\begin
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%%\documentclass[pdflatex,ml4h-basic]{ml4h-jnl}% Basic Springer Nature Reference Style/Chemistry Reference Style
%%\documentclass[ml4h-basic]{ml4h-jnl}% Basic Springer Nature Reference Style/Chemistry Reference Style
\documentclass[ml4h-mathphys]{ml4h-jnl}% Math and Physical Sciences Reference Style
%%\documentclass[ml4h-aps]{ml4h-jnl}% American Physical Society (APS) Reference Style
%%\documentclass[ml4h-vancouver]{ml4h-jnl}% Vancouver Reference Style
%%\documentclass[ml4h-apa]{ml4h-jnl}% APA Reference Style
%%\documentclass[ml4h-chicago]{ml4h-jnl}% Chicago-based Humanities Reference Style
%%\documentclass[ml4h-standardnature]{ml4h-jnl}% Standard Nature Portfolio Reference Style
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%% LaTeX2e Style for ML4H Auditing purposes - Fraunhofer HHI
%% Author: Kaushik Manjunatha, Fraunhofer HHI, Germany
%% Contact: https://www.linkedin.com/in/kaushik-manjunatha/
%% Please feel free to send issues, suggestions: kaushik.manjunatha@fraunhofer.hhi.de
%% Based on the template created by Springer Nature and Emma Rocheteau
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%%%% Remarks: This template is provided to aid authors with the preparation of ML4H %%%% reports.
%%%% Editorial and presentation requirements differ among journal portfolios and
%%%% research disciplines. You may find sections in this template are irrelevant
%%%% to your work and are empowered to omit any such section if allowed by the
%%%% journal you intend to submit to. The submission guidelines and policies of the %%%% journal take precedence.
%%%% Please do changes accordingly as per the submission requirements
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\jyear{2021}%
%% as per the requirement new theorem styles can be included as shown below
\theoremstyle{thmstyleone}%
\newtheorem{theorem}{Theorem}% meant for continuous numbers
%%\newtheorem{theorem}{Theorem}[section]% meant for sectionwise numbers
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\newtheorem{proposition}[theorem]{Proposition}%
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\theoremstyle{thmstyletwo}%
\newtheorem{example}{Example}%
\newtheorem{remark}{Remark}%
\theoremstyle{thmstylethree}%
\newtheorem{definition}{Definition}%
\raggedbottom
%%\unnumbered% uncomment this for unnumbered level heads
\begin{document}
\title[ML4H Auditing - Report Template (Your short title)]{ML4H Auditing - Report Template \\(Your long title)}
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%% Prefix -> \pfx{Dr}
%% GivenName -> \fnm{Kaushik.}
%% Particle -> \spfx{Manjunatha} -> surname prefix
%% FamilyName -> \sur{Upadhya}
%% Suffix -> \sfx{IV}
%% NatureName -> \tanm{Poet Laureate} -> Title after name
%% Degrees -> \dgr{MSc, PhD}
%% \author*[1,2]{\pfx{Dr} \fnm{Kaushik} \spfx{Manjunatha} \sur{Upadhya} \sfx{IV} \tanm{Poet Laureate}
%% \dgr{MSc, PhD}}\email{iauthor@gmail.com}
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\author*[1,2]{\fnm{First} \sur{Author}}\email{iauthor@gmail.com}
\author[2,3]{\fnm{Second} \sur{Author}}\email{iiauthor@gmail.com}
\equalcont{These authors contributed equally to this work.}
\author[1,2]{\fnm{Third} \sur{Author}}\email{iiiauthor@gmail.com}
\equalcont{These authors contributed equally to this work.}
\affil*[1]{\orgdiv{Department}, \orgname{Organization}, \orgaddress{\street{Street}, \city{City}, \postcode{100190}, \state{State}, \country{Country}}}
\affil[2]{\orgdiv{Department}, \orgname{Organization}, \orgaddress{\street{Street}, \city{City}, \postcode{10587}, \state{State}, \country{Country}}}
\affil[3]{\orgdiv{Department}, \orgname{Organization}, \orgaddress{\street{Street}, \city{City}, \postcode{610101}, \state{State}, \country{Country}}}
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%% Sample for unstructured abstract %%
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\abstract{The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. Authors are advised to check the author instructions for the journal they are submitting to for word limits and if structural elements like subheadings, citations, or equations are permitted.}
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%% Sample for structured abstract %%
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\abstract{\textbf{Purpose:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.
\textbf{Methods:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.
\textbf{Results:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.
\textbf{Conclusion:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.}
\keywords{keyword1, Keyword2, Keyword3, Keyword4}
%%\pacs[JEL Classification]{D8, H51}
%%\pacs[MSC Classification]{35A01, 65L10, 65L12, 65L20, 65L70}
\maketitle
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% Adding extra sections can be done by using the below commands.
% \section{This is an example for first level head---section head}\label{sec3}
% \subsection{This is an example for second level head---subsection head}\label{subsec2}
% \subsubsection{This is an example for third level head---subsubsection head}\label{subsubsec2}
% Sample body text. Sample body text.
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This document provides a template for the second iteration of ML4H Trial Audits to help you structure your group work. If you have ideas for changes or improvements feel free to share them on slack.
\section{Introduction}\label{sec1}
The Introduction section, of referenced text \cite{bib1} expands on the background of the work (some overlap with the Abstract is acceptable). The introduction should not include subheadings.
\section{Use Case}
This section contains the description of the Use case(s) and the data you are auditing.
\subsection{Data collection and preparation}
This section contains information on the data that was used to train the model and that you use to test the model. It often makes sense to perform additional data quality assessments alongside the ML4H model itself. The methods and results for the data quality assessment you can include in Sections \ref{sec11} and \ref{sec111}.
\section{Planning and Scope of the Audit}
In this section you can detail how you approached the audit, which process you used, what you could and could not do.
\section{Audit Methods}\label{sec11}
In this section you should describe the concrete methods you used to assess the quality of the ML4H model and potentially the data you used.
\subsection{Technical}
\subsection{Clinical}
\subsection{Regulatory}
\subsection{Ethical}
\section{Audit Report}\label{sec111}
This section contains a summary of the audit results for each category
\textbf{Technical}
\textbf{Clinical}
\textbf{Regulatory}
\textbf{Ethical}
Please include a version of the ITU/WHO FG-AI4H Audit Reporting Template (\url{https://aiaudit.org/assets/pdf/standards/FGAI4H-J-048.pdf}) to summarize your findings in the appendices. An example which has been filled out can be found in the appendices of \url{http://proceedings.mlr.press/v136/oala20a/oala20a.pdf}.
\section{Discussion}\label{sec12}
Discussions should be brief and focused. In some disciplines use of Discussion or `Conclusion' is interchangeable. It is not mandatory to use both. Some prefer a section `Results and Discussion' followed by a section `Conclusion'. Please alter according to any specific requirements.
\section{Actionable Recommendations}\label{sec13}
If you have actionable recommendations for the ML4H tool developer (e.g. "try doing X to solve problem Y" you should include them here.
% In some disciplines use of Discussion or 'Conclusion' is interchangeable. It is not mandatory to use both. Please refer to Journal-level guidance for any specific requirements.
\section{References}
This section contains the bibliography information related to the paper.
\backmatter
\bmhead{Supplementary information}
If your article has accompanying supplementary files please state so here.
\bmhead{Acknowledgments}
Acknowledgments are not compulsory. Where included they should be brief. Grant or contribution numbers should go into funding under "Declarations".
\section*{Declarations}
This section may contain the declarations that needs to be submitted in a standardised format. If yes, your cript must contain the following sections under the heading `Declarations':
\begin{itemize}
\item Funding
\item Conflict of interest/Competing interests (check journal-specific guidelines for which heading to use)
\item Ethics approval
\item Consent to participate
\item Consent for publication
\item Availability of data and materials
\item Code availability
\item Authors' contributions
\end{itemize}
\noindent
If any of the sections are not relevant to your manuscript, please include the heading and write `Not applicable' for that section.
% If your manuscript includes potentially identifying patient/participant information, or if it describes human transplantation research, or if it reports results of a clinical trial then additional information will be required. Please visit (\url{https://www.nature.com/nature-research/editorial-policies}) for Nature Portfolio journals, (\url{https://www.springer.com/gp/authors-editors/journal-author/journal-author-helpdesk/publishing-ethics/14214}) for Springer Nature journals, or (\url{https://www.biomedcentral.com/getpublished/editorial-policies\#ethics+and+consent}) for BMC.
% \section{Discussion}\label{sec12}
% Discussions should be brief and focused. In some disciplines use of Discussion or `Conclusion' is interchangeable. It is not mandatory to use both. Some journals prefer a section `Results and Discussion' followed by a section `Conclusion'. Please refer to Journal-level guidance for any specific requirements.
%%===================================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%===================================================%%
% \bigskip
% \begin{flushleft}%
% Editorial Policies for:
% \bigskip\noindent
% Springer journals and proceedings: \url{https://www.springer.com/gp/editorial-policies}
% \bigskip\noindent
% Nature Portfolio journals: \url{https://www.nature.com/nature-research/editorial-policies}
% \bigskip\noindent
% \textit{Scientific Reports}: \url{https://www.nature.com/srep/journal-policies/editorial-policies}
% \bigskip\noindent
% BMC journals: \url{https://www.biomedcentral.com/getpublished/editorial-policies}
% \end{flushleft}
% \bibliography{ml4h-bibliography}
\begin{appendices}
\section{Section title of first appendix}\label{secA1}
An appendix contains supplementary information that is not an essential part of the text itself but which may be helpful in providing a more comprehensive understanding of the research problem or it is information that is too cumbersome to be included in the body of the paper.
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%% For submissions to Portfolio Journals %%
%% please use the heading ``Extended Data''. %%
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%% Sample for another appendix section %%
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%% \section{Example of another appendix section}\label{secA2}%
%% Appendices may be used for helpful, supporting or essential material that would otherwise
%% clutter, break up or be distracting to the text. Appendices can consist of sections, figures,
%% tables and equations etc.
\end{appendices}
%%===========================================================================================%%
%% If you are submitting to one of the Nature Portfolio journals, using the eJP submission %%
%% system, please include the references within the manuscript file itself. You may do this %%
%% by copying the reference list from your .bbl file, paste it into the main manuscript .tex %%
%% file, and delete the associated \verb+\bibliography+ commands. %%
%%===========================================================================================%%
% \nocite{*}
%Any of the below method can be used for citing the source of resources used.
% \bibliography{bibliography.bib} % Use the/ bibliography.bib file as the source of references
% %% if required, the content of .bbl file can be included here once bbl is generated
% %%\input ml4h-article.bbl
%% Default %%
\input ml4h-sample-bib.tex
\pagebreak
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%%%%%%%%%%%%% Sample Section of Examples %%%%%%%%%%%%%
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%%%%%% Remove this section in the actual Report %%%%%%
\section*{Sample section containing examples}
The below section contains the examples to add the equations, tables, code snippets etc.
\subsection{Equations}\label{sec4}
Equations in \LaTeX\ can either be inline or on-a-line by itself (``display equations''). For
inline equations use the \verb+$...$+ commands. E.g.: The equation
$H\psi = E \psi$ is written via the command \verb+$H \psi = E \psi$+.
For display equations (with auto generated equation numbers)
one can use the equation or align environments:
\begin{equation}
\|\tilde{X}(k)\|^2 \leq\frac{\sum\limits_{i=1}^{p}\left\|\tilde{Y}_i(k)\right\|^2+\sum\limits_{j=1}^{q}\left\|\tilde{Z}_j(k)\right\|^2 }{p+q}.\label{eq1}
\end{equation}
where,
\begin{align}
D_\mu &= \partial_\mu - ig \frac{\lambda^a}{2} A^a_\mu \nonumber \\
F^a_{\mu\nu} &= \partial_\mu A^a_\nu - \partial_\nu A^a_\mu + g f^{abc} A^b_\mu A^a_\nu \label{eq2}
\end{align}
Notice the use of \verb+\nonumber+ in the align environment at the end
of each line, except the last, so as not to produce equation numbers on
lines where no equation numbers are required. The \verb+\label{}+ command
should only be used at the last line of an align environment where
\verb+\nonumber+ is not used.
\begin{equation}
Y_\infty = \left( \frac{m}{\textrm{GeV}} \right)^{-3}
\left[ 1 + \frac{3 \ln(m/\textrm{GeV})}{15}
+ \frac{\ln(c_2/5)}{15} \right]
\end{equation}
The class file also supports the use of \verb+\mathbb{}+, \verb+\mathscr{}+ and
\verb+\mathcal{}+ commands. As such \verb+\mathbb{R}+, \verb+\mathscr{R}+
and \verb+\mathcal{R}+ produces $\mathbb{R}$, $\mathscr{R}$ and $\mathcal{R}$ respectively.
\subsection{Cross-Referencing}
Always use \verb|\label| and \verb|\ref| (or one of the commands
described below) when cross-referencing. For example, the next
section is Section~\ref{sec:math} but you can also refer to it using
\ref{sec:math}.
\subsection{Equations (contd..)}
\label{sec:math}
(See the \textsf{amsmath} documentation for further
details.\footnote{Either \texttt{texdoc amsmath} or
\url{http://www.ctan.org/pkg/amsmath}})
Unnumbered single-lined equations should be displayed using
\verb|\[| and \verb|\]|. For example:
\[E = m c^2\]
or you can use the \texttt{displaymath} environment:
\begin{displaymath}
E = m c^2
\end{displaymath}
Numbered single-line equations should be displayed using the
\texttt{equation} environment. For example:
\begin{equation}\label{eq:trigrule}
\cos^2\theta + \sin^2\theta \equiv 1
\end{equation}
This can be referenced using \verb|\label| and \verb|\equationref|.
For example, \ref{eq:trigrule}.
Multi-lined numbered equations should be displayed using the
\texttt{align} environment.\footnote{For reasons why you
shouldn't use the obsolete \texttt{eqnarray} environment, see
Lars Madsen, \emph{Avoid eqnarray!} TUGboat 33(1):21--25, 2012.} For example:
\begin{align}
f(x) &= x^2 + x\label{eq:f}\\
f'(x) &= 2x + 1\label{eq:df}
\end{align}
Unnumbered multi-lined equations can be displayed using the
\texttt{align*} environment. For example:
\begin{align*}
f(x) &= (x+1)(x-1)\\
&= x^2 - 1
\end{align*}
If you want to mix numbered with unnumbered lines use the
\texttt{align} environment and suppress unwanted line numbers with
\verb|\nonumber|. For example:
\begin{align}
y &= x^2 + 3x - 2x + 1\nonumber\\
&= x^2 + x + 1\label{eq:y}
\end{align}
An equation that is too long to fit on a single line can be
displayed using the \texttt{split} environment.
Text can be embedded in an equation using \verb|\text| or
\verb|\intertext| (as used in \ref{thm:eigenpow}).
See the \textsf{amsmath} documentation for further details.
\subsection{Operator Names}
\label{sec:op}
Predefined operator names are listed in \ref{table:operatornames}.
For additional operators, either use \verb|\operatorname|,
for example $\operatorname{var}(X)$ or declare it with
\verb|\DeclareMathOperator|, for example
\begin{verbatim}
\DeclareMathOperator{\var}{var}
\end{verbatim}
and then use this new command. If you want limits that go above and
below the operator (like \verb|\sum|) use the starred versions
(\verb|\operatorname*| or \verb|\DeclareMathOperator*|).
\begin{table*}[htbp]
\label{table:operatornames}%
{\caption{Predefined Operator Names (taken from
\textsf{amsmath} documentation)}}%
{%
\begin{tabular}{rlrlrlrl}
arccos & $\arccos$ & deg & $\deg$ & lg & $\lg$ & projlim & $\projlim$ \\
{arcsin} & $\arcsin$ & {det} & $\det$ & {lim} & $\lim$ & {sec} & $\sec$ \\
{arctan} & $\arctan$ & {dim} & $\dim$ & {liminf} & $\liminf$ & {sin} & $\sin$ \\
{arg} & $\arg$ & {exp} & $\exp$ & {limsup} & $\limsup$ & {sinh} & $\sinh$ \\
{cos} & $\cos$ & {gcd} & $\gcd$ & {ln} & $\ln$ & {sup} & $\sup$ \\
{cosh} & $\cosh$ & {hom} & $\hom$ & {log} & $\log$ & {tan} & $\tan$ \\
{cot} & $\cot$ & {inf} & $\inf$ & {max} & $\max$ & {tanh} & $\tanh$ \\
{coth} & $\coth$ & {injlim} & $\injlim$ & {min} & $\min$ \\
{csc} & $c$ & {ker} & $\ker$ & {Pr} & $\Pr$
\end{tabular}\par
\begin{tabular}{rlrl}
{varlimsup} & $\varlimsup$
& {varinjlim} & $\varinjlim$\\
{varliminf} & $\varliminf$
& {varprojlim} & $\varprojlim$
\end{tabular}
}
\end{table*}
\subsection{Floats}
\label{sec:floats}
Floats, such as figures, tables and algorithms, are moving
objects and are supposed to float to the nearest convenient
location. Please don't force them to go in a particular place. In
general it's best to use the \texttt{htbp} specifier and don't
put the figure or table in the middle of a paragraph (that is
make sure there's a paragraph break above and below the float).
Floats are supposed to have a little extra space above and below
them to make them stand out from the rest of the text. This extra
spacing is put in automatically and shouldn't need modifying.
If your article will later be reprinted in the Challenges for
Machine Learning, please be aware that the CiML books use a
different paper size, so if you want to resize any images use a
scale relative to the line width (\verb|\linewidth|), text width
(\verb|\textwidth|) or text height (\verb|\textheight|).
To ensure consistency, please \emph{don't} try changing the format of the caption by doing
something like:
\begin{verbatim}
\caption{\textit{A Sample Caption.}}
\end{verbatim}
or
\begin{verbatim}
\caption{\em A Sample Caption.}
\end{verbatim}
You can, of course, change the font for individual words or
phrases, for example:
\begin{verbatim}
\caption{A Sample Caption With Some \emph{Emphasized Words}.}
\end{verbatim}
\subsection{Description Lists}
The description class also provides a description-like
environment and has an
argument that should be the widest label in the list. Compare:
\begin{description}
\item[add] A method that adds two variables.
\item[differentiate] A method that differentiates a function.
\end{description}
\subsection{Tables - 1}
\label{sec:tables}
Tables should go in the \texttt{table} environment.
The location of the caption depends on the \verb|tablecaption|
setting in the document class options.
\begin{table}[htbp]
% The first argument is the label.
% The caption goes in the second argument, and the table contents
% go in the third argument.
% \floatconts{tab:example}%
{\caption{An Example Table}}%
{\begin{tabular}{ll}
\bfseries Dataset & \bfseries Result\\
Data1 & 0.12345\\
Data2 & 0.67890\\
Data3 & 0.54321\\
Data4 & 0.09876
\end{tabular}}
\end{table}
If you want horizontal rules you can use the \textsf{booktabs}
package which provides the commands \verb|\toprule|,
\verb|\midrule| and \verb|\bottomrule|. For example, see
\ref{table:example-booktabs}.
\begin{table}[hbtp]
\label{table:example-booktabs}
{\caption{A Table With Horizontal Lines}}
{\begin{tabular}{ll}
\toprule
\bfseries Dataset & \bfseries Result\\
\midrule
Data1 & 0.12345\\
Data2 & 0.67890\\
Data3 & 0.54321\\
Data4 & 0.09876\\
\bottomrule
\end{tabular}}
\end{table}
If you really want vertical lines as well, you can't use the
\textsf{booktabs} commands as there'll be some unwanted gaps.
Instead you can use \LaTeX's \verb|\hline|, but the rows may
appear a bit cramped. You can add extra space above or below a
row using \verb|\abovestrut| and \verb|\belowstrut|. For example,
see \ref{table:example-hline}. However, you might want to read
the \textsf{booktabs} documentation regarding the use of vertical
lines.
\begin{table}[htbp]
\label{table:example-hline}
{\caption{A Table With Horizontal and Vertical Lines}}%
{%
\begin{tabular}{|l|l|}
\hline
\bfseries Dataset & \bfseries Result\\\hline
Data1 & 0.12345\\
Data2 & 0.67890\\
Data3 & 0.54321\\
Data4 & 0.09876\\\hline
\end{tabular}
}
\end{table}
If the table is too wide, you can adjust the inter-column
spacing by changing the value of \verb|\tabcolsep|. For
example:
\begin{verbatim}
\setlength{\tabcolsep}{3pt}
\end{verbatim}
If the table is very wide but not very long, you can use the
\texttt{sidewaystable} environment defined in the
\textsf{rotating} package (so use \verb|\usepackage{rotating}|).
If the table is too long to fit on a page, you can use the
\texttt{longtable} environment defined in the \textsf{longtable}
package (so use \verb|\usepackage{longtable}|).
\subsection{Figures - 1}
\label{sec:figures}
Figures should go in the \texttt{figure} environment. Within this
environment, use \verb|\floatconts| to correctly position the
caption and center the image. Use \verb|\includegraphics|
for external graphics files but omit the file extension. Do not
use \verb|\epsfig| or \verb|\psfig|. If you want to scale the
image, it's better to use a fraction of the line width rather
than an explicit length. For example, see figure \ref{fig:nodes}.
\begin{figure}[htbp]
% Caption and label go in the first argument and the figure contents
% go in the second argument
{
\caption{Example Image}
\label{fig:nodes}
{\includegraphics[width=0.5\linewidth]{images/nodes}}}
\end{figure}
If the figure is too wide to fit on the page, you can use the
\texttt{sidewaysfigure} environment defined in the
\textsf{rotating} package.
If the images are contained in a subdirectory, specify this when you include the image, for
example \verb|\includegraphics{figures/mypic}|.
% \subsubsection{Sub-Figures}
% \label{sec:subfigures}
% The optional argument allows
% you to provide a subcaption. The label should be placed in the
% mandatory argument of \verb|\subfigure|. You can reference the
% entire figure, for example \figureref{fig:subfigex}, or you can
% reference part of the figure using \verb|\figureref|, for example
% \figureref{fig:circle}. Alternatively you can reference the
% subfigure using \verb|\subfigref|, for example
% \subfigref{fig:circle,fig:square} in \figureref{fig:subfigex}.
% \begin{figure}[htbp]
% \floatconts
% {fig:subfigex}
% {\caption{An Example With Sub-Figures.}}
% {%
% \subfigure[A Circle]{\label{fig:circle}%
% \includegraphics[width=0.2\linewidth]{images/circle}}%
% \qquad
% \subfigure[A Square]{\label{fig:square}%
% \includegraphics[width=0.2\linewidth]{images/square}}
% }
% \end{figure}
% By default, the sub-figures are aligned on the baseline.
% This can be changed using the second optional argument
% of \verb|\subfigure|. This may be \texttt{t} (top), \texttt{c}
% (centered) or \texttt{b} (bottom). For example, the subfigures
% \subfigref{fig:circle2,fig:square2} in \figureref{fig:subfigex2}
% both have \verb|[c]| as the second optional argument.
% \begin{figure}[htbp]
% \floatconts
% {fig:subfigex2}
% {\caption{Another Example With Sub-Figures.}}
% {%
% \subfigure[A Small Circle][c]{\label{fig:circle2}%
% \includegraphics[width=0.1\linewidth]{images/circle}}%
% \qquad
% \subfigure[A Square][c]{\label{fig:square2}%
% \includegraphics[width=0.2\linewidth]{images/square}}
% }
% \end{figure}
% \subsection{Sub-Tables}
% \label{sec:subtables}
% There is an analogous command \verb|\subtable| for sub-tables.
% It has the same syntax as \verb|\subfigure| described above.
% You can reference the table using \verb|\tableref|, for example
% \ref{tab:subtabex} or you can reference part of the table,
% for example \ref{tab:ab}. Alternatively you can reference the
% subtable using \verb|\subtabref|, for example
% \ref{tab:ab,tab:cd} in \ref{tab:subtabex}.
% \begin{table}[htbp]
% {\label{tab:subtabex}
% {\caption{An Example With Sub-Tables}}
% {%
% \subtable{%
% \label{tab:ab}%
% \begin{tabular}{cc}
% \bfseries A & \bfseries B\\
% 1 & 2
% \end{tabular}
% }\qquad
% \subtable{%
% \label{tab:cd}%
% \begin{tabular}{cc}
% \bfseries C & \bfseries D\\
% 3 & 4\\
% 5 & 6
% \end{tabular}
% }
% }}
% \end{table}
% By default, the sub-tables are aligned on the top.
% This can be changed using the second optional argument
% of \verb|\subtable|. This may be \texttt{t} (top), \texttt{c}
% (centered) or \texttt{b} (bottom). For example, the sub-tables
% \subtabref{tab:ab2,tab:cd2} in \tableref{tab:subtabex2}
% both have \verb|[c]| as the second optional argument.
% \begin{table}[htbp]
% \floatconts
% {tab:subtabex2}
% {\caption{Another Example With Sub-Tables}}
% {%
% \subtable[][c]{%
% \label{tab:ab2}%
% \begin{tabular}{cc}
% \bfseries A & \bfseries B\\
% 1 & 2
% \end{tabular}
% }\qquad
% \subtable[][c]{%
% \label{tab:cd2}%
% \begin{tabular}{cc}
% \bfseries C & \bfseries D\\
% 3 & 4\\
% 5 & 6
% \end{tabular}
% }
% }
% \end{table}
\subsection{Tables - 2}\label{sec5}
Tables can be inserted via the normal table and tabular environment. To put
footnotes inside tables you should use \verb+\footnotetext[]{...}+ tag.
The footnote appears just below the table itself (refer Tables~\ref{tab1} and \ref{tab2}).
For the corresponding footnotemark use \verb+\footnotemark[...]+
\begin{table}[h]
\begin{center}
\begin{minipage}{174pt}
\caption{Caption text}\label{tab1}%
\begin{tabular}{@{}llll@{}}
\toprule
Column 1 & Column 2 & Column 3 & Column 4\\
\midrule
row 1 & data 1 & data 2 & data 3 \\
row 2 & data 4 & data 5\footnotemark[1] & data 6 \\
row 3 & data 7 & data 8 & data 9\footnotemark[2] \\
\botrule
\end{tabular}
\footnotetext{Source: This is an example of table footnote. This is an example of table footnote.}
\footnotetext[1]{Example for a first table footnote. This is an example of table footnote.}
\footnotetext[2]{Example for a second table footnote. This is an example of table footnote.}
\end{minipage}
\end{center}
\end{table}
\noindent
The input format for the above table is as follows:
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
\bigskip
\begin{verbatim}
\begin{table}[<placement-specifier>]
\begin{center}
\begin{minipage}{<preferred-table-width>}
\caption{<table-caption>}\label{<table-label>}%
\begin{tabular}{@{}llll@{}}
\toprule
Column 1 & Column 2 & Column 3 & Column 4\\
\midrule
row 1 & data 1 & data 2 & data 3 \\
row 2 & data 4 & data 5\footnotemark[1] & data 6 \\
row 3 & data 7 & data 8 & data 9\footnotemark[2]\\
\botrule
\end{tabular}
\footnotetext{Source: This is an example of table footnote.
This is an example of table footnote.}
\footnotetext[1]{Example for a first table footnote.
This is an example of table footnote.}
\footnotetext[2]{Example for a second table footnote.
This is an example of table footnote.}
\end{minipage}
\end{center}
\end{table}
\end{verbatim}
\bigskip
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
\begin{table}[h]
\begin{center}
\begin{minipage}{\textwidth}
\caption{Example of a lengthy table which is set to full textwidth}\label{tab2}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}lcccccc@{\extracolsep{\fill}}}
\toprule%
& \multicolumn{3}{@{}c@{}}{Row 1\footnotemark[1]} & \multicolumn{3}{@{}c@{}}{Row 2\footnotemark[2]} \\\cmidrule{2-4}\cmidrule{5-7}%
Project & Example & $\sigma_{calc}$ & $\sigma_{expt}$ & Example & $\sigma_{calc}$ & $\sigma_{expt}$ \\
\midrule
Row 3 & 990 A & 1168 & $1547\pm12$ & 780 A & 1166 & $1239\pm100$\\
Row 4 & 500 A & 961 & $922\pm10$ & 900 A & 1268 & $1092\pm40$\\
\botrule
\end{tabular*}
\footnotetext{Note: This is an example of table footnote. This is an example of table footnote this is an example of table footnote this is an example of~table footnote this is an example of table footnote.}
\footnotetext[1]{Example for a first table footnote.}
\footnotetext[2]{Example for a second table footnote.}
\end{minipage}
\end{center}
\end{table}
In case of double column layout, tables which do not fit in single column width should be set to full text width. For this, you need to use \verb+\begin{table*}+ \verb+...+ \verb+\end{table*}+ instead of \verb+\begin{table}+ \verb+...+ \verb+\end{table}+ environment. Lengthy tables which do not fit in textwidth should be set as rotated table. For this, you need to use \verb+\begin{sidewaystable}+ \verb+...+ \verb+\end{sidewaystable}+ instead of \verb+\begin{table*}+ \verb+...+ \verb+\end{table*}+ environment. This environment puts tables rotated to single column width. For tables rotated to double column width, use \verb+\begin{sidewaystable*}+ \verb+...+ \verb+\end{sidewaystable*}+.
\begin{sidewaystable}
\sidewaystablefn%
\begin{center}
\begin{minipage}{\textheight}
\caption{Tables which are too long to fit, should be written using the ``sidewaystable'' environment as shown here}\label{tab3}
\begin{tabular*}{\textheight}{@{\extracolsep{\fill}}lcccccc@{\extracolsep{\fill}}}
\toprule%
& \multicolumn{3}{@{}c@{}}{Row 1\footnotemark[1]}& \multicolumn{3}{@{}c@{}}{Row\footnotemark[2]} \\\cmidrule{2-4}\cmidrule{5-7}%
Project & Example & $\sigma_{calc}$ & $\sigma_{expt}$ & Example & $\sigma_{calc}$ & $\sigma_{expt}$ \\
\midrule
Row 3 & 990 A & 1168 & $1547\pm12$ & 780 A & 1166 & $1239\pm100$ \\
Row 4 & 500 A & 961 & $922\pm10$ & 900 A & 1268 & $1092\pm40$ \\
Row 5 & 990 A & 1168 & $1547\pm12$ & 780 A & 1166 & $1239\pm100$ \\
Row 6 & 500 A & 961 & $922\pm10$ & 900 A & 1268 & $1092\pm40$ \\
\botrule
\end{tabular*}
\footnotetext{Note: This is an example of table footnote this is an example of table footnote this is an example of table footnote this is an example of~table footnote this is an example of table footnote.}
\footnotetext[1]{This is an example of table footnote.}
\end{minipage}
\end{center}
\end{sidewaystable}
\subsection{Figures - 2}\label{sec6}
As per the \LaTeX\ standards you need to use eps images for \LaTeX\ compilation and \verb+pdf/jpg/png+ images for \verb+PDFLaTeX+ compilation. This is one of the major difference between \LaTeX\ and \verb+PDFLaTeX+. Each image should be from a single input .eps/vector image file. Avoid using subfigures. The command for inserting images for \LaTeX\ and \verb+PDFLaTeX+ can be generalized. The package used to insert images in \verb+LaTeX/PDFLaTeX+ is the graphicx package. Figures can be inserted via the normal figure environment as shown in the below example:
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
\bigskip
\begin{verbatim}
\begin{figure}[<placement-specifier>]
\centering
\includegraphics{<eps-file>}
\caption{<figure-caption>}\label{<figure-label>}
\end{figure}
\end{verbatim}
\bigskip
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
\begin{figure}[h]%
\centering
\includegraphics[width=0.9\textwidth]{fig.eps}
\caption{This is a widefig. This is an example of long caption this is an example of long caption this is an example of long caption this is an example of long caption}\label{fig1}
\end{figure}
In case of double column layout, the above format puts figure captions/images to single column width. To get spanned images, we need to provide \verb+\begin{figure*}+ \verb+...+ \verb+\end{figure*}+.
For sample purpose, we have included the width of images in the optional argument of \verb+\includegraphics+ tag. Please ignore this.
\subsection{Algorithms}
\label{sec:algorithms}
Enumerated textual algorithms can be displayed using the
\texttt{algorithm} environment. Within this environment, use
\verb|\caption| to set the caption and you can use an
\texttt{enumerate} or nested \texttt{enumerate} environments.
For example, see Algorithm \ref{alg:gauss}. Note that algorithms
float like figures and tables.
\begin{algorithm}[htbp]
{ %
{\caption{The Gauss-Seidel Algorithm}\label{alg:gauss}}%
{%
\begin{enumerate}
\item For $k=1$ to maximum number of iterations
\begin{enumerate}
\item For $i=1$ to $n$
\begin{enumerate}
\item $x_i^{(k)} =
\frac{b_i - \sum_{j=1}^{i-1}a_{ij}x_j^{(k)}
- \sum_{j=i+1}^{n}a_{ij}x_j^{(k-1)}}{a_{ii}}$
\item If $\|\vec{x}^{(k)}-\vec{x}^{(k-1)} < \epsilon\|$,
where $\epsilon$ is a specified stopping criteria, stop.
\end{enumerate}
\end{enumerate}
\end{enumerate}}
}%
\end{algorithm}
If you'd rather have the same numbering throughout the algorithm
but still want the convenient indentation of nested
\texttt{enumerate} environments. For example, see Algorithm \ref{alg:moore}.
\begin{algorithm}
%
{\caption{Moore's Shortest Path} \label{alg:moore}}%
{%
Given a connected graph $G$, where the length of each edge is 1:
\begin{enumerate}
\item Set the label of vertex $s$ to 0
\item Set $i=0$
\begin{enumerate}
\item \label{step:locate}Locate all unlabelled vertices
adjacent to a vertex labelled $i$ and label them $i+1$
\item If vertex $t$ has been labelled,
\begin{enumerate}
\item[] the shortest path can be found by backtracking, and
the length is given by the label of $t$.
\end{enumerate}
otherwise
\begin{enumerate}
\item[] increment $i$ and return to step 2(a)
\end{enumerate}
\end{enumerate}
\end{enumerate}
}%
\end{algorithm}
\subsection{Program codes and Listings}\label{sec7}
Packages \verb+algorithm+, \verb+algorithmicx+ and \verb+algpseudocode+ are used for setting algorithms in \LaTeX\ using the format:
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
\bigskip
\begin{verbatim}
\begin{algorithm}
\caption{<alg-caption>}\label{<alg-label>}
\begin{algorithmic}[1]
. . .
\end{algorithmic}
\end{algorithm}
\end{verbatim}
\bigskip
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
You may refer above listed package documentations for more details before setting \verb+algorithm+ environment. For program codes, the ``program'' package is required and the command to be used is \verb+\begin{program}+ \verb+...+ \verb+\end{program}+. A fast exponentiation procedure:
\begin{program}
\BEGIN \\ %
\FOR i:=1 \TO 10 \STEP 1 \DO
|expt|(2,i); \\ |newline|() \OD %
\rcomment{Comments will be set flush to the right margin}
\WHERE
\PROC |expt|(x,n) \BODY
z:=1;
\DO \IF n=0 \THEN \EXIT \FI;
\DO \IF |odd|(n) \THEN \EXIT \FI;
\COMMENT{This is a comment statement};
n:=n/2; x:=x*x \OD;
\{ n>0 \};
n:=n-1; z:=z*x \OD;
|print|(z) \ENDPROC
\END
\end{program}
\begin{algorithm}
\caption{Calculate $y = x^n$}\label{algo1}
\begin{algorithmic}[1]
\Require $n \geq 0 \vee x \neq 0$
\Ensure $y = x^n$
\State $y \Leftarrow 1$
\If{$n < 0$}\label{algln2}
\State $X \Leftarrow 1 / x$
\State $N \Leftarrow -n$
\Else
\State $X \Leftarrow x$
\State $N \Leftarrow n$
\EndIf
\While{$N \neq 0$}
\If{$N$ is even}
\State $X \Leftarrow X \times X$
\State $N \Leftarrow N / 2$
\Else[$N$ is odd]
\State $y \Leftarrow y \times X$
\State $N \Leftarrow N - 1$
\EndIf
\EndWhile
\end{algorithmic}
\end{algorithm}
\bigskip
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
Similarly, for \verb+listings+, use the \verb+listings+ package. \verb+\begin{lstlisting}+ \verb+...+ \verb+\end{lstlisting}+ is used to set environments similar to \verb+verbatim+ environment. Refer to the \verb+lstlisting+ package documentation for more details.
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
\bigskip
\begin{minipage}{\hsize}%
\lstset{frame=single,framexleftmargin=-1pt,framexrightmargin=-17pt,framesep=12pt,linewidth=0.98\textwidth,language=pascal}% Set your language (you can change the language for each code-block optionally)
%%% Start your code-block
\begin{lstlisting}
for i:=maxint to 0 do
begin
{ do nothing }
end;
Write('Case insensitive ');
Write('Pascal keywords.');
\end{lstlisting}
\end{minipage}
\subsection{Cross referencing}\label{sec8}
Environments such as figure, table, equation and align can have a label
declared via the \verb+\label{#label}+ command. For figures and table
environments use the \verb+\label{}+ command inside or just
below the \verb+\caption{}+ command. You can then use the
\verb+\ref{#label}+ command to cross-reference them. As an example, consider
the label declared for Figure~\ref{fig1} which is
\verb+\label{fig1}+. To cross-reference it, use the command
\verb+Figure \ref{fig1}+, for which it comes up as
``Figure~\ref{fig1}''.
To reference line numbers in an algorithm, consider the label declared for the line number 2 of Algorithm~\ref{algo1} is \verb+\label{algln2}+. To cross-reference it, use the command \verb+\ref{algln2}+ for which it comes up as line~\ref{algln2} of Algorithm~\ref{algo1}.
\subsection{Details on reference citations}\label{subsec7}
Standard \LaTeX\ permits only numerical citations. To support both numerical and author-year citations this template uses \verb+natbib+ \LaTeX\ package. For style guidance please refer to the template user manual.
Here is an example for \verb+\cite{...}+: \cite{bib1}. Another example for \verb+\citep{...}+: \citep{bib2}. For author-year citation mode, \verb+\cite{...}+ prints Jones et al. (1990) and \verb+\citep{...}+ prints (Jones et al., 1990).
All cited bib entries are printed at the end of this article: \cite{bib3}, \cite{bib4}, \cite{bib5}, \cite{bib6} and \cite{bib7}.
\subsection{Examples for theorem like environments}\label{sec10}
For theorem like environments, we require \verb+amsthm+ package. There are three types of predefined theorem styles exists---\verb+thmstyleone+, \verb+thmstyletwo+ and \verb+thmstylethree+
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
\bigskip
\begin{tabular}{|l|p{19pc}|}
\hline
\verb+thmstyleone+ & Numbered, theorem head in bold font and theorem text in italic style \\\hline
\verb+thmstyletwo+ & Numbered, theorem head in roman font and theorem text in italic style \\\hline
\verb+thmstylethree+ & Numbered, theorem head in bold font and theorem text in roman style \\\hline
\end{tabular}
\bigskip
%%=============================================%%
%% For presentation purpose, we have included %%
%% \bigskip command. please ignore this. %%
%%=============================================%%
For mathematics journals, theorem styles can be included as shown in the following examples:
\begin{theorem}[Theorem subhead]\label{thm1}
Example theorem text. Example theorem text.
\end{theorem}
Sample body text. Sample body text.
\begin{proposition}
Example proposition text. Example proposition text.
\end{proposition}
Sample body text. Sample body text.
\begin{example}
Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem.
\end{example}
Sample body text. Sample body text.
\begin{remark}
Phasellus adipiscing semper elit. Proin fermentum massa
ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem.
\end{remark}
Sample body text. Sample body text.
\begin{definition}[Definition sub head]
Example definition text. Example definition text.
\end{definition}
Additionally a predefined ``proof'' environment is available: \verb+\begin{proof}+ \verb+...+ \verb+\end{proof}+. This prints a ``Proof'' head in italic font style and the ``body text'' in roman font style with an open square at the end of each proof environment.
\begin{proof}
Example for proof text. Example for proof text.
\end{proof}
Sample body text. Sample body text.
\begin{proof}[Proof of Theorem~{\upshape\ref{thm1}}]
Example for proof text. Example for proof text.
\end{proof}
\noindent
For a quote environment, use \verb+\begin{quote}...\end{quote}+
\begin{quote}
Quoted text example. Aliquam porttitor quam a lacus. Praesent vel arcu ut tortor cursus volutpat. In vitae pede quis diam bibendum placerat. Fusce elementum
convallis neque. Sed dolor orci, scelerisque ac, dapibus nec, ultricies ut, mi. Duis nec dui quis leo sagittis commodo.
\end{quote}
Sample body text. Sample body text. (refer Figure~\ref{fig1}). Sample body text. Sample body text. Sample body text (refer Table~\ref{tab3}).
The following theorem-like environments are predefined by
the \texttt{theorem}, \texttt{example},
\texttt{lemma}, \texttt{proposition}, \texttt{remark},
\texttt{corollary}, \texttt{definition}, \texttt{conjecture}
and \texttt{axiom}. You can use the \texttt{proof} environment
to display the proof if need be, as in Theorem \ref{thm:eigenpow}.
\begin{theorem}[Eigenvalue Powers]\label{thm:eigenpow}
If $\lambda$ is an eigenvalue of $\vec{B}$ with eigenvector
$\vec{\xi}$, then $\lambda^n$ is an eigenvalue of $\vec{B}^n$
with eigenvector $\vec{\xi}$.
\begin{proof}
Let $\lambda$ be an eigenvalue of $\vec{B}$ with eigenvector
$\xi$, then
\begin{align*}
\vec{B}\vec{\xi} &= \lambda\vec{\xi}
\intertext{premultiply by $\vec{B}$:}
\vec{B}\vec{B}\vec{\xi} &= \vec{B}\lambda\vec{\xi}\\
\Rightarrow \vec{B}^2\vec{\xi} &= \lambda\vec{B}\vec{\xi}\\
&= \lambda\lambda\vec{\xi}\qquad
\text{since }\vec{B}\vec{\xi}=\lambda\vec{\xi}\\
&= \lambda^2\vec{\xi}
\end{align*}
Therefore true for $n=2$. Now assume true for $n=k$:
\begin{align*}
\vec{B}^k\vec{\xi} &= \lambda^k\vec{\xi}
\intertext{premultiply by $\vec{B}$:}
\vec{B}\vec{B}^k\vec{\xi} &= \vec{B}\lambda^k\vec{\xi}\\
\Rightarrow \vec{B}^{k+1}\vec{\xi} &= \lambda^k\vec{B}\vec{\xi}\\
&= \lambda^k\lambda\vec{\xi}\qquad
\text{since }\vec{B}\vec{\xi}=\lambda\vec{\xi}\\
&= \lambda^{k+1}\vec{\xi}
\end{align*}
Therefore true for $n=k+1$. Therefore, by induction, true for all
$n$.
\end{proof}
\end{theorem}
\begin{remark}[A Sample Remark]\label{rem:sample}
This is a remark.
\end{remark}
\end{document}