black,dashed] (1,0)--(9.5,1.7);
\draw[black,dashed] (1,0)--(9.5,1.4166);
\draw[black,dashed] (1,0)--(9.5,1.214);
\draw[black,dashed] (1,0)--(9.5,1.0625);
\draw[black,dashed] (1,0)--(9.5,0.95);
\foreach \x in {2,3,4,5,6,7,8,9} \fill[blue,draw=black] (\x,1) circle (0.1);
\foreach \x in {3,5,7,9} \fill[red,draw=black] (\x,2) circle (0.1) ; %tau^n sigma tau
\foreach \x in {4,7} \fill[red,draw=black] (\x,3) circle (0.1);
\foreach \x in {5,9} \fill[red,draw=black] (\x,4) circle (0.1);
\foreach \x in {2,3,4,5,6,7,8,9} \fill[red,draw=black] (1,\x) circle (0.1);
\fill[red,draw=black] (6,5) circle (0.1);
\fill[red,draw=black] (7,6) circle (0.1);
\fill[red,draw=black] (8,7) circle (0.1);
\fill[red,draw=black] (9,8) circle (0.1);
\fill[black] (1,0) circle (0.1) node[below] {$(1|0)$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1906.01911 | arxiv | 2019-06-06T02:11:07 |
|
A hangar having 2 bigons, 2 (curved) squares and a hexagon in the boundary. | \documentclass[english,12pt,leqno]{article}
\usepackage[latin1]{inputenc}
\usepackage{tikz-cd}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{pgfplots}
\usetikzlibrary{patterns}
\usetikzlibrary{calc}
\usepackage[OT2,T1]{fontenc}
\begin{document}
\begin{tikzpicture}[scale=0.5]
\node (a) at (10, -3){}; \fill(a) circle (0.2);
\node (b) at (15,2){}; \fill(b) circle (0.2);
\node(c) at (8,4){}; \fill(c) circle (0.2);
\node (d) at (-9,2){}; \fill(d) circle (0.2);
\node (e) at (-14, -3){}; \fill(e) circle (0.2);
\node (f) at (1,-6){}; \fill(f) circle (0.2);
\draw[line width =0.9] (e.center) -- (f.center) -- (a.center) -- (b.center);
\draw [dotted, line width=1.9] (e.center) -- (d.center) -- (c.center) -- (b.center);
\draw [line width=0.9] (10,-3) .. controls (11,2) and (12,3) .. (15,2);
\draw [line width=0.9] (-14,-3) .. controls (-13,2) and (-12,3) .. (-9,2);
\draw [line width=0.9] (1,-6) .. controls (3, 5) and (4, 6) .. (8,4);
\draw (-11.45,2.28) -- (5,4.78);
\draw (5,4.78) -- (12,2);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1909.09793 | arxiv | 2019-10-03T02:03:55 |
|
A point z in a Fox-Neuwirth-Fuchs cell. | \documentclass[english,12pt,leqno]{article}
\usepackage[latin1]{inputenc}
\usepackage{tikz-cd}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{pgfplots}
\usetikzlibrary{patterns}
\usetikzlibrary{calc}
\usepackage[OT2,T1]{fontenc}
\begin{document}
\begin{tikzpicture}[scale=.4, baseline=(current bounding box.center)]
\draw[->] (-2,0) -- (13,0);
\draw[->] (0,-2) -- (0,11);
\draw[dashed] (0,2) -- (11,2);
\draw[dashed] (0,4) -- (11,4);
\draw[dashed] (0,7) -- (11,7);
\node at (2,2){$\bullet$};
\node at (2,1.1){$\gamma^{(1)}_1$};
\node at (5,2){$\bullet$};
\node at (5,1.1){$\gamma^{(1)}_2$};
\node at (6.5, 1) {$\cdots$};
\node at (8,2){$\bullet$};
\node at (8,1.1){$\gamma^{(1)}_{p_1}$};
\node at (3,4){$\bullet$};
\node at (3, 3.1){$\gamma^{(2)}_1$};
\node at (5,3){$\cdots$};
\node at (7,4){$\bullet$};
\node at (7, 3.1){$\gamma^{(2)}_{p_2}$};
\node at (1,7){$\bullet$};
\node at (1, 8){$\gamma^{(q)}_1$};
\node at (4,7){$\bullet$};
\node at (4, 8){$\gamma^{(q)}_2$};
\node at (9,7){$\bullet$};
\node at (7,8){$\cdots$};
\node at (11,7){$\bullet$};
\node at (11, 8){$\gamma^{(q)}_{p_q}$};
\node at (6,5.5){$\cdots\cdots$};
\node at (-1,2){$y_1$}; \node at (-1,4){$y_2$}; \node at (-1,7){$y_q$};
\node at (-1, 5.8){$\vdots$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1909.09793 | arxiv | 2019-10-03T02:03:55 |
|
The contingency matrix () associated to z^n(). | \documentclass[english,12pt,leqno]{article}
\usepackage[latin1]{inputenc}
\usepackage{tikz-cd}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{pgfplots}
\usetikzlibrary{patterns}
\usetikzlibrary{calc}
\usepackage[OT2,T1]{fontenc}
\begin{document}
\begin{tikzpicture}[scale=.4, baseline=(current bounding box.center)]
\draw[->] (-2,0) -- (13,0);
\draw[->] (0,-2) -- (0,11);
\draw[dashed] (0,2) -- (11,2);
\draw[dashed] (0,4) -- (11,4);
\draw[dashed] (0,7) -- (11,7);
\node at (-1,2){$y_1$}; \node at (-1,4){$y_2$};
\node at (-1,5.5){$\vdots$};
\node at (-1,7){$y_q$};
\node at (2,7){$\bullet$};
\node at (2,2){$\bullet$};
\node at (8,2){$\bullet$};
\node at (5,4){$\bullet$};
\node at (8,7){$\bullet$}; \node at (8,4){$\bullet$};
\draw[dashed] (2,0) -- (2,9);
\draw[dashed] (5,0) -- (5,9);
\draw[dashed] (8,0) -- (8,9);
\node at (2,-1){$x_1$}; \node at (5,-1){$x_2$}; \node at (8,-1){$x_p$};
\node at (6.5, -1){$\cdots$};
\node at (2.9, 2.5){ \small{$\mu_{11}$}};
\node at (2.9, 7.5){\small {$\mu_{1q}$}};
\node at (5.9,4.5){\small {$\mu_{22}$}};
\node at (8.9,2.5){\small {$\mu_{p1}$}}; \node at (8.9,4.5){\small {$\mu_{p2}$}};
\node at (8.9,7.5){\small {$\mu_{pq}$}};
\iffalse
\node at (3,4){$\bullet$}; \node at (7,4){$\bullet$};
\node at (1,7){$\bullet$}; \node at (4,7){$\bullet$};
\node at (9,7){$\bullet$}; \node at (11,7){$\bullet$};
\node at (3,4){$\bullet$}; \node at (7,4){$\bullet$};
\node at (6,5.5){$\cdots\cdots$};
\node at (-1, 5.8){$\vdots$};
\node at (13,2){${\bf z} _1$}; \node at (13,4){${\bf z}_2$}; \node at (13,7){${\bf z}_p$};
\fi
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1909.09793 | arxiv | 2019-10-03T02:03:55 |
|
Let S(5)=\{x Z : x 5 \{0,3,4\}\}. We have Pairs_5(X) = \{(bb,aaabb),(abb,aabb),(aabb,abb)\}, and Pairs_5(Y) = \{(ba,ababa),(aba,baba),(baba,aba)\}. The compacted trie T(F) is illustrated above with light edges dotted. As a result, Pairs_5^(1)(X)=Pairs_5(X)\;\\\{(redab,aaabb),(breda,aaabb),(bb,aredbabb), (abreda,aabb),(abb,aaredab),(aabb,abreda),(aaredab,abb)\} and Pairs_5^(1)(Y)=Pairs_5(Y)\{(redaa,ababa),(aba,redaaba),(redaaba,aba)\} Consequently, (Pairs_5^(1)(X),Pairs_5^(0)(Y))=LCP(bb,ba)+LCP(aredbabb,ababa)=5, and (Pairs_5^(0)(X),Pairs_5^(1)(Y))=LCP(abb,aba)+LCP(aabb,redaaba)=\\=LCP(aabb,redaaba)+LCP(abb,aba)=5. All these pairs correspond to factors baaab of X and babab of Y. % | \documentclass{article}
\usepackage{amsthm,amssymb,amsmath}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amsfonts}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{decorations.pathmorphing,shapes}
\usetikzlibrary{calc,decorations.pathmorphing,shapes}
\usetikzlibrary{snakes}
\usepackage{tikz-qtree}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\tikzset{
treenode/.style = {align=center, inner sep=2pt, text centered,
font=\sffamily},
arn_r/.style = {treenode, circle, black, font=\sffamily\bfseries, draw=black,
text width=1.5em},
arn_t/.style = {treenode, circle, black, thick, double, font=\sffamily\bfseries, draw=black,
text width=1.5em},
every edge/.append style={anchor=south,auto=falseanchor=south,auto=false,font=3.5 em},
}
\begin{document}
\begin{tikzpicture}[yscale=-1]
\begin{scope}
\begin{scope}[every node/.style={circle,minimum size=.1cm,draw=black,inner sep = 0pt}, final/.style={minimum size=.2cm, fill=black}]
\draw(0,0) node[circle](eps){};
\draw(-2,1) node(a){};
\draw(-3,2) node(aa){};
\draw(-3.5,5) node[final](aaabb){};
\draw(-2.5,4) node[final](aabb){};
\draw(-1,2) node(ab){};
\draw (-1.5,3) node[final](aba){};
\draw (-1.5,5) node[final](ababa){};
\draw (-0.5,3) node[final](abb){};
\draw(2,1) node(b){};
\draw(1,2) node[final](ba){};
\draw(1,4) node[final](baba){};
\draw(3,2) node[final](bb){};
\end{scope}
\draw[thick] (eps) --node[left]{$\texttt{a}$} (a);
\draw[thick,dotted] (a) --node[left]{$\texttt{a}$} (aa);
\draw[thick] (aa) --node[left]{$\texttt{abb}$} (aaabb);
\draw[thick,dotted] (aa) --node[right]{$\texttt{bb}$} (aabb);
\draw[thick] (a) --node[right]{$\texttt{b}$} (ab);
\draw[thick] (ab) --node[left]{$\texttt{a}$} (aba);
\draw[thick] (aba) --node[right]{$\texttt{ba}$} (ababa);
\draw[thick,dotted] (ab) --node[right]{$\texttt{b}$} (abb);
\draw[thick,dotted] (eps) --node[right]{$\texttt{b}$} (b);
\draw[thick] (b) --node[left]{$\texttt{a}$} (ba);
\draw[thick] (ba) --node[right]{$\texttt{ba}$} (baba);
\draw[thick,dotted] (b) --node[right]{$\texttt{b}$} (bb);
\end{scope}
\begin{scope}[xshift=5cm]
\draw (0,0) node[left]{$\texttt{aaabbb}\:\leadsto$};
\draw (0,0) node[right]{$\texttt{aaabbb}\ \texttt{a\textcolor{red}{b}abbb}$};
\draw (0,1/2) node[left]{$\texttt{aabb}\:\leadsto$};
\draw (0,1/2) node[right]{$\texttt{aabb}\ \texttt{a\textcolor{red}{b}bb}$};
\draw (0,2/2) node[left]{$\texttt{aba}\:\leadsto$};
\draw (0,2/2) node[right]{$\texttt{aba}$};
\draw (0,3/2) node[left]{$\texttt{ababa}\:\leadsto$};
\draw (0,3/2) node[right]{$\texttt{ababa}$};
\draw (0,4/2) node[left]{$\texttt{abb}\:\leadsto$};
\draw (0,4/2) node[right]{$\texttt{abb}\ \texttt{ab\textcolor{red}{a}}$};
\draw (0,5/2) node[left]{$\texttt{ba}\:\leadsto$};
\draw (0,5/2) node[right]{$\texttt{ba}\ \texttt{\textcolor{red}{a}a}$};
\draw (0,6/2) node[left]{$\texttt{baba}\:\leadsto$};
\draw (0,6/2) node[right]{$\texttt{baba}\ \texttt{\textcolor{red}{a}aba}$};
\draw (0,7/2) node[left]{$\texttt{bb}\:\leadsto$};
\draw (0,7/2) node[right]{$\texttt{bb}\ \texttt{\textcolor{red}{a}b}\ \texttt{b\textcolor{red}{a}}$};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1802.06369 | arxiv | 2018-02-20T02:08:44 |
|
If LCF_k(X,Y), then there exist (U_1,U_2)Pairs_(X) and (V_1,V_2)Pairs_(Y) such that LCF_k(X,Y)=LCP_p(U_1,U_2)+LCP_q(V_1,V_2) for some p+q=k. | \documentclass{article}
\usepackage{amsthm,amssymb,amsmath}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amsfonts}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{decorations.pathmorphing,shapes}
\usetikzlibrary{calc,decorations.pathmorphing,shapes}
\usetikzlibrary{snakes}
\usepackage{tikz-qtree}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\tikzset{
treenode/.style = {align=center, inner sep=2pt, text centered,
font=\sffamily},
arn_r/.style = {treenode, circle, black, font=\sffamily\bfseries, draw=black,
text width=1.5em},
arn_t/.style = {treenode, circle, black, thick, double, font=\sffamily\bfseries, draw=black,
text width=1.5em},
every edge/.append style={anchor=south,auto=falseanchor=south,auto=false,font=3.5 em},
}
\newcommand{\LCP}{\mathsf{LCP}}
\begin{document}
\begin{tikzpicture}[scale=0.5,every node/.style={font={\footnotesize}}]
\begin{scope}
\draw (0,0) rectangle (18,1);
\draw[fill=black!20] (1,0.1) rectangle (10, 0.9);
\draw (0,.5) node[left]{$X\!:\!$};
\draw[very thick] (5,1.5) -- (5,-1) node[below]{$a$};
\draw[-latex] (5,1.25) -- node[above]{$U_1$} (0,1.25);
\draw[-latex] (5,1.25) -- node[above]{$U_2$} (18,1.25);
\draw[latex-latex] (5,-.25) --node[below]{$\LCP_p(U_1,V_1)$} (1,-.25);
\draw[latex-latex] (5,-.25) --node[below]{$\LCP_q(U_2,V_2)$} (10,-.25);
\end{scope}
\begin{scope}[yshift=-3cm,xshift=7cm]
\draw (0,0) rectangle (18,1);
\draw[fill=black!20] (5,0.1) rectangle (14, 0.9);
\draw (0,.5) node[left]{$Y\!:\!$};
\draw[very thick] (9,1.5) -- (9,-1) node[below]{$b$};
\draw[-latex] (9,1.25) -- node[above]{$V_1$} (0,1.25);
\draw[-latex] (9,1.25) -- node[above]{$V_2$} (18,1.25);
\draw[latex-latex] (9,-.25) --node[below]{$\LCP_p(U_1,V_1)$} (5,-.25);
\draw[latex-latex] (9,-.25) --node[below]{$\LCP_q(U_2,V_2)$} (14,-.25);
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1802.06369 | arxiv | 2018-02-20T02:08:44 |
|
An example of a 6-cover S_24(6)=\{2,3,5, 8,9,11, 14,15,19, 20,21,23\}, with the elements marked as black circles. For example, we may have h(3,10)=5 since 3+5,\,10+5S_24(6). | \documentclass{article}
\usepackage{amsthm,amssymb,amsmath}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amsfonts}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{decorations.pathmorphing,shapes}
\usetikzlibrary{calc,decorations.pathmorphing,shapes}
\usetikzlibrary{snakes}
\usepackage{tikz-qtree}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\tikzset{
treenode/.style = {align=center, inner sep=2pt, text centered,
font=\sffamily},
arn_r/.style = {treenode, circle, black, font=\sffamily\bfseries, draw=black,
text width=1.5em},
arn_t/.style = {treenode, circle, black, thick, double, font=\sffamily\bfseries, draw=black,
text width=1.5em},
every edge/.append style={anchor=south,auto=falseanchor=south,auto=false,font=3.5 em},
}
\begin{document}
\begin{tikzpicture}[scale=0.5]
\tikzstyle{s} = [draw, circle, fill=black, minimum size = 3pt, inner sep = 0 pt, color=black]
\draw (1,0)--(24,0);
\foreach \i in {1,...,24} {
\draw (\i,-0.1)--+(0,0.2);
\node at (\i, 0.2) [above] {\small \i};
}
\foreach \i in {2,3,5,8,9,11,14,15,17,20,21,23} {
\node [s] at (\i,0) {};
}
\foreach \i/\l in {3/5, 10/5} {
\draw [dotted] (\i,0)--+(0,-1.1);
\draw [dotted] (\i+\l,0)--+(0,-1.1);
\draw [-latex] (\i,-.8)--node[midway,below] {$h(3,10)=5$} +(\l,0);
}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1802.06369 | arxiv | 2018-02-20T02:08:44 |
|
Example instance for Colored Trees Problem. Assuming that each node has weight equal to the distance from the root, the optimal solution is a pair of nodes (v_1,v_2) as shown in the figure. Both v_1 and v_2 have as a descendant a blue leaf with number 4 and a red leaf with number 2. | \documentclass{article}
\usepackage{amsthm,amssymb,amsmath}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amsfonts}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{decorations.pathmorphing,shapes}
\usetikzlibrary{calc,decorations.pathmorphing,shapes}
\usetikzlibrary{snakes}
\usepackage{tikz-qtree}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\tikzset{
treenode/.style = {align=center, inner sep=2pt, text centered,
font=\sffamily},
arn_r/.style = {treenode, circle, black, font=\sffamily\bfseries, draw=black,
text width=1.5em},
arn_t/.style = {treenode, circle, black, thick, double, font=\sffamily\bfseries, draw=black,
text width=1.5em},
every edge/.append style={anchor=south,auto=falseanchor=south,auto=false,font=3.5 em},
}
\begin{document}
\begin{tikzpicture}
\tikzset{
sibling distance=0.6em,
level distance=2em,
edge from parent/.style={draw, edge from parent path={(\tikzparentnode) -- (\tikzchildnode)}},
inner/.style = {circle, fill=black, inner sep=0pt, minimum size=2pt, draw},
leafR/.style = {shape=rectangle, draw, align=center, color=red!80!black},
leafB/.style = {shape=circle, draw, align=center, color=blue!80!black, inner sep=2pt}
}
\matrix{
\tikzset{frontier/.style={distance from root=7em}}
\Tree [
. \node[inner] {} node[above, xshift=-3em, yshift=1em] {$T_1$};
[
.\node[inner] {};
[
.\node[inner] {};
[ \node[leafB] {$1$}; ]
[ \node[leafB] {$2$}; ]
]
[
.\node[inner] {};
[ \node[leafR] {$1$}; ]
[ \node[leafB] {$3$}; ]
]
]
[
.\node[inner] {} node[above, right, yshift=0.2em] {$v_1$};
[
.\node[inner] {};
[ \node[leafR] {$2$}; ]
[ \node[leafR] {$3$}; ]
]
[
.\node[inner] {};
[ \node[leafB] {$4$}; ]
[ \node[leafR] {$4$}; ]
]
]
]
&
\draw[white] (0,0)--+(2em,0);
&
\tikzset{frontier/.style={distance from root=7em}}
\Tree [
. \node[inner] {} node[above, xshift=-3em, yshift=1em] {$T_1$};
[
.\node[inner] {};
[
.\node[inner] {};
[ \node[leafB] {$1$}; ]
[ \node[leafB] {$3$}; ]
]
[
.\node[inner] {} node[above, right, yshift=0.2em] {$v_2$};
[ \node[leafB] {$4$}; ]
[ \node[leafR] {$2$}; ]
]
]
[
.\node[inner] {};
[
.\node[inner] {};
[ \node[leafR] {$1$}; ]
[ \node[leafR] {$3$}; ]
]
[
.\node[inner] {};
[ \node[leafR] {$4$}; ]
[ \node[leafB] {$2$}; ]
]
]
]
\\
};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1802.06369 | arxiv | 2018-02-20T02:08:44 |
|
Star-triangle move on a lozenge graph. The angles satisfy _1 + _2 + _3 = 2. | \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts,amssymb}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows,decorations,matrix,calc,decorations.markings,arrows.meta}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[scale=0.7]
\begin{scope}[yshift=0cm] %star-triangle
\begin{scope}[xshift=9cm]
\coordinate (hh) at (0 ,2.31) ;
\coordinate (bd) at (1.633,-1.633) ;
\coordinate (bg) at (-2.08,-1.002) ;
\coordinate (hd) at ($(hh)+(bd)$) ;
\coordinate (hg) at ($(hh)+(bg)$) ;
\coordinate (bb) at ($(bd)+(bg)$) ;
\coordinate (cc) at ($(hd) + (bb)- (bd)$);
\draw [gray] (hh) -- (hd) -- (bd) -- (bb) -- (bg) -- (hg) -- cycle;
\draw [gray] (hd) -- (cc);
\draw [gray] (hg) -- (cc);
\draw [gray] (bb) -- (cc);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (hh) {};
\node [draw=black, fill=white,circle,thick,inner sep=0pt,minimum size=4pt] at (hd) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (hg) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (bd) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (bg) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (bb) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (cc) {};
\draw [dashed] (hh) -- (cc);
\draw [dashed] (bg) -- (cc);
\draw [dashed] (bd) -- (cc);
\draw ($(cc)+(1.5,0)$) node [] {$\frac{\pi}{2} - \theta_1$};
\draw ($(cc)+(-0.6,1.1)$) node [] {$\frac{\pi}{2} - \theta_2$};
\draw ($(cc)+(-0.6,-1)$) node [] {$\frac{\pi}{2} - \theta_3$};
\draw ($(cc) + 0.25*(hh) - 0.25*(cc)$) arc (80:133:0.7cm);
\draw ($(cc) + 0.25*(bd) - 0.25*(cc)$) arc (-45:30:0.5cm);
\draw ($(cc) + 0.25*(bb) - 0.25*(cc)$) arc (-90:-155:0.6cm);
\end{scope}
\begin{scope}[xshift=3.5cm, yshift=-0.2cm]
\draw[>=stealth,<->, line width = 1pt] (0,0) -- (2,0);
\end{scope}
\begin{scope}[xshift=0cm]
\coordinate (hh) at (0 ,2.31) ;
\coordinate (bd) at (1.633,-1.633) ;
\coordinate (bg) at (-2.08,-1.002) ;
\coordinate (hd) at ($(hh)+(bd)$) ;
\coordinate (hg) at ($(hh)+(bg)$) ;
\coordinate (bb) at ($(bd)+(bg)$) ;
\draw [gray] (hh) -- (hd) -- (bd) -- (bb) -- (bg) -- (hg) -- cycle;
\draw [gray] (bd) -- (0,0);
\draw [gray] (bg) -- (0,0);
\draw [gray] (hh) -- (0,0);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (hh) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (hd) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (hg) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (bd) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (bg) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (bb) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,0) {};
\draw [dashed] (hh) -- (bg) -- (bd) -- (hh);
\draw ($(hh)+(-0.3,-1.2)$) node [] {$\theta_1$};
\draw ($(bg)+(1.3,0.2)$) node [] {$\theta_2$};
\draw ($(bd)+(-0.8,1.3)$) node [] {$\theta_3$};
\draw ($(hh) + 0.22*(bg) - 0.22*(hh)$) arc (-115:-80:0.8cm);
\draw ($(bg) + 0.22*(bd) - 0.22*(bg)$) arc (-25:20:0.7cm);
\draw ($(bd) + 0.22*(hh) - 0.22*(bd)$) arc (110:133:0.9cm);
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1811.02026 | arxiv | 2018-11-07T02:03:12 |
|
The quadrangulation Q(dashed) at a face f and the decorated graph of Fan and Wu FanWu(solid lines) with its dimer weights. The functions A,B,C,D are implicitly evaluated at f. | \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts,amssymb}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows,decorations,matrix,calc,decorations.markings,arrows.meta}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[scale=2]
\draw [color=gray, dashed] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=6pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=6pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=6pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=6pt] at (0,-1) {};
\draw (-1.3,0.6) -- (-0.8,0.4) -- (-0.8,-0.4) -- (0.8,-0.4) -- (0.8,0.4) -- (-0.8,0.4);
\draw (0.8,0.4) -- (1.3,0.6);
\draw (0.8,-0.4) -- (1.3,-0.6);
\draw (-0.8,-0.4) -- (-1.3,-0.6);
\draw (0.8,0.4) -- (0.25,0);
\draw (-0.8,0.4) -- (-0.25,0);
\draw (0.8,-0.4) -- (0.25,0);
\draw (-0.8,-0.4) -- (-0.25,0);
\draw (-0.25,0) -- (0.25,0);
\draw (0,0.35) node [above] {$(A-D)/C$};
\draw (0,-0.35) node [below] {$(A-D)/C$};
\draw (-0.75,0) node [left] {$B/C$};
\draw (0.75,0) node [right] {$B/C$};
\draw (0,-0.04) node [above] {$C$};
\draw (-0.55,0.2) node [] {$\sqrt{D}$};
\draw (-0.55,-0.2) node [] {$\sqrt{D}$};
\draw (0.55,0.2) node [] {$\sqrt{D}$};
\draw (0.55,-0.2) node [] {$\sqrt{D}$};
\draw (-1,0.5) node [above] {$1$};
\draw (-1,-0.5) node [below] {$1$};
\draw (1,0.5) node [above] {$1$};
\draw (1,-0.5) node [below] {$1$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1811.02026 | arxiv | 2018-11-07T02:03:12 |
|
Coefficients of the matrix $-TD +\frac12\left(K_{\alpha,\beta'} + K_{\alpha',\beta}\right)$ at a face. | \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts,amssymb}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows,decorations,matrix,calc,decorations.markings,arrows.meta}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[scale=2]
\draw [color=gray, dashed] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=6pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=6pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=6pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=6pt] at (0,-1) {};
\draw [-{Latex[length=2mm,width=2mm]}] (-0.8,0.4) -- (-0.14,0.07);
\draw (-0.22,0.11) -- (0.8,-0.4);
\draw [-{Latex[length=2mm,width=2mm]}] (-0.8,-0.4) -- (-0.14,-0.07);
\draw (-0.22,-0.11) -- (0.8,0.4);
\draw [-{Latex[length=2mm,width=2mm]}] (-0.8,0.4) -- (-0.2,0.4);
\draw (-0.22,0.4) -- (0.8,0.4);
\draw [-{Latex[length=2mm,width=2mm]}] (-0.8,0.4) -- (-0.8,0.1);
\draw (-0.8,0.12) -- (-0.8,-0.4);
\draw [-{Latex[length=2mm,width=2mm]}] (0.8,-0.4) -- (0.2,-0.4);
\draw (0.22,-0.4) -- (-0.8,-0.4);
\draw [-{Latex[length=2mm,width=2mm]}] (0.8,-0.4) -- (0.8,-0.1);
\draw (0.8,-0.12) -- (0.8,0.4);
\draw (0,0.35) node [above] {$i\tilde{a}$};
\draw (0,-0.35) node [below] {$i\tilde{a}$};
\draw (-0.75,0) node [left] {$\tilde{b}$};
\draw (0.75,0) node [right] {$\tilde{b}$};
\draw (-0.15,0.22) node [] {$i\tilde{d}$};
\draw (-0.15,-0.2) node [] {$i\tilde{d}$};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=3pt] at (-0.8,0.4) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=3pt] at (-0.8,-0.4) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=3pt] at (0.8,-0.4) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=3pt] at (0.8,0.4) {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1811.02026 | arxiv | 2018-11-07T02:03:12 |
|
The decorated graph G^T of Hsue, Lin and Wu HsueLinWu with its dimer weights. | \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts,amssymb}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows,decorations,matrix,calc,decorations.markings,arrows.meta}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[scale=2]
\draw [color=gray, dashed] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=6pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=6pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=6pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=6pt] at (0,-1) {};
\draw (0.8,0.4) -- (1.3,0.6);
\draw (0.8,-0.4) -- (1.3,-0.6);
\draw (-0.8,0.4) -- (-1.3,0.6);
\draw (-0.8,-0.4) -- (-1.3,-0.6);
\draw (-0.8,0.4) -- (0.8,-0.4);
\draw (-0.8,-0.4) -- (0.8,0.4);
\draw (-0.8,0.4) -- (0.8,0.4);
\draw (-0.8,0.4) -- (-0.8,-0.4);
\draw (0.8,-0.4) -- (-0.8,-0.4);
\draw (0.8,-0.4) -- (0.8,0.4);
\draw (0,0.35) node [above] {$A/C$};
\draw (0,-0.35) node [below] {$A/C$};
\draw (-0.75,0) node [left] {$B/C$};
\draw (0.75,0) node [right] {$B/C$};
\draw (-0.3,0.2) node [] {$D/C$};
\draw (-0.3,-0.2) node [] {$D/C$};
\draw (-1,0.5) node [above] {$1$};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=3pt] at (-0.8,0.4) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=3pt] at (-0.8,-0.4) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=3pt] at (0.8,-0.4) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=3pt] at (0.8,0.4) {};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1811.02026 | arxiv | 2018-11-07T02:03:12 |
|
The eight possible configurations for at a face f and their local weight w_f(). | \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts,amssymb}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows,decorations,matrix,calc,decorations.markings,arrows.meta}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[scale=0.4]
\draw [color=gray] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\draw [ultra thick] (-1.5,0.75) -- (0,0) -- (1.5,0.75);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,-1) {};
\begin{scope}[xshift = 3.3cm]
\node [] at (0,0) {$A(f)$};
\end{scope}
\begin{scope}[xshift=0cm, yshift=-3.5cm]
\draw [color=gray] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\draw [ultra thick] (-1.5,-0.75) -- (0,0) -- (1.5,-0.75);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,-1){};
\begin{scope}[xshift = 3.3cm]
\node [] at (0,0) {$A(f)$};
\end{scope}
\end{scope}
\begin{scope}[xshift=8cm]
\draw [color=gray] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\draw [ultra thick] (-1.5,0.75) -- (0,0) -- (-1.5,-0.75);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,-1) {};
\begin{scope}[xshift = 3.3cm]
\node [] at (0,0) {$B(f)$};
\end{scope}
\begin{scope}[xshift=0cm, yshift=-3.5cm]
\draw [color=gray] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\draw [ultra thick] (1.5,-0.75) -- (0,0) -- (1.5,0.75);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,-1){};
\begin{scope}[xshift = 3.3cm]
\node [] at (0,0) {$B(f)$};
\end{scope}
\end{scope}
\end{scope}
\begin{scope}[xshift=16cm]
\draw [color=gray] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\draw [ultra thick] (-1.5,0.75) -- (1.5,-0.75);
\draw [ultra thick] (1.5,0.75) -- (-1.5,-0.75);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,-1) {};
\begin{scope}[xshift = 3.3cm]
\node [] at (0,0) {$C(f)$};
\end{scope}
\begin{scope}[xshift=0cm, yshift=-3.5cm]
\draw [color=gray] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,-1){};
\begin{scope}[xshift = 3.3cm]
\node [] at (0,0) {$C(f)$};
\end{scope}
\end{scope}
\end{scope}
\begin{scope}[xshift=24cm]
\draw [color=gray] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\draw [ultra thick] (-1.5,0.75) -- (1.5,-0.75);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,-1) {};
\begin{scope}[xshift = 3.3cm]
\node [] at (0,0) {$D(f)$};
\end{scope}
\begin{scope}[xshift=0cm, yshift=-3.5cm]
\draw [color=gray] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\draw [ultra thick] (1.5,0.75) -- (-1.5,-0.75);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,-1){};
\begin{scope}[xshift = 3.3cm]
\node [] at (0,0) {$D(f)$};
\end{scope}
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1811.02026 | arxiv | 2018-11-07T02:03:12 |
|
Entries of R(f)(left) and R(f)(right) are indexed by the occupation state of (i_1,i_2) and (o_1,o_2), in the order (absent, absent), (absent,present), (present,absent), (present,present). | \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts,amssymb}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows,decorations,matrix,calc,decorations.markings,arrows.meta}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[scale=0.7]
\draw [] (-2,0) -- (0,-1) -- (2,0) -- (0,1) -- cycle;
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=6pt] at (-2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=6pt] at (0,1) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=6pt] at (2,0) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=6pt] at (0,-1) {};
\draw [color=gray, dashed] (-1.3,0.6) -- (1.3,-0.6);
\draw [color=gray, dashed] (-1.3,-0.6) -- (1.3,0.6);
\draw (-1.3,0.6) node [above] {$i_1$};
\draw (-1.3,-0.6) node [below] {$i_2$};
\draw (1.3,-0.6) node [below] {$o_1$};
\draw (1.3,0.6) node [above] {$o_2$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1811.02026 | arxiv | 2018-11-07T02:03:12 |
|
``Star-triangle'' move on the quadrangulation (solid lines) and its dual on which the 8V-configurations are defined (dashed lines). | \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts,amssymb}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows,decorations,matrix,calc,decorations.markings,arrows.meta}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[scale=0.6]
\begin{scope}[yshift=0cm] %star-triangle
\begin{scope}[xshift=9cm]
\coordinate (hh) at (0,2.31) ;
\coordinate (hd) at (2,1.155) ;
\coordinate (hg) at (-2,1.155) ;
\coordinate (bd) at (2,-1.155) ;
\coordinate (bg) at (-2,-1.155) ;
\coordinate (bb) at (0,-2.31) ;
\coordinate (x) at (0,1.155) ;
\coordinate (y) at (1,-0.577) ;
\coordinate (z) at (-1,-0.577) ;
\draw [gray] (hh) -- (hd) -- (bd) -- (bb) -- (bg) -- (hg) -- cycle;
\draw [gray] (hd) -- (0,0);
\draw [gray] (hg) -- (0,0);
\draw [gray] (bb) -- (0,0);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (hh) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (hd) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (hg) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (bd) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (bg) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (bb) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum
size=4pt] at (0,0) {};
\draw [draw=gray,dashed] (-2.5,0) to[out=-30,in=210] (2.5,0);
\draw [draw=gray,dashed] (-1.2,1.9) to[out=-30,in=90] (1.2,-1.9);
\draw [draw=gray,dashed] (1.2,1.9) to[out=210,in=90] (-1.2,-1.9);
\draw (x) node [] {$f'_2$};
\draw (z) node [] {$f'_3$};
\draw (y) node [] {$f'_1$};
\end{scope}
\begin{scope}[xshift=3.5cm, yshift=-0.2cm]
\draw[>=stealth,<->, line width = 1pt] (0,0) -- (2,0);
\end{scope}
\begin{scope}[xshift=0cm]
\coordinate (hh) at (0,2.31) ;
\coordinate (hd) at (2,1.155) ;
\coordinate (hg) at (-2,1.155) ;
\coordinate (bd) at (2,-1.155) ;
\coordinate (bg) at (-2,-1.155) ;
\coordinate (bb) at (0,-2.31) ;
\coordinate (x) at (0,-1.155) ;
\coordinate (y) at (1,0.577) ;
\coordinate (z) at (-1,0.577) ;
\draw [gray] (hh) -- (hd) -- (bd) -- (bb) -- (bg) -- (hg) -- cycle;
\draw [gray] (bd) -- (0,0);
\draw [gray] (bg) -- (0,0);
\draw [gray] (hh) -- (0,0);
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (hh) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (hd) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (hg) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (bd) {};
\node [draw=black, fill=black,thick,circle,inner sep=0pt,minimum size=4pt] at (bg) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (bb) {};
\node [draw=black, fill=white,thick,circle,inner sep=0pt,minimum size=4pt] at (0,0) {};
\draw [draw=gray,dashed] (-2.5,0) to[out=30,in=-210] (2.5,0);
\draw [draw=gray,dashed] (-1.2,1.9) to[out=-80,in=150] (1.2,-1.9);
\draw [draw=gray,dashed] (1.2,1.9) to[out=-100,in=30] (-1.2,-1.9);
\draw (x) node [] {$f_2$};
\draw (y) node [] {$f_3$};
\draw (z) node [] {$f_1$};
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1811.02026 | arxiv | 2018-11-07T02:03:12 |
|
A portion of a lozenge graph. | \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts,amssymb}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows,decorations,matrix,calc,decorations.markings,arrows.meta}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm,scale=0.8]
\clip(-8.5,-5.1) rectangle (4.5,3.5);
\draw [line width=1pt] (-4.44,-1.44)-- (-1.48,-2.72);
\draw [line width=1pt] (-1.48,-2.72)-- (1.0930448057625224,-0.7759217023127627);
\draw [line width=1pt] (1.0930448057625224,-0.7759217023127627)-- (-1.8669551942374785,0.5040782976872384);
\draw [line width=1pt] (-1.8669551942374785,0.5040782976872384)-- (-4.44,-1.44);
\draw [line width=1pt] (1.0930448057625224,-0.7759217023127627)-- (-0.45743625558097656,2.0517997264024395);
\draw [line width=1pt] (-0.45743625558097656,2.0517997264024395)-- (-3.417436255580978,3.3317997264024406);
\draw [line width=1pt] (-1.8669551942374785,0.5040782976872384)-- (-3.417436255580978,3.3317997264024406);
\draw [line width=1pt] (-5.990481061343502,1.3877214287152015)-- (-4.44,-1.44);
\draw [line width=1pt] (-5.990481061343502,1.3877214287152015)-- (-3.417436255580978,3.3317997264024406);
\draw [line width=1pt] (-5.990481061343502,1.3877214287152015)-- (-9.20369753036258,1.6620203955826813);
\draw [line width=1pt] (-9.20369753036258,1.6620203955826813)-- (-6.630652724600058,3.606098693269918);
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\draw [line width=1pt] (-7.653216469019079,-1.165701033132518)-- (-4.44,-1.44);
\draw [line width=1pt] (-4.44,-1.44)-- (-6.32010847092546,-4.0601511669280335);
\draw [line width=1pt] (-9.533324939944535,-3.7858522000605497)-- (-6.32010847092546,-4.0601511669280335);
\draw [line width=1pt] (-9.533324939944535,-3.7858522000605497)-- (-7.653216469019079,-1.165701033132518);
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\draw [line width=1pt] (-0.45743625558097656,2.0517997264024395)-- (2.3708194809749847,3.6013059344049454);
\draw [line width=1pt] (3.921300542318484,0.7735845056897428)-- (2.3708194809749847,3.6013059344049454);
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\draw [line width=1pt] (-3.8021105142764045,-8.534620480237146)-- (-1.9220020433509475,-5.914469313309112);
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\draw [line width=1pt] (-0.43660240457052013,-5.771445797954142)-- (-1.48,-2.72);
\draw [line width=1pt] (-0.8786044479214705,-8.965915111263255)-- (-1.9220020433509475,-5.914469313309112);
\draw [line width=1pt] (-0.8786044479214705,-8.965915111263255)-- (-0.43660240457052013,-5.771445797954142);
\draw [line width=1pt] (-0.43660240457052013,-5.771445797954142)-- (1.5731691553734533,-8.29351206925638);
\draw [line width=1pt] (0.5297715599439718,-5.24206627130224)-- (1.5731691553734533,-8.29351206925638);
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\draw [line width=1pt] (0.5297715599439718,-5.24206627130224)-- (3.34781959628696,-6.810060297076392);
\draw [line width=1pt] (1.3380480363429872,-4.287994025774154)-- (3.34781959628696,-6.810060297076392);
\draw [line width=1pt] (1.3380480363429872,-4.287994025774154)-- (4.506301426788489,-4.889800019372249);
\draw [line width=1pt] (4.506301426788489,-4.889800019372249)-- (7.079346232551011,-2.945721721685012);
\draw [line width=1pt] (3.9110928421055102,-2.3439157280869165)-- (7.079346232551011,-2.945721721685012);
\draw [line width=1pt] (-0.45743625558097656,2.0517997264024395)-- (-1.7388619432577967,5.011182805181191);
\draw [line width=1pt] (-0.45743625558097656,2.0517997264024395)-- (1.7771401207285915,4.377024106637434);
\draw [line width=1pt] (3.921300542318484,0.7735845056897428) -- (5,1);
\draw [fill=black] (-3.417436255580978,3.3317997264024406) circle (4pt);
\draw [fill=black] (-4.44,-1.44) circle (4pt);
\draw (-1.6,-1.1) node [] {$f$};
\draw [dashed] (-4.44,-1.44) -- (-2.52,-1.26);
\path [->] (-3.02,-1.27) edge[bend right] node[right] {$\theta_f$} (-3.4,-0.8);
\draw [fill=white] (-1.48,-2.72) circle (4pt);
\draw [fill=white] (-1.8669551942374785,0.5040782976872384) circle (4pt);
\draw [fill=black] (1.0930448057625224,-0.7759217023127627) circle (4pt);
\draw [fill=white] (-0.45743625558097656,2.0517997264024395) circle (4pt);
\draw [fill=white] (-5.990481061343502,1.3877214287152015) circle (4pt);
\draw [fill=white] (-7.653216469019079,-1.165701033132518) circle (4pt);
\draw [fill=white] (-6.32010847092546,-4.0601511669280335) circle (4pt);
\draw [fill=white] (3.921300542318484,0.7735845056897428) circle (4pt);
\draw [fill=white] (3.9110928421055102,-2.3439157280869165) circle (4pt);
\draw [fill=black] (-3.360108470925459,-5.340151166928035) circle (4pt);
\draw [fill=black] (1.3380480363429872,-4.287994025774154) circle (4pt);
\draw [fill=white] (4.506301426788489,-4.889800019372249) circle (4pt);
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1811.02026 | arxiv | 2018-11-07T02:03:12 |
|
Two equivalent representations of an eight-vertex configuration on ^2. | \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts,amssymb}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows,decorations,matrix,calc,decorations.markings,arrows.meta}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}
\newcommand\nord[2]{
\draw [ultra thick] (#1,#2) -- (#1,#2+1);
}
\newcommand\est[2]{
\draw [ultra thick] (#1,#2) -- (#1+1,#2);
}
\newcommand\haut[2]{
\draw [decoration={markings,
mark=at position 0.5 with {\arrow{>}}},postaction={decorate}] (#1,#2) -- (#1,#2+1);
}
\newcommand\bas[2]{
\draw [decoration={markings,
mark=at position 0.5 with {\arrow{>}}},postaction={decorate}] (#1,#2) -- (#1,#2-1);
}
\newcommand\gauche[2]{
\draw [decoration={markings,
mark=at position 0.5 with {\arrow{>}}},postaction={decorate}] (#1,#2) -- (#1-1,#2);
}
\newcommand\droite[2]{
\draw [decoration={markings,
mark=at position 0.5 with {\arrow{>}}},postaction={decorate}] (#1,#2) -- (#1+1,#2);
}
\begin{scope}[xshift=6.5cm]
\clip (-0.7,-0.7) rectangle (4.7,4.7);
\foreach \x in {-1,...,4} \foreach \y in {-1,...,4}
{
\pgfmathparse{mod(\x+\y,2) ? "gray!50" : "white"}
\edef\colour{\pgfmathresult}
\path[fill=\colour] (\x,\y) rectangle (\x+1,\y+1);
}
\nord{0}{-1};
\nord{1}{-1};
\nord{3}{-1};
\nord{4}{-1};
\nord{1}{0};
\nord{2}{0};
\nord{3}{0};
\nord{2}{1};
\nord{3}{1};
\nord{0}{2};
\nord{2}{2};
\nord{3}{2};
\nord{4}{2};
\nord{0}{3};
\nord{2}{3};
\nord{3}{3};
\nord{4}{3};
\nord{0}{4};
\nord{3}{4};
\nord{4}{4};
\est{-1}{0};
\est{2}{0};
\est{3}{0};
\est{1}{1};
\est{2}{1};
\est{3}{1};
\est{4}{1};
\est{1}{2};
\est{2}{2};
\est{3}{2};
\est{0}{2};
\est{-1}{4};
\est{0}{4};
\est{1}{4};
\end{scope}
\begin{scope}[xshift=0cm]
\clip (-0.7,-0.7) rectangle (4.7,4.7);
\foreach \x in {-1,...,4} \foreach \y in {-1,...,4}
{
\pgfmathparse{mod(\x+\y,2) ? "gray!50" : "white"}
\edef\colour{\pgfmathresult}
\path[fill=\colour] (\x,\y) rectangle (\x+1,\y+1);
}
\haut{0}{-1};
\haut{4}{-1};
\gauche{0}{0};
\haut{0}{0};
\gauche{1}{0};
\haut{1}{0};
\droite{1}{0};
\bas{1}{0};
\droite{2}{0};
\bas{2}{0};
\haut{3}{0};
\bas{3}{0};
\gauche{4}{0};
\haut{4}{0};
\gauche{5}{0};
\gauche{0}{1};
\droite{0}{1};
\haut{1}{1};
\droite{1}{1};
\haut{2}{1};
\bas{2}{1};
\gauche{3}{1};
\droite{3}{1};
\gauche{5}{1};
\droite{-1}{2};
\droite{0}{2};
\bas{0}{2};
\gauche{2}{2};
\droite{2}{2};
\haut{3}{2};
\bas{3}{2};
\gauche{4}{2};
\bas{4}{2};
\gauche{5}{2};
\gauche{0}{3};
\haut{0}{3};
\droite{0}{3};
\bas{0}{3};
\haut{1}{3};
\bas{1}{3};
\gauche{2}{3};
\haut{2}{3};
\droite{2}{3};
\bas{2}{3};
\gauche{4}{3};
\haut{4}{3};
\droite{4}{3};
\bas{4}{3};
\gauche{0}{4};
\droite{0}{4};
\gauche{2}{4};
\haut{2}{4};
\gauche{3}{4};
\haut{3}{4};
\droite{3}{4};
\bas{3}{4};
\gauche{5}{4};
\bas{0}{5};
\bas{1}{5};
\bas{4}{5};
\end{scope}
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1811.02026 | arxiv | 2018-11-07T02:03:12 |
|
Example of the decomposition in eq:mudec for =(5,4,2,1,1). We have =(1,1,1), =(1,1) and =(4,3,1) | \documentclass[12pt,psamsfonts,reqno]{amsart}
\usepackage[utf8]{inputenc}
\usepackage{mathtools,amsmath,amssymb}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}
\foreach \a in {2,3,4,5} {
\begin{scope}[shift={(0.5*\a,0)}]
\draw (0,0) rectangle (0.5,0.5);
\end{scope}
}
\foreach \a in {2,3,4} {
\begin{scope}[shift={(0.5*\a,0.5)}]
\draw (0,0) rectangle (0.5,0.5);
\end{scope}
}
\foreach \a in {2} {
\begin{scope}[shift={(0.5*\a,1)}]
\draw (0,0) rectangle (0.5,0.5);
\end{scope}
}
\foreach \a in {1} {
\begin{scope}[shift={(0.5*\a-0.1,1.5+0.1)}]
\draw (0,0) rectangle (0.5,0.5);
\end{scope}
}
\foreach \a in {1} {
\begin{scope}[shift={(0.5*\a-0.1,2+0.1)}]
\draw (0,0) rectangle (0.5,0.5);
\end{scope}
}
\foreach \a in {1} {
\begin{scope}[shift={(0.5*\a-0.1,1)}]
\draw (0,0) rectangle (0.5,0.5);
\end{scope}
}
\foreach \a in {1} {
\begin{scope}[shift={(0.5*\a-0.1,0.5)}]
\draw (0,0) rectangle (0.5,0.5);
\end{scope}
}
\foreach \a in {1} {
\begin{scope}[shift={(0.5*\a-0.1,0)}]
\draw (0,0) rectangle (0.5,0.5);
\end{scope}
}
\draw [decorate,decoration={brace,amplitude=5pt},xshift=10pt,yshift=17pt]
(0,1) -- (0,2)node [black,midway,xshift=-10pt] {\footnotesize
$\beta$};
\draw [decorate,decoration={brace,amplitude=5pt},xshift=10pt,yshift=-14.5pt]
(0,0.5) -- (0,2)node [black,midway,xshift=-10pt] {\footnotesize
$\alpha$};
\draw [decorate,decoration={brace,amplitude=5pt},xshift=85.5pt,yshift=-3pt
,rotate=90]
(0,0) -- (0,2)node [black,midway,xshift=0pt,yshift=-10pt] {\footnotesize
$\gamma$};
\end{tikzpicture}
\end{document} | https://arxiv.org/abs/1808.00799 | arxiv | 2018-08-03T02:11:19 |