diff --git a/publications/hasy/00README.XXX b/publications/hasy/00README.XXX new file mode 100644 index 0000000..c7146ab --- /dev/null +++ b/publications/hasy/00README.XXX @@ -0,0 +1,2 @@ +main.tex toplevelfile +nohypertex diff --git a/publications/hasy/Makefile b/publications/hasy/Makefile new file mode 100644 index 0000000..f26d622 --- /dev/null +++ b/publications/hasy/Makefile @@ -0,0 +1,22 @@ +DOKUMENT = main + +make: + pdflatex $(DOKUMENT).tex -output-format=pdf # Referenzen erstellen + bibtex $(DOKUMENT) + pdflatex $(DOKUMENT).tex -output-format=pdf # Referenzen einbinden + pdflatex $(DOKUMENT).tex -output-format=pdf # Referenzen einbinden + make clean + +ebook: + latexml --dest=$(DOKUMENT).xml $(DOKUMENT).tex + latexmlpost -dest=$(DOKUMENT).html $(DOKUMENT).xml + ebook-convert $(DOKUMENT).html $(DOKUMENT).epub --language de --no-default-epub-cover + +arxiv: + zip -r upload.zip . -x \*.git\* -x MAKEFILE -x *.zip -x *.pdf + +clean: + rm -rf $(TARGET) *.class *.html *.aux *.out *.thm *.idx *.toc *.ilg *.glg *.glo *.gls *.ist *.xdy *.fdb_latexmk *.bak *.blg *.glsdefs *.acn *.acr *.alg *.nls *.nlo *.bak *.pyg *.lot *.lof *.xmpdata *.xmpi *.bbl + rm -rf _minted-booka4 + rm -rf *.log # Analyze this for errors + # rm -rf *.bbl *.ind # Needed for arxiv \ No newline at end of file diff --git a/publications/hasy/abstract.tex b/publications/hasy/abstract.tex new file mode 100644 index 0000000..476faed --- /dev/null +++ b/publications/hasy/abstract.tex @@ -0,0 +1,5 @@ +\begin{abstract} +This paper describes a dataset of single symbols similar to MNIST. It contains +\dbTotalInstances~instances of \dbTotalClasses~classes, split into training +and test set in a stratified manner. +\end{abstract} diff --git a/publications/hasy/appendix.tex b/publications/hasy/appendix.tex new file mode 100644 index 0000000..1c5db3d --- /dev/null +++ b/publications/hasy/appendix.tex @@ -0,0 +1,4 @@ +%!TEX root = main.tex + +\appendix +\input{used-latex-symbols} \ No newline at end of file diff --git a/publications/hasy/literatur.bib b/publications/hasy/literatur.bib new file mode 100644 index 0000000..7f916e9 --- /dev/null +++ b/publications/hasy/literatur.bib @@ -0,0 +1,67 @@ +% This file was created with JabRef 2.10. +% Encoding: UTF-8 + + +@Misc{Kirsch2014, + Title = {Detexify data}, + + Author = {Daniel Kirsch}, + Month = jul, + Year = {2014}, + + Url = {https://github.com/kirel/detexify-data} +} + +@MastersThesis{Kirsch, + Title = {Detexify: Erkennung handgemalter {L}a{T}e{X}-Symbole}, + Author = {Daniel Kirsch}, + School = {Westfälische Wilhelms-Universität Münster}, + Year = {2010}, + Month = {10}, + Type = {Diploma thesis}, + + Url = {http://danielkirs.ch/thesis.pdf} +} + +@Article{LeNet-5, + Title = {Gradient-based learning applied to document recognition}, + Author = {LeCun, Yann and Bottou, L{\'e}on and Bengio, Yoshua and Haffner, Patrick}, + Journal = {Proceedings of the IEEE}, + Year = {1998}, + + Month = nov, + Number = {11}, + Pages = {2278-2324}, + Volume = {86}, + + Doi = {10.1109/5.726791}, + ISSN = {0018-9219}, + Keywords = {backpropagation;convolution;multilayer perceptrons;optical character recognition;2D shape variability;GTN;back-propagation;cheque reading;complex decision surface synthesis;convolutional neural network character recognizers;document recognition;document recognition systems;field extraction;gradient based learning technique;gradient-based learning;graph transformer networks;handwritten character recognition;handwritten digit recognition task;high-dimensional patterns;language modeling;multilayer neural networks;multimodule systems;performance measure minimization;segmentation recognition;Character recognition;Feature extraction;Hidden Markov models;Machine learning;Multi-layer neural network;Neural networks;Optical character recognition software;Optical computing;Pattern recognition;Principal component analysis}, + Url = {http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf} +} + +@MastersThesis{Thoma:2014, + Title = {On-line {Recognition} of {Handwritten} {Mathematical} {Symbols}}, + Author = {Martin Thoma}, + School = {Karlsruhe Institute of Technology}, + Year = {2014}, + + Address = {Karlsruhe, Germany}, + Month = nov, + Type = {Bachelor’s Thesis}, + + Keywords = {handwriting recognition; on-line; machine learning; +artificial neural networks; mathematics; classification; +supervised learning; MLP; multilayer perceptrons; hwrt; +write-math}, + Url = {http://martin-thoma.com/write-math} +} + +@Misc{TF-MNIST-2016, + Title = {Deep MNIST for Experts}, + Month = dec, + Year = {2016}, + + Url = {https://www.tensorflow.org/tutorials/mnist/pros/} +} + diff --git a/publications/hasy/main.tex b/publications/hasy/main.tex new file mode 100644 index 0000000..323fa1f --- /dev/null +++ b/publications/hasy/main.tex @@ -0,0 +1,116 @@ +\documentclass[technote,a4paper,leqno]{IEEEtran} +\pdfoutput=1 + +\usepackage[utf8]{inputenc} % this is needed for umlauts +\usepackage[USenglish]{babel} % this is needed for umlauts +\usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf +\usepackage{graphicx} +\usepackage{amsmath,amssymb} +\usepackage[absolute,overlay]{textpos} +\usepackage{vmargin} % Adjust margins in a simple way +\usepackage{tikz} +\usepackage{csquotes} +\usepackage[binary-units=true]{siunitx} +\DeclareSIUnit\pixel{px} +\usepackage{listings} % needed for the inclusion of source code +\usepackage{caption} +\DeclareCaptionFont{white}{\color{white}} +\DeclareCaptionFormat{listing}{\colorbox{gray}{\parbox{\linewidth}{#3}}} +\captionsetup[lstlisting]{format=listing,labelfont=white,textfont=white} + +\lstset{ + aboveskip={1.3\baselineskip}, + basicstyle=\small\ttfamily\linespread{4}, + breaklines=false, + columns=flexible, + commentstyle=\color[rgb]{0.127,0.427,0.514}\ttfamily\itshape, + escapechar=@, + extendedchars=true, + frame=none, + identifierstyle=\color{black}, + inputencoding=latin1, + keywordstyle=\color[HTML]{228B22}\bfseries, + language=C, + ndkeywordstyle=\color[HTML]{228B22}\bfseries, + numbers=left, + numberstyle=\scriptsize, + prebreak = \raisebox{0ex}[0ex][0ex]{\ensuremath{\hookleftarrow}}, + stringstyle=\color[rgb]{0.639,0.082,0.082}\ttfamily, + showstringspaces=false, + xleftmargin=5.0ex +} + +\usepackage{url} +\usepackage{breakurl} +\usepackage[raiselinks=true, + bookmarks=true, + bookmarksopenlevel=1, + bookmarksopen=true, + bookmarksnumbered=true, + breaklinks, + hyperindex=true, + plainpages=false, + pdfpagelabels=true, + pdfborder={0 0 0.5}]{hyperref} +\def\UrlBreaks{\do\/\do-} + +\usepackage{xspace} +\newcommand*\elide{\textup{[\,\dots]}\xspace} + +\usepackage[german,nameinlink, noabbrev,capitalise]{cleveref} + +\title{HASY dataset} +\author{% + \IEEEauthorblockN{Martin Thoma}\\ + \IEEEauthorblockA{E-Mail: info@martin-thoma.de} % ORCID: http://orcid.org/0000-0002-6517-1690 +} + +\hypersetup{ + pdfauthor = {Martin Thoma}, + pdfkeywords = {dataset}, + pdfsubject = {HASY, dataset}, + pdftitle = {HASY dataset}, +} +\usepackage[inline]{enumitem} +\usepackage{longtable} +\usepackage{booktabs} % \toprule +% Packages for symbols +\usepackage{mathtools} +\usepackage{mathrsfs} +\def\wasyfamily{\fontencoding{U}\fontfamily{wasy}\selectfont} +\usepackage{upgreek} +\usepackage{marvosym} +\usepackage{textcomp} +\usepackage{dsfont} +\usepackage{esint} +\usepackage{cmll} +\usepackage{stmaryrd} +\usepackage{skull} + +% Make document nicer +\usepackage{parskip} +\usepackage{microtype} + +% Variables +\newcommand{\dbTotalClasses}{369} +\newcommand{\dbTrainInstances}{\num{151159}} +\newcommand{\dbTestInstances}{\num{17074}} +\newcommand{\dbTotalInstances}{\num{168233}} +\newcommand{\dbName}{HASY} +\newcommand{\dbSizeMB}{33.3} +\newcommand{\dbDownloadURL}{\url{http://TODO.com/_me}} +\newcommand{\dbMDfivesum}{1b452c44895e44e4357141822a38de8f} + +% Start +\begin{document} +\maketitle +\input{abstract} +\input{content} +\bibliographystyle{IEEEtranSA} +\bibliography{literatur} +\clearpage% +\onecolumn +\input{appendix} +\twocolumn + +\end{document} diff --git a/publications/hasy/used-latex-symbols.tex b/publications/hasy/used-latex-symbols.tex new file mode 100644 index 0000000..6f8049f --- /dev/null +++ b/publications/hasy/used-latex-symbols.tex @@ -0,0 +1,280 @@ +%!TEX root = "../thesis.tex" +\subsection{Symbol Classes} + \begin{longtable}{lc|lc} + \toprule + \LaTeX & Rendered & \LaTeX & Rendered \\ + \midrule + \endhead + \hline \multicolumn{4}{r}{{Continued on next page}} \\ + \endfoot + \bottomrule + \caption{112 symbols of \dbName.} + \endlastfoot +\verb+\&+ & $\&$ &\verb+\nmid+ & $\nmid$\\ +\verb+\Im+ & $\Im$ &\verb+\nvDash+ & $\nvDash$\\ +\verb+\Re+ & $\Re$ &\verb+\int+ & $\int$\\ +\verb+\S+ & $\S$ &\verb+\fint+ & $\fint$\\ +\verb+\Vdash+ & $\Vdash$ &\verb+\odot+ & $\odot$\\ +\verb+\aleph+ & $\aleph$ &\verb+\oiint+ & $\oiint$\\ +\verb+\amalg+ & $\amalg$ &\verb+\oint+ & $\oint$\\ +\verb+\angle+ & $\angle$ &\verb+\varoiint+ & $\varoiint$\\ +\verb+\ast+ & $\ast$ &\verb+\ominus+ & $\ominus$\\ +\verb+\asymp+ & $\asymp$ &\verb+\oplus+ & $\oplus$\\ +\verb+\backslash+ & $\backslash$ &\verb+\otimes+ & $\otimes$\\ +\verb+\between+ & $\between$ &\verb+\parallel+ & $\parallel$\\ +\verb+\blacksquare+ & $\blacksquare$ &\verb+\parr+ & $\parr$\\ +\verb+\blacktriangleright+ & $\blacktriangleright$ &\verb+\partial+ & $\partial$\\ +\verb+\bot+ & $\bot$ &\verb+\perp+ & $\perp$\\ +\verb+\bowtie+ & $\bowtie$ &\verb+\pitchfork+ & $\pitchfork$\\ +\verb+\boxdot+ & $\boxdot$ &\verb+\pm+ & $\pm$\\ +\verb+\boxplus+ & $\boxplus$ &\verb+\prime+ & $\prime$\\ +\verb+\boxtimes+ & $\boxtimes$ &\verb+\prod+ & $\prod$\\ +\verb+\bullet+ & $\bullet$ &\verb+\propto+ & $\propto$\\ +\verb+\checkmark+ & $\checkmark$ &\verb+\rangle+ & $\rangle$\\ +\verb+\circ+ & $\circ$ &\verb+\rceil+ & $\rceil$\\ +\verb+\circledR+ & $\circledR$ &\verb+\rfloor+ & $\rfloor$\\ +\verb+\circledast+ & $\circledast$ &\verb+\rrbracket+ & $\rrbracket$\\ +\verb+\circledcirc+ & $\circledcirc$ &\verb+\rtimes+ & $\rtimes$\\ +\verb+\clubsuit+ & $\clubsuit$ &\verb+\sharp+ & $\sharp$\\ +\verb+\coprod+ & $\coprod$ &\verb+\sphericalangle+ & $\sphericalangle$\\ +\verb+\copyright+ & $\copyright$ &\verb+\sqcap+ & $\sqcap$\\ +\verb+\dag+ & $\dag$ &\verb+\sqcup+ & $\sqcup$\\ +\verb+\dashv+ & $\dashv$ &\verb+\sqrt{}+ & $\sqrt{}$\\ +\verb+\diamond+ & $\diamond$ &\verb+\square+ & $\square$\\ +\verb+\diamondsuit+ & $\diamondsuit$ &\verb+\star+ & $\star$\\ +\verb+\div+ & $\div$ &\verb+\sum+ & $\sum$\\ +\verb+\ell+ & $\ell$ &\verb+\times+ & $\times$\\ +\verb+\flat+ & $\flat$ &\verb+\top+ & $\top$\\ +\verb+\frown+ & $\frown$ &\verb+\triangle+ & $\triangle$\\ +\verb+\guillemotleft+ & $\guillemotleft$ &\verb+\triangledown+ & $\triangledown$\\ +\verb+\hbar+ & $\hbar$ &\verb+\triangleleft+ & $\triangleleft$\\ +\verb+\heartsuit+ & $\heartsuit$ &\verb+\trianglelefteq+ & $\trianglelefteq$\\ +\verb+\infty+ & $\infty$ &\verb+\triangleq+ & $\triangleq$\\ +\verb+\langle+ & $\langle$ &\verb+\triangleright+ & $\triangleright$\\ +\verb+\lceil+ & $\lceil$ &\verb+\uplus+ & $\uplus$\\ +\verb+\lfloor+ & $\lfloor$ &\verb+\vDash+ & $\vDash$\\ +\verb+\lhd+ & $\lhd$ &\verb+\varnothing+ & $\varnothing$\\ +\verb+\lightning+ & $\lightning$ &\verb+\varpropto+ & $\varpropto$\\ +\verb+\llbracket+ & $\llbracket$ &\verb+\vartriangle+ & $\vartriangle$\\ +\verb+\lozenge+ & $\lozenge$ &\verb+\vdash+ & $\vdash$\\ +\verb+\ltimes+ & $\ltimes$ &\verb+\with+ & $\with$\\ +\verb+\mathds{1}+ & $\mathds{1}$ &\verb+\wp+ & $\wp$\\ +\verb+\mathsection+ & $\mathsection$ &\verb+\wr+ & $\wr$\\ +\verb+\mid+ & $\mid$ &\verb+\{+ & $\{$\\ +\verb+\models+ & $\models$ &\verb+\|+ & $\|$\\ +\verb+\mp+ & $\mp$ &\verb+\}+ & $\}$\\ +\verb+\multimap+ & $\multimap$ &\verb+\vee+ & $\vee$\\ +\verb+\nabla+ & $\nabla$ &\verb+\wedge+ & $\wedge$\\ +\verb+\neg+ & $\neg$ &\verb+\barwedge+ & $\barwedge$ + \label{table:symbols-of-db-0} + \end{longtable} + + +\begin{table}[ht] + \centering + + \begin{tabular}{lc|lc|lc|lc} + \toprule + \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\ + \midrule +\verb+\#+ & $\#$ &\verb+A+ & $A$ &\verb+S+ & $S$ &\verb+i+ & $i$\\ +\verb+\$+ & $\$$ &\verb+B+ & $B$ &\verb+T+ & $T$ &\verb+j+ & $j$\\ +\verb+\%+ & $\%$ &\verb+C+ & $C$ &\verb+U+ & $U$ &\verb+k+ & $k$\\ +\verb+++ & $+$ &\verb+D+ & $D$ &\verb+V+ & $V$ &\verb+l+ & $l$\\ +\verb+-+ & $-$ &\verb+E+ & $E$ &\verb+W+ & $W$ &\verb+m+ & $m$\\ +\verb+/+ & $/$ &\verb+F+ & $F$ &\verb+X+ & $X$ &\verb+n+ & $n$\\ +\verb+0+ & $0$ &\verb+G+ & $G$ &\verb+Y+ & $Y$ &\verb+o+ & $o$\\ +\verb+1+ & $1$ &\verb+H+ & $H$ &\verb+Z+ & $Z$ &\verb+p+ & $p$\\ +\verb+2+ & $2$ &\verb+I+ & $I$ &\verb+[+ & $[$ &\verb+q+ & $q$\\ +\verb+3+ & $3$ &\verb+J+ & $J$ &\verb+]+ & $]$ &\verb+r+ & $r$\\ +\verb+4+ & $4$ &\verb+K+ & $K$ &\verb+a+ & $a$ &\verb+s+ & $s$\\ +\verb+5+ & $5$ &\verb+L+ & $L$ &\verb+b+ & $b$ &\verb+u+ & $u$\\ +\verb+6+ & $6$ &\verb+M+ & $M$ &\verb+c+ & $c$ &\verb+v+ & $v$\\ +\verb+7+ & $7$ &\verb+N+ & $N$ &\verb+d+ & $d$ &\verb+w+ & $w$\\ +\verb+8+ & $8$ &\verb+O+ & $O$ &\verb+e+ & $e$ &\verb+x+ & $x$\\ +\verb+9+ & $9$ &\verb+P+ & $P$ &\verb+f+ & $f$ &\verb+y+ & $y$\\ +\verb+<+ & $<$ &\verb+Q+ & $Q$ &\verb+g+ & $g$ &\verb+z+ & $z$\\ +\verb+>+ & $>$ &\verb+R+ & $R$ &\verb+h+ & $h$ &\verb+|+ & $|$\\ + + \bottomrule + \end{tabular} + + \caption{72 ASCII symbols of \dbName, including all + ten digits, the Latin alphabet in lower and upper case and + a few more symbols.} + \label{table:symbols-of-db-1} +\end{table} + + +\begin{table}[ht] + \centering + \begin{tabular}{lc|lc|lc} + \toprule + \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\ + \midrule +\verb+\approx+ & $\approx$ &\verb+\geqslant+ & $\geqslant$ &\verb+\lesssim+ & $\lesssim$\\ +\verb+\doteq+ & $\doteq$ &\verb+\neq+ & $\neq$ &\verb+\backsim+ & $\backsim$\\ +\verb+\simeq+ & $\simeq$ &\verb+\not\equiv+ & $\not\equiv$ &\verb+\sim+ & $\sim$\\ +\verb+\equiv+ & $\equiv$ &\verb+\preccurlyeq+ & $\preccurlyeq$ &\verb+\succ+ & $\succ$\\ +\verb+\geq+ & $\geq$ &\verb+\preceq+ & $\preceq$ &\verb+\prec+ & $\prec$\\ +\verb+\leq+ & $\leq$ &\verb+\succeq+ & $\succeq$ &\verb+\gtrless+ & $\gtrless$\\ +\verb+\leqslant+ & $\leqslant$ &\verb+\gtrsim+ & $\gtrsim$ &\verb+\cong+ & $\cong$\\ + \bottomrule + \end{tabular} + + \caption{21 symbols which are in \dbName and indicate a relationship.} + \label{table:symbols-of-db-2} +\end{table} + + +\begin{table}[ht] + \centering + + \begin{tabular}{lc|lc} + \toprule + \LaTeX & Rendered & \LaTeX & Rendered \\ + \midrule +\verb+\Downarrow+ & $\Downarrow$ &\verb+\nrightarrow+ & $\nrightarrow$\\ +\verb+\Leftarrow+ & $\Leftarrow$ &\verb+\rightarrow+ & $\rightarrow$\\ +\verb+\Leftrightarrow+ & $\Leftrightarrow$ &\verb+\rightleftarrows+ & $\rightleftarrows$\\ +\verb+\Longleftrightarrow+ & $\Longleftrightarrow$ &\verb+\rightrightarrows+ & $\rightrightarrows$\\ +\verb+\Longrightarrow+ & $\Longrightarrow$ &\verb+\rightsquigarrow+ & $\rightsquigarrow$\\ +\verb+\Rightarrow+ & $\Rightarrow$ &\verb+\searrow+ & $\searrow$\\ +\verb+\circlearrowleft+ & $\circlearrowleft$ &\verb+\shortrightarrow+ & $\shortrightarrow$\\ +\verb+\circlearrowright+ & $\circlearrowright$ &\verb+\twoheadrightarrow+ & $\twoheadrightarrow$\\ +\verb+\curvearrowright+ & $\curvearrowright$ &\verb+\uparrow+ & $\uparrow$\\ +\verb+\downarrow+ & $\downarrow$ &\verb+\rightharpoonup+ & $\rightharpoonup$\\ +\verb+\hookrightarrow+ & $\hookrightarrow$ &\verb+\rightleftharpoons+ & $\rightleftharpoons$\\ +\verb+\leftarrow+ & $\leftarrow$ &\verb+\longmapsto+ & $\longmapsto$\\ +\verb+\leftrightarrow+ & $\leftrightarrow$ &\verb+\mapsfrom+ & $\mapsfrom$\\ +\verb+\longrightarrow+ & $\longrightarrow$ &\verb+\mapsto+ & $\mapsto$\\ +\verb+\nRightarrow+ & $\nRightarrow$ &\verb+\leadsto+ & $\leadsto$\\ +\verb+\nearrow+ & $\nearrow$ &\verb+\upharpoonright+ & $\upharpoonright$\\ + + \bottomrule + \end{tabular} + + \caption{32 arrow symbols of \dbName.} + \label{table:symbols-of-db-3} +\end{table} + + +\begin{table}[ht] + \centering + + \begin{tabular}{lc|lc|lc} + \toprule + \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\ + \midrule +\verb+\alpha+ & $\alpha$ &\verb+\xi+ & $\xi$ &\verb+\Xi+ & $\Xi$\\ +\verb+\beta+ & $\beta$ &\verb+\pi+ & $\pi$ &\verb+\Pi+ & $\Pi$\\ +\verb+\gamma+ & $\gamma$ &\verb+\rho+ & $\rho$ &\verb+\Sigma+ & $\Sigma$\\ +\verb+\delta+ & $\delta$ &\verb+\sigma+ & $\sigma$ &\verb+\Phi+ & $\Phi$\\ +\verb+\epsilon+ & $\epsilon$ &\verb+\tau+ & $\tau$ &\verb+\Psi+ & $\Psi$\\ +\verb+\zeta+ & $\zeta$ &\verb+\phi+ & $\phi$ &\verb+\Omega+ & $\Omega$\\ +\verb+\eta+ & $\eta$ &\verb+\chi+ & $\chi$ &\verb+\varepsilon+ & $\varepsilon$\\ +\verb+\theta+ & $\theta$ &\verb+\psi+ & $\psi$ &\verb+\varkappa+ & $\varkappa$\\ +\verb+\iota+ & $\iota$ &\verb+\omega+ & $\omega$ &\verb+\varpi+ & $\varpi$\\ +\verb+\kappa+ & $\kappa$ &\verb+\Gamma+ & $\Gamma$ &\verb+\varrho+ & $\varrho$\\ +\verb+\lambda+ & $\lambda$ &\verb+\Delta+ & $\Delta$ &\verb+\varphi+ & $\varphi$\\ +\verb+\mu+ & $\mu$ &\verb+\Theta+ & $\Theta$ &\verb+\vartheta+ & $\vartheta$\\ +\verb+\nu+ & $\nu$ &\verb+\Lambda+ & $\Lambda$ &\verb+ + & $ $\\ + + \bottomrule + \end{tabular} + + \caption{All Greek letters and some variations of Greek letters were + used for evaluation. 38 of them are in this table, the rest + is identical to Latin letters.} + \label{table:symbols-of-db-4} +\end{table} + + +\begin{table}[ht] + \centering + + \begin{tabular}{lc|lc|lc} + \toprule + \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\ + \midrule +\verb+\mathcal{A}+ & $\mathcal{A}$ &\verb+\mathcal{T}+ & $\mathcal{T}$ &\verb+\mathds{Z}+ & $\mathds{Z}$\\ +\verb+\mathcal{B}+ & $\mathcal{B}$ &\verb+\mathcal{U}+ & $\mathcal{U}$ &\verb+\mathfrak{A}+ & $\mathfrak{A}$\\ +\verb+\mathcal{C}+ & $\mathcal{C}$ &\verb+\mathcal{X}+ & $\mathcal{X}$ &\verb+\mathfrak{M}+ & $\mathfrak{M}$\\ +\verb+\mathcal{D}+ & $\mathcal{D}$ &\verb+\mathcal{Z}+ & $\mathcal{Z}$ &\verb+\mathfrak{S}+ & $\mathfrak{S}$\\ +\verb+\mathcal{E}+ & $\mathcal{E}$ &\verb+\mathbb{H}+ & $\mathbb{H}$ &\verb+\mathfrak{X}+ & $\mathfrak{X}$\\ +\verb+\mathcal{F}+ & $\mathcal{F}$ &\verb+\mathbb{N}+ & $\mathbb{N}$ &\verb+\mathscr{A}+ & $\mathscr{A}$\\ +\verb+\mathcal{G}+ & $\mathcal{G}$ &\verb+\mathbb{Q}+ & $\mathbb{Q}$ &\verb+\mathscr{C}+ & $\mathscr{C}$\\ +\verb+\mathcal{H}+ & $\mathcal{H}$ &\verb+\mathbb{R}+ & $\mathbb{R}$ &\verb+\mathscr{D}+ & $\mathscr{D}$\\ +\verb+\mathcal{L}+ & $\mathcal{L}$ &\verb+\mathbb{Z}+ & $\mathbb{Z}$ &\verb+\mathscr{E}+ & $\mathscr{E}$\\ +\verb+\mathcal{M}+ & $\mathcal{M}$ &\verb+\mathds{C}+ & $\mathds{C}$ &\verb+\mathscr{F}+ & $\mathscr{F}$\\ +\verb+\mathcal{N}+ & $\mathcal{N}$ &\verb+\mathds{E}+ & $\mathds{E}$ &\verb+\mathscr{H}+ & $\mathscr{H}$\\ +\verb+\mathcal{O}+ & $\mathcal{O}$ &\verb+\mathds{N}+ & $\mathds{N}$ &\verb+\mathscr{L}+ & $\mathscr{L}$\\ +\verb+\mathcal{P}+ & $\mathcal{P}$ &\verb+\mathds{P}+ & $\mathds{P}$ &\verb+\mathscr{P}+ & $\mathscr{P}$\\ +\verb+\mathcal{R}+ & $\mathcal{R}$ &\verb+\mathds{Q}+ & $\mathds{Q}$ &\verb+\mathscr{S}+ & $\mathscr{S}$\\ +\verb+\mathcal{S}+ & $\mathcal{S}$ &\verb+\mathds{R}+ & $\mathds{R}$ &\verb+ + & $ $\\ + + \bottomrule + \end{tabular} + + \caption{44 variants of Latin letters in \dbName.} + \label{table:symbols-of-db-5} +\end{table} + + +\begin{table}[ht] + \centering + + \begin{tabular}{lc|lc|lc} + \toprule + \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\ + \midrule +\verb+\therefore+ & $\therefore$ &\verb+\cdot+ & $\cdot$ &\verb+\dots+ & $\dots$\\ +\verb+\because+ & $\because$ &\verb+\vdots+ & $\vdots$ &\verb+\ddots+ & $\ddots$\\ +\verb+\dotsc+ & $\dotsc$ &\verb+ + & &\verb+ + & \\ + \bottomrule + \end{tabular} + + \caption{7 symbols that contain only dots in \dbName.} + \label{table:symbols-of-db-6} +\end{table} + + +\begin{table}[ht] + \centering + \begin{tabular}{lc|lc|lc|lc|lc} + \toprule + \LaTeX & R & \LaTeX & R & \LaTeX & R & \LaTeX & R & \LaTeX & R \\ + \midrule +\verb+\AA+ & {\r A} &\verb+\L+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/L.pdf} &\verb+\male+ & {\mbox {\wasyfamily \char 26}} &\verb+\ohm+ & $\Omega $ &\verb+\sun+ & {\mbox {\wasyfamily \char 46}} \\ +\verb+\AE+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/AE.pdf} &\verb+\O+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/L.pdf} &\verb+\mars+ & {\leavevmode \lower 0.2ex\hbox {\wasyfamily \char 26}} &\verb+\fullmoon+ & {\mbox {\wasyfamily \char 35}} &\verb+\degree+ & {\ensuremath {^\circ }}\\ +\verb+\aa+ & {\r a} &\verb+\o+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/o.pdf} &\verb+\female+ & {\mbox {\wasyfamily \char 25}} &\verb+\leftmoon+ & {\mbox {\wasyfamily \char 36}} &\verb+\iddots+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/iddots.pdf}\\ +\verb+\ae+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/AE.pdf} &\verb+\Bowtie+ & {\mbox {\wasyfamily \char 49}} &\verb+\venus+ & {\leavevmode \raise 0.2ex\hbox {\wasyfamily \char 25}} &\verb+\checked+ & {\mbox {\wasyfamily \char 8}} &\verb+\diameter+ & {\mbox {\wasyfamily \char 31}} \\ +\verb+\ss+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/ss.pdf} &\verb+\celsius+ & $^\circ \mathrm {C}$ &\verb+\astrosun+ & {\mbox {$\odot $}} &\verb+\pounds+ & \textsterling &\verb+\mathbb{1}+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/mathbb-1.pdf}\\ + \bottomrule + \end{tabular} + \caption{25 symbols of \dbName.} + \label{table:symbols-of-db-7} +\end{table} + + +\begin{table}[ht] + \centering + + \begin{tabular}{lc|lc|lc} + \toprule + \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\ + \midrule +\verb+\cup+ & $\cup$ &\verb+\varsubsetneq+ & $\varsubsetneq$ &\verb+\exists+ & $\exists$\\ +\verb+\cap+ & $\cap$ &\verb+\nsubseteq+ & $\nsubseteq$ &\verb+\nexists+ & $\nexists$\\ +\verb+\emptyset+ & $\emptyset$ &\verb+\sqsubseteq+ & $\sqsubseteq$ &\verb+\forall+ & $\forall$\\ +\verb+\setminus+ & $\setminus$ &\verb+\subseteq+ & $\subseteq$ &\verb+\in+ & $\in$\\ +\verb+\supset+ & $\supset$ &\verb+\subsetneq+ & $\subsetneq$ &\verb+\ni+ & $\ni$\\ +\verb+\subset+ & $\subset$ &\verb+\supseteq+ & $\supseteq$ &\verb+\notin+ & $\notin$\\ + + \bottomrule + \end{tabular} + + \caption{18 set related symbols of \dbName.} + \label{table:symbols-of-db-8} +\end{table} +\clearpage \ No newline at end of file