506 lines
18 KiB
TeX
506 lines
18 KiB
TeX
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\documentclass[aos]{imsart}
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%% Packages
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\RequirePackage{amsthm,amsmath,amsfonts,amssymb}
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\RequirePackage[numbers,sort&compress]{natbib}
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%\RequirePackage[authoryear]{natbib}%% uncomment this for author-year citations
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\RequirePackage[colorlinks,citecolor=blue,urlcolor=blue]{hyperref}
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\RequirePackage{graphicx}
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\startlocaldefs
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% %%
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%% Uncomment next line to change %%
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%% the type of equation numbering %%
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%% %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\numberwithin{equation}{section}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% %%
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%% For Axiom, Claim, Corollary, Hypothesis, %%
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%% Lemma, Theorem, Proposition %%
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%% use \theoremstyle{plain} %%
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%% %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\theoremstyle{plain}
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\newtheorem{axiom}{Axiom}
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\newtheorem{claim}[axiom]{Claim}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{lemma}[theorem]{Lemma}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% %%
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%% For Assumption, Definition, Example, %%
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%% Notation, Property, Remark, Fact %%
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%% use \theoremstyle{remark} %%
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%% %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\theoremstyle{remark}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem*{example}{Example}
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\newtheorem*{fact}{Fact}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Please put your definitions here: %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\endlocaldefs
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\begin{document}
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\begin{frontmatter}
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\title{A sample article title}
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%\title{A sample article title with some additional note\thanksref{t1}}
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\runtitle{A sample running head title}
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%\thankstext{T1}{A sample additional note to the title.}
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\begin{aug}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Only one address is permitted per author. %%
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%% Only division, organization and e-mail is %%
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%% included in the address. %%
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%% Additional information can be included in %%
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%% the Acknowledgments section if necessary. %%
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%% ORCID can be inserted by command: %%
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%% \orcid{0000-0000-0000-0000} %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\author[A]{\fnms{First}~\snm{Author}\ead[label=e1]{first@somewhere.com}},
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\author[B]{\fnms{Second}~\snm{Author}\ead[label=e2]{second@somewhere.com}\orcid{0000-0000-0000-0000}}
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\and
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\author[B]{\fnms{Third}~\snm{Author}\ead[label=e3]{third@somewhere.com}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Addresses %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\address[A]{Department,
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University or Company Name\printead[presep={,\ }]{e1}}
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\address[B]{Department,
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University or Company Name\printead[presep={,\ }]{e2,e3}}
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\end{aug}
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\begin{abstract}
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The abstract should summarize the contents of the paper.
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It should be clear, descriptive, self-explanatory and not longer
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than 200 words. It should also be suitable for publication in
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abstracting services. Formulas should be used as sparingly as
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possible within the abstract. The abstract should not make
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reference to results, bibliography or formulas in the body
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of the paper---it should be self-contained.
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This is a sample input file. Comparing it with the output it
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generates can show you how to produce a simple document of
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your own.
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\end{abstract}
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\begin{keyword}[class=MSC]
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\kwd[Primary ]{00X00}
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\kwd{00X00}
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\kwd[; secondary ]{00X00}
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\end{keyword}
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\begin{keyword}
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\kwd{First keyword}
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\kwd{second keyword}
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\end{keyword}
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\end{frontmatter}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Please use \tableofcontents for articles %%
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%% with 50 pages and more %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\tableofcontents
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\section{Introduction}
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This template helps you to create a properly formatted \LaTeXe\ manuscript.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% `\ ' is used here because TeX ignores %%
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%% spaces after text commands. %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Prepare your paper in the same style as used in this sample .pdf file.
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Try to avoid excessive use of italics and bold face.
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Please do not use any \LaTeXe\ or \TeX\ commands that affect the layout
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or formatting of your document (i.e., commands like \verb|\textheight|,
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\verb|\textwidth|, etc.).
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\section{Section headings}
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Here are some sub-sections:
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\subsection{A sub-section}
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Regular text.
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\subsubsection{A sub-sub-section}
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Regular text.
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\section{Text}
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\subsection{Lists}
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The following is an example of an \emph{itemized} list,
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two levels deep.
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\begin{itemize}
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\item
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This is the first item of an itemized list. Each item
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in the list is marked with a ``tick.'' The document
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style determines what kind of tick mark is used.
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\item
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This is the second item of the list. It contains another
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list nested inside it.
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\begin{itemize}
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\item This is the first item of an itemized list that
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is nested within the itemized list.
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\item This is the second item of the inner list. \LaTeX\
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allows you to nest lists deeper than you really should.
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\end{itemize}
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This is the rest of the second item of the outer list.
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\item
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This is the third item of the list.
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\end{itemize}
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The following is an example of an \emph{enumerated} list of one level.
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\begin{longlist}
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\item This is the first item of an enumerated list.
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\item This is the second item of an enumerated list.
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\end{longlist}
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The following is an example of an \emph{enumerated} list, two levels deep.
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\begin{longlist}
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\item[1.]
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This is the first item of an enumerated list. Each item
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in the list is marked with a ``tick.'' The document
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style determines what kind of tick mark is used.
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\item[2.]
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This is the second item of the list. It contains another
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list nested inside of it.
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\begin{longlist}
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\item
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This is the first item of an enumerated list that
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is nested within.
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\item
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This is the second item of the inner list. \LaTeX\
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allows you to nest lists deeper than you really should.
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\end{longlist}
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This is the rest of the second item of the outer list.
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\item[3.]
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This is the third item of the list.
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\end{longlist}
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\subsection{Punctuation}
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Dashes come in three sizes: a hyphen, an intra-word dash like ``$U$-statistics'' or ``the time-homogeneous model'';
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a medium dash (also called an ``en-dash'') for number ranges or between two equal entities like ``1--2'' or ``Cauchy--Schwarz inequality'';
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and a punctuation dash (also called an ``em-dash'') in place of a comma, semicolon,
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colon or parentheses---like this.
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Generating an ellipsis \ldots\ with the right spacing
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around the periods requires a special command.
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\subsection{Citation}
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Only include in the reference list entries for which there are text citations,
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and make sure all citations are included in the reference list.
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Simple cite: \cite{r1}.
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Multiple bibliography items cite: \cite{r1,r2,r3,r4}.
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Citing bibliography with object: \cite{r1}, Theorem 1.
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\section{Fonts}
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Please use text fonts in text mode, e.g.:
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\begin{itemize}
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\item[]\textrm{Roman}
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\item[]\textit{Italic}
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\item[]\textbf{Bold}
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\item[]\textsc{Small Caps}
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\item[]\textsf{Sans serif}
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\item[]\texttt{Typewriter}
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\end{itemize}
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Please use mathematical fonts in mathematical mode, e.g.:
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\begin{itemize}
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\item[] $\mathrm{ABCabc123}$
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\item[] $\mathit{ABCabc123}$
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\item[] $\mathbf{ABCabc123}$
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\item[] $\boldsymbol{ABCabc123\alpha\beta\gamma}$
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\item[] $\mathcal{ABC}$
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\item[] $\mathbb{ABC}$
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\item[] $\mathsf{ABCabc123}$
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\item[] $\mathtt{ABCabc123}$
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\item[] $\mathfrak{ABCabc123}$
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\end{itemize}
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Note that \verb|\mathcal, \mathbb| belongs to capital letters-only font typefaces.
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\section{Notes}
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Footnotes\footnote{This is an example of a footnote.}
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pose no problem.\footnote{Note that footnote number is after punctuation.}
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\section{Quotations}
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Text is displayed by indenting it from the left margin. There are short quotations
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\begin{quote}
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This is a short quotation. It consists of a
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single paragraph of text. There is no paragraph
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indentation.
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\end{quote}
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and longer ones.
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\begin{quotation}
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This is a longer quotation. It consists of two paragraphs
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of text. The beginning of each paragraph is indicated
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by an extra indentation.
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This is the second paragraph of the quotation. It is just
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as dull as the first paragraph.
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\end{quotation}
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\section{Environments}
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\subsection{Examples for \emph{\texttt{plain}}-style environments}
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\begin{axiom}\label{ax1}
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This is the body of Axiom \ref{ax1}.
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\end{axiom}
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\begin{proof}
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This is the body of the proof of the axiom above.
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\end{proof}
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\begin{claim}\label{cl1}
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This is the body of Claim \ref{cl1}. Claim \ref{cl1} is numbered after
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Axiom \ref{ax1} because we used \verb|[axiom]| in \verb|\newtheorem|.
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\end{claim}
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\begin{theorem}\label{th1}
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This is the body of Theorem \ref{th1}. Theorem \ref{th1} numbering is
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dependent on section because we used \verb|[section]| after \verb|\newtheorem|.
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\end{theorem}
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\begin{theorem}[Title of the theorem]\label{th2}
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This is the body of Theorem \ref{th2}. Theorem \ref{th2} has additional title.
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\end{theorem}
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\begin{lemma}\label{le1}
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This is the body of Lemma \ref{le1}. Lemma \ref{le1} is numbered after
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Theorem \ref{th2} because we used \verb|[theorem]| in \verb|\newtheorem|.
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\end{lemma}
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\begin{proof}[Proof of Lemma \ref{le1}]
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This is the body of the proof of Lemma \ref{le1}.
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\end{proof}
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\subsection{Examples for \emph{\texttt{remark}}-style environments}
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\begin{definition}\label{de1}
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This is the body of Definition \ref{de1}. Definition \ref{de1} is numbered after
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Lemma \ref{le1} because we used \verb|[theorem]| in \verb|\newtheorem|.
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\end{definition}
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\begin{example}
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This is the body of the example. Example is unnumbered because we used \verb|\newtheorem*|
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instead of \verb|\newtheorem|.
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\end{example}
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\begin{fact}
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This is the body of the fact. Fact is unnumbered because we used \verb|\newtheorem*|
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instead of \verb|\newtheorem|.
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\end{fact}
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\section{Tables and figures}
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Cross-references to labeled tables: As you can see in Table~\ref{sphericcase}
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and also in Table~\ref{parset}.
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\begin{table*}
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\caption{The spherical case ($I_1=0$, $I_2=0$)}
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\label{sphericcase}
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\begin{tabular}{@{}lrrrrc@{}}
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\hline
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Equil. \\
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points & \multicolumn{1}{c}{$x$}
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& \multicolumn{1}{c}{$y$} & \multicolumn{1}{c}{$z$}
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& \multicolumn{1}{c}{$C$} & S \\
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\hline
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$L_1$ & $-$2.485252241 & 0.000000000 & 0.017100631 & 8.230711648 & U \\
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$L_2$ & 0.000000000 & 0.000000000 & 3.068883732 & 0.000000000 & S \\
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$L_3$ & 0.009869059 & 0.000000000 & 4.756386544 & $-$0.000057922 & U \\
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$L_4$ & 0.210589855 & 0.000000000 & $-$0.007021459 & 9.440510897 & U \\
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$L_5$ & 0.455926604 & 0.000000000 & $-$0.212446624 & 7.586126667 & U \\
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$L_6$ & 0.667031314 & 0.000000000 & 0.529879957 & 3.497660052 & U \\
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$L_7$ & 2.164386674 & 0.000000000 & $-$0.169308438 & 6.866562449 & U \\
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$L_8$ & 0.560414471 & 0.421735658 & $-$0.093667445 & 9.241525367 & U \\
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$L_9$ & 0.560414471 & $-$0.421735658 & $-$0.093667445 & 9.241525367 & U \\
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$L_{10}$ & 1.472523232 & 1.393484549 & $-$0.083801333 & 6.733436505 & U \\
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$L_{11}$ & 1.472523232 & $-$1.393484549 & $-$0.083801333 & 6.733436505 & U \\
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\hline
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\end{tabular}
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\end{table*}
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\begin{table}
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\caption{Sample posterior estimates for each model}
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\label{parset}
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%
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\begin{tabular}{@{}lcrcrrr@{}}
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\hline
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&& & &\multicolumn{3}{c}{Quantile} \\
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\cline{5-7}
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Model &Parameter &
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\multicolumn{1}{c}{Mean} &
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Std. dev.&
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\multicolumn{1}{c}{2.5\%} &
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\multicolumn{1}{c}{50\%}&
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\multicolumn{1}{c@{}}{97.5\%} \\
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\hline
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{Model 0} & $\beta_0$ & $-$12.29 & 2.29 & $-$18.04 & $-$11.99 & $-$8.56 \\
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& $\beta_1$ & 0.10 & 0.07 & $-$0.05 & 0.10 & 0.26 \\
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& $\beta_2$ & 0.01 & 0.09 & $-$0.22 & 0.02 & 0.16 \\[6pt]
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{Model 1} & $\beta_0$ & $-$4.58 & 3.04 & $-$11.00 & $-$4.44 & 1.06 \\
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& $\beta_1$ & 0.79 & 0.21 & 0.38 & 0.78 & 1.20 \\
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& $\beta_2$ & $-$0.28 & 0.10 & $-$0.48 & $-$0.28 & $-$0.07 \\[6pt]
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{Model 2} & $\beta_0$ & $-$11.85 & 2.24 & $-$17.34 & $-$11.60 & $-$7.85 \\
|
||
|
|
& $\beta_1$ & 0.73 & 0.21 & 0.32 & 0.73 & 1.16 \\
|
||
|
|
& $\beta_2$ & $-$0.60 & 0.14 & $-$0.88 & $-$0.60 & $-$0.34 \\
|
||
|
|
& $\beta_3$ & 0.22 & 0.17 & $-$0.10 & 0.22 & 0.55 \\
|
||
|
|
\hline
|
||
|
|
\end{tabular}
|
||
|
|
%
|
||
|
|
\end{table}
|
||
|
|
|
||
|
|
\begin{figure}
|
||
|
|
\includegraphics{figure1}
|
||
|
|
\caption{Pathway of the penicillin G biosynthesis.}
|
||
|
|
\label{penG}
|
||
|
|
\end{figure}
|
||
|
|
|
||
|
|
Sample of cross-reference to figure.
|
||
|
|
Figure~\ref{penG} shows that it is not easy to get something on paper.
|
||
|
|
|
||
|
|
\section{Equations and the like}
|
||
|
|
|
||
|
|
Two equations:
|
||
|
|
\begin{equation}
|
||
|
|
C_{s} = K_{M} \frac{\mu/\mu_{x}}{1-\mu/\mu_{x}} \label{ccs}
|
||
|
|
\end{equation}
|
||
|
|
and
|
||
|
|
\begin{equation}
|
||
|
|
G = \frac{P_{\mathrm{opt}} - P_{\mathrm{ref}}}{P_{\mathrm{ref}}} 100(\%).
|
||
|
|
\end{equation}
|
||
|
|
|
||
|
|
Equation arrays:
|
||
|
|
\begin{eqnarray}
|
||
|
|
\frac{dS}{dt} & = & - \sigma X + s_{F} F,\\
|
||
|
|
\frac{dX}{dt} & = & \mu X,\\
|
||
|
|
\frac{dP}{dt} & = & \pi X - k_{h} P,\\
|
||
|
|
\frac{dV}{dt} & = & F.
|
||
|
|
\end{eqnarray}
|
||
|
|
One long equation:
|
||
|
|
\begin{eqnarray}
|
||
|
|
\mu_{\text{normal}} & = & \mu_{x} \frac{C_{s}}{K_{x}C_{x}+C_{s}} \nonumber\\
|
||
|
|
& = & \mu_{\text{normal}} - Y_{x/s}\bigl(1-H(C_{s})\bigr)(m_{s}+\pi /Y_{p/s})\\
|
||
|
|
& = & \mu_{\text{normal}}/Y_{x/s}+ H(C_{s}) (m_{s}+ \pi /Y_{p/s}).\nonumber
|
||
|
|
\end{eqnarray}
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
%% Example with single Appendix: %%
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
\begin{appendix}
|
||
|
|
\section*{Title}\label{appn} %% if no title is needed, leave empty \section*{}.
|
||
|
|
Appendices should be provided in \verb|{appendix}| environment,
|
||
|
|
before Acknowledgements.
|
||
|
|
|
||
|
|
If there is only one appendix,
|
||
|
|
then please refer to it in text as \ldots\ in the \hyperref[appn]{Appendix}.
|
||
|
|
\end{appendix}
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
%% Example with multiple Appendixes: %%
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
\begin{appendix}
|
||
|
|
\section{Title of the first appendix}\label{appA}
|
||
|
|
If there are more than one appendix, then please refer to it
|
||
|
|
as \ldots\ in Appendix \ref{appA}, Appendix \ref{appB}, etc.
|
||
|
|
|
||
|
|
\section{Title of the second appendix}\label{appB}
|
||
|
|
\subsection{First subsection of Appendix \protect\ref{appB}}
|
||
|
|
|
||
|
|
Use the standard \LaTeX\ commands for headings in \verb|{appendix}|.
|
||
|
|
Headings and other objects will be numbered automatically.
|
||
|
|
\begin{equation}
|
||
|
|
\mathcal{P}=(j_{k,1},j_{k,2},\dots,j_{k,m(k)}). \label{path}
|
||
|
|
\end{equation}
|
||
|
|
|
||
|
|
Sample of cross-reference to the formula (\ref{path}) in Appendix \ref{appB}.
|
||
|
|
\end{appendix}
|
||
|
|
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
%% Support information, if any, %%
|
||
|
|
%% should be provided in the %%
|
||
|
|
%% Acknowledgements section. %%
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
\begin{acks}[Acknowledgments]
|
||
|
|
The authors would like to thank the anonymous referees, an Associate
|
||
|
|
Editor and the Editor for their constructive comments that improved the
|
||
|
|
quality of this paper.
|
||
|
|
\end{acks}
|
||
|
|
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
%% Funding information, if any, %%
|
||
|
|
%% should be provided in the %%
|
||
|
|
%% funding section. %%
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
\begin{funding}
|
||
|
|
The first author was supported by NSF Grant DMS-??-??????.
|
||
|
|
|
||
|
|
The second author was supported in part by NIH Grant ???????????.
|
||
|
|
\end{funding}
|
||
|
|
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
%% Supplementary Material, including data %%
|
||
|
|
%% sets and code, should be provided in %%
|
||
|
|
%% {supplement} environment with title %%
|
||
|
|
%% and short description. It cannot be %%
|
||
|
|
%% available exclusively as external link. %%
|
||
|
|
%% All Supplementary Material must be %%
|
||
|
|
%% available to the reader on Project %%
|
||
|
|
%% Euclid with the published article. %%
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
\begin{supplement}
|
||
|
|
\stitle{Title of Supplement A}
|
||
|
|
\sdescription{Short description of Supplement A.}
|
||
|
|
\end{supplement}
|
||
|
|
\begin{supplement}
|
||
|
|
\stitle{Title of Supplement B}
|
||
|
|
\sdescription{Short description of Supplement B.}
|
||
|
|
\end{supplement}
|
||
|
|
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
%% The Bibliography %%
|
||
|
|
%% %%
|
||
|
|
%% imsart-???.bst will be used to %%
|
||
|
|
%% create a .BBL file for submission. %%
|
||
|
|
%% %%
|
||
|
|
%% Note that the displayed Bibliography will not %%
|
||
|
|
%% necessarily be rendered by Latex exactly as specified %%
|
||
|
|
%% in the online Instructions for Authors. %%
|
||
|
|
%% %%
|
||
|
|
%% MR numbers will be added by VTeX. %%
|
||
|
|
%% %%
|
||
|
|
%% Use \cite{...} to cite references in text. %%
|
||
|
|
%% %%
|
||
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
|
||
|
|
%% if your bibliography is in bibtex format, uncomment commands:
|
||
|
|
%\bibliographystyle{imsart-number} % Style BST file (imsart-number.bst or imsart-nameyear.bst)
|
||
|
|
%\bibliography{bibliography} % Bibliography file (usually '*.bib')
|
||
|
|
|
||
|
|
%% or include bibliography directly:
|
||
|
|
\begin{thebibliography}{4}
|
||
|
|
%%
|
||
|
|
\bibitem{r1}
|
||
|
|
\textsc{Billingsley, P.} (1999). \textit{Convergence of
|
||
|
|
Probability Measures}, 2nd ed.
|
||
|
|
Wiley, New York.
|
||
|
|
|
||
|
|
\bibitem{r2}
|
||
|
|
\textsc{Bourbaki, N.} (1966). \textit{General Topology} \textbf{1}.
|
||
|
|
Addison--Wesley, Reading, MA.
|
||
|
|
|
||
|
|
\bibitem{r3}
|
||
|
|
\textsc{Ethier, S. N.} and \textsc{Kurtz, T. G.} (1985).
|
||
|
|
\textit{Markov Processes: Characterization and Convergence}.
|
||
|
|
Wiley, New York.
|
||
|
|
|
||
|
|
\bibitem{r4}
|
||
|
|
\textsc{Prokhorov, Yu.} (1956).
|
||
|
|
Convergence of random processes and limit theorems in probability
|
||
|
|
theory. \textit{Theory Probab. Appl.}
|
||
|
|
\textbf{1} 157--214.
|
||
|
|
\end{thebibliography}
|
||
|
|
|
||
|
|
\end{document}
|