diff --git a/papers/variational_smoother/changelog.txt b/papers/variational_smoother/changelog.txt
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+Change Log
+-----------
+
+* elsarticle.dtx
+
+1. Frontmatter: Overfull \hbox has occurred while \output is active
+
+https://tex.stackexchange.com/questions/514218/elsarticle-frontmatter-overfull-hbox-has-occurred-while-output-is-active/515199
+
+2. Footnotes: Updated to use non Arabic footnote numbers. 
+
+https://tex.stackexchange.com/questions/669879/elsarticle-changing-symbol-used-in-fnref
+
+3. Author-affiliation:  Updated for author-wise affiliation coding.
+Last author affiliation repeating for all authors problem is fixed.
+
+4. Accent characters in address:  A bug fix. Accented characters in
+organisation field showed error. Hence loaded fontenc package.
+
+5. Updated for accent problems in TeXLive 2022. Font encoding T1 used
+by default
+
+6. Removed extra space appearing after 'Appendix' label
+
+7. updated for listing author affiliation below author names if
+\affiliation command is used immediately after \author (To match
+behaviour of \address command)
+
+*  elsarticle-template-harv.tex, \
+   elsarticle-template-num-names.tex, \
+   elsarticle-template-num.tex
+
+1. Added examples for figures, tables and equations
+------------------------------------------------------------------------
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+%% 
+%% Copyright 2007-2024 Elsevier Ltd
+%% 
+%% This file is part of the 'Elsarticle Bundle'.
+%% ---------------------------------------------
+%% 
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.3 of this license or (at your option) any
+%% later version.  The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%% 
+%% The list of all files belonging to the 'Elsarticle Bundle' is
+%% given in the file `manifest.txt'.
+%%
+%% $Id: elsdoc.tex 261 2024-04-09 06:37:35Z rishi $
+%%
+\documentclass[a4paper,12pt]{article}
+
+\usepackage[xcolor,qtwo]{rvdtx}
+\usepackage{multicol}
+\usepackage{color}
+\usepackage{xspace}
+\usepackage{pdfwidgets}
+\usepackage{enumerate}
+
+\def\ttdefault{cmtt}
+
+\headsep4pc
+
+\makeatletter
+\def\bs{\expandafter\@gobble\string\\}
+\def\lb{\expandafter\@gobble\string\{}
+\def\rb{\expandafter\@gobble\string\}}
+\def\@pdfauthor{C.V.Radhakrishnan}
+\def\@pdftitle{elsarticle.cls -- A documentation}
+\def\@pdfsubject{Document formatting with elsarticle.cls}
+\def\@pdfkeywords{LaTeX, Elsevier Ltd, document class}
+\def\file#1{\textsf{#1}\xspace}
+
+%\def\LastPage{19}
+
+\DeclareRobustCommand{\LaTeX}{L\kern-.26em%
+        {\sbox\z@ T%
+         \vbox to\ht\z@{\hbox{\check@mathfonts
+           \fontsize\sf@size\z@
+           \math@fontsfalse\selectfont
+          A\,}%
+         \vss}%
+        }%
+     \kern-.15em%
+    \TeX}
+\makeatother
+
+\def\figurename{Clip}
+
+\setcounter{tocdepth}{1}
+
+\begin{document}
+
+\def\testa{This is a specimen document. }
+\def\testc{\testa\testa\testa\testa}
+\def\testb{\testc\testc\testc\testc\testc}
+\long\def\test{\testb\par\testb\par\testb\par}
+
+\pinclude{\copy\contbox\printSq{\LastPage}}
+
+\title{elsarticle.cls -- A better way to format your document}
+
+\author{Elsevier Ltd}
+\contact{elsarticle@stmdocs.in}
+
+\version{3.4}
+\date{\today}
+\maketitle
+
+\section{Introduction}
+
+\file{elsarticle.cls} is a thoroughly re-written document class
+for formatting \LaTeX{} submissions to Elsevier journals.
+The class uses the environments and commands defined in \LaTeX{} kernel
+without any change in the signature so that clashes with other
+contributed \LaTeX{} packages such as \file{hyperref.sty},
+\file{preview-latex.sty}, etc., will be minimal.
+\file{elsarticle.cls} is primarily built upon the default
+\file{article.cls}.  This class depends on the following packages
+for its proper functioning:
+
+\begin{enumerate}
+\item \file{natbib.sty} for citation processing;
+\item \file{geometry.sty} for margin settings;
+\item \file{fleqn.clo} for left aligned equations;
+\item \file{graphicx.sty} for graphics inclusion;
+\item \file{txfonts.sty} optional font package, if the document is to
+  be formatted with Times and compatible math fonts;
+\item \file{hyperref.sty} optional packages if hyperlinking is
+  required in the document;
+%*%
+\item \file{endfloat.sty} optional packages if floats to be placed at
+ end of the PDF.
+\end{enumerate}
+
+All the above packages (except some optional packages) are part of any
+standard \LaTeX{} installation. Therefore, the users need not be
+bothered about downloading any extra packages.  Furthermore, users are
+free to make use of \textsc{ams} math packages such as
+\file{amsmath.sty}, \file{amsthm.sty}, \file{amssymb.sty},
+\file{amsfonts.sty}, etc., if they want to.  All these packages work in
+tandem with \file{elsarticle.cls} without any problems.
+
+\section{Major Differences}
+
+Following are the major differences between \file{elsarticle.cls}
+and its predecessor package, \file{elsart.cls}:
+
+\begin{enumerate}[\textbullet]
+\item \file{elsarticle.cls} is built upon \file{article.cls}
+while \file{elsart.cls} is not. \file{elsart.cls} redefines
+many of the commands in the \LaTeX{} classes/kernel, which can
+possibly cause surprising clashes with other contributed
+\LaTeX{} packages;
+
+\item provides preprint document formatting by default, and
+optionally formats the document as per the final
+style of models $1+$, $3+$ and $5+$ of Elsevier journals;
+
+\item some easier ways for formatting \verb+list+ and
+\verb+theorem+ environments are provided while people can still
+use \file{amsthm.sty} package;
+
+\item \file{natbib.sty} is the main citation processing package
+  which can comprehensively handle all kinds of citations and
+works perfectly with \file{hyperref.sty} in combination with
+\file{hypernat.sty};
+
+\item long title pages are processed correctly in preprint and
+  final formats.
+
+\end{enumerate}
+
+\section{Installation}
+
+The package is available at author resources page at Elsevier
+(\url{http://www.elsevier.com/locate/latex}).
+It can also be found in Comprehensive
+\TeX{} Archive Network (\textsc{ctan}), 
+\url{https://ctan.org/pkg/elsarticle}.
+
+Please download the \file{elsarticle.dtx} which is a composite
+class with documentation and \file{elsarticle.ins} which is the
+\LaTeX{} installer file. When we compile the
+\file{elsarticle.ins} with \LaTeX{} it provides the class file,
+\file{elsarticle.cls} by
+stripping off all the documentation from the \verb+*.dtx+ file.
+The class may be moved or copied to a place, usually,
+\verb+$TEXMF/tex/latex/+ %$%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\verb+elsevier/+, 
+or a folder which will be read                   
+by \LaTeX{} during document compilation.  The \TeX{} file
+database needs updation after moving/copying class file.  Usually,
+we use commands like \verb+mktexlsr+ or \verb+texhash+ depending
+upon the distribution and operating system.
+
+
+\section{Usage}\label{sec:usage}
+The class should be loaded with the command:
+
+\begin{vquote}
+ \documentclass[<options>]{elsarticle}
+\end{vquote}
+
+\noindent where the \verb+options+ can be the following:
+
+
+\begin{description}
+
+\item [{\tt\color{verbcolor} preprint}]  default option which format the
+  document for submission to Elsevier journals.
+
+\item [{\tt\color{verbcolor} review}]  similar to the \verb+preprint+
+option, but increases the baselineskip to facilitate easier review
+process.
+
+\item [{\tt\color{verbcolor} 1p}]  formats the article to the look and
+feel of the final format of model 1+ journals. This is always single
+column style.
+
+\item [{\tt\color{verbcolor} 3p}] formats the article to the look and
+feel of the final format of model 3+ journals. If the journal is a two
+column model, use \verb+twocolumn+ option in combination.
+
+\item [{\tt\color{verbcolor} 5p}] formats for model 5+ journals. This
+is always of two column style.
+
+\item [{\tt\color{verbcolor} authoryear}] author-year citation style of
+\file{natbib.sty}. If you want to add extra options of
+\file{natbib.sty}, you may use the options as comma delimited strings
+as arguments to \verb+\biboptions+ command. An example would be:
+\end{description}
+
+\begin{vquote}
+ \biboptions{longnamesfirst,angle,semicolon}
+\end{vquote}
+
+\begin{description}
+\item [{\tt\color{verbcolor} number}] numbered citation style. Extra options
+  can be loaded with\linebreak \verb+\biboptions+ command.
+
+\item [{\tt\color{verbcolor} sort\&compress}] sorts and compresses the
+numbered citations. For example, citation [1,2,3] will become [1--3].
+
+\item [{\tt\color{verbcolor} longtitle}] if front matter is unusually long, use
+  this option to split the title page across pages with the correct
+placement of title and author footnotes in the first page.
+
+\item [{\tt\color{verbcolor} times}] loads \file{txfonts.sty}, if
+available in the system to use Times and compatible math fonts.
+
+%*%
+\item [{\tt\color{verbcolor} reversenotenum}] Use alphabets as
+author--affiliation linking labels and use numbers for author
+footnotes. By default, numbers will be used as author--affiliation
+linking labels and alphabets for author footnotes. 
+
+\item [{\tt\color{verbcolor} lefttitle}] To move title and
+author/affiliation block to flushleft. \verb+centertitle+ is the
+default option which produces center alignment.
+
+\item [{\tt\color{verbcolor} endfloat}] To place all floats at the end
+of the document.
+
+\item [{\tt\color{verbcolor} nonatbib}] To unload natbib.sty.
+%*%
+
+\item [{\tt\color{verbcolor} doubleblind}] To hide author name, 
+affiliation, email address etc. for double blind refereeing purpose.
+%*%
+
+\item[] All options of \file{article.cls} can be used with this
+  document class.
+
+\item[] The default options loaded are \verb+a4paper+, \verb+10pt+,
+  \verb+oneside+, \verb+onecolumn+ and \verb+preprint+.
+
+\end{description}
+
+\section{Frontmatter}
+
+There are two types of frontmatter coding:
+\begin{enumerate}[(1)]
+\item each author is
+connected to an affiliation with a footnote marker; hence all
+authors are grouped together and affiliations follow;
+%\pagebreak
+\item authors of same affiliations are grouped together and the
+relevant affiliation follows this group. 
+\end{enumerate}
+
+An example of coding the first type is provided below.
+
+\begin{vquote}
+ \title{This is a specimen title\tnoteref{t1,t2}}
+ \tnotetext[t1]{This document is the results of the research
+    project funded by the National Science Foundation.}
+ \tnotetext[t2]{The second title footnote which is a longer 
+    text matter to fill through the whole text width and 
+    overflow into another line in the footnotes area of the 
+    first page.}
+\end{vquote}
+
+\begin{vquote}
+\author[1]{Jos Migchielsen\corref{cor1}%
+  \fnref{fn1}}
+\ead{J.Migchielsen@elsevier.com}
+
+\author[2]{CV Radhakrishnan\fnref{fn2}}
+\ead{cvr@sayahna.org}
+
+\author[3]{CV Rajagopal\fnref{fn1,fn3}}
+\ead[url]{www.stmdocs.in}
+
+ \cortext[cor1]{Corresponding author}
+ \fntext[fn1]{This is the first author footnote.}
+ \fntext[fn2]{Another author footnote, this is a very long 
+   footnote and it should be a really long footnote. But this 
+   footnote is not yet sufficiently long enough to make two 
+   lines of footnote text.}
+ \fntext[fn3]{Yet another author footnote.}
+\end{vquote}
+
+\begin{vquote}
+
+ \affiliation[1]{organization={Elsevier B.V.}, 
+                 addressline={Radarweg 29},
+                 postcode={1043 NX}, 
+                 city={Amsterdam}, 
+                 country={The Netherlands}}
+
+ \affiliation[2]{organization={Sayahna Foundation},
+                 addressline={JWRA 34, Jagathy}, 
+                 city={Trivandrum},
+                 postcode={695014}, 
+                 country={India}}
+
+
+ \affiliation[3]{organization={STM Document Engineering 
+                               Pvt Ltd.},
+                 addressline={Mepukada, Malayinkil}, 
+                 city={Trivandrum}
+                 postcode={695571}, 
+                 country={India}}
+\end{vquote}
+
+The output of the above \TeX{} source is given in Clips~\ref{clip1} and
+\ref{clip2}. The header portion or title area is given in
+Clip~\ref{clip1} and the footer area is given in Clip~\ref{clip2}.
+
+\vspace*{1pc}
+
+\def\rulecolor{blue!70}
+\src{Header of the title page.}
+\includeclip{1}{130 612 477 707}{1psingleauthorgroup.pdf}%%{elstest-1p.pdf}%single author group
+\def\rulecolor{orange}
+
+\pagebreak
+
+\def\rulecolor{blue!70}
+\src{Footer of the title page.}
+\includeclip{1}{93 135 499 255}{1pseperateaug.pdf}%%{elstest-1p.pdf}%single author group
+\def\rulecolor{orange}
+
+Most of the commands such as \verb+\title+, \verb+\author+,
+\verb+\affiliation+ are self explanatory.  Various components are
+linked to each other by a label--reference mechanism; for
+instance, title footnote is linked to the title with a footnote
+mark generated by referring to the \verb+\label+ string of
+the \verb=\tnotetext=.  We have used similar commands
+such as \verb=\tnoteref= (to link title note to title);
+\verb=\corref= (to link corresponding author text to
+corresponding author); \verb=\fnref= (to link footnote text to
+the relevant author names).  \TeX{} needs two compilations to
+resolve the footnote marks in the preamble part.  
+Given below are the syntax of various note marks and note texts.
+
+
+\begin{vquote}
+  \tnoteref{<label(s)>}
+  \corref{<label(s)>}
+  \fnref{<label(s)>}
+  \tnotetext[<label>]{<title note text>}
+  \cortext[<label>]{<corresponding author note text>}
+  \fntext[<label>]{<author footnote text>}
+\end{vquote}
+
+\noindent where \verb=<label(s)>= can be either one or more comma
+delimited label strings. The optional arguments to the
+\verb=\author= command holds the ref label(s) of the address(es)
+to which the author is affiliated while each \verb=\affiliation=
+command can have an optional argument of a label. In the same
+manner, \verb=\tnotetext=, \verb=\fntext=, \verb=\cortext= will
+have optional arguments as their respective labels and note text
+as their mandatory argument.
+
+The following example code provides the markup of the second type
+of author-affiliation.
+
+\begin{vquote}
+\author{Jos Migchielsen\corref{cor1}%
+  \fnref{fn1}}
+\ead{J.Migchielsen@elsevier.com}
+ \affiliation[1]{organization={Elsevier B.V.}, 
+                 addressline={Radarweg 29},
+                 postcode={1043 NX}, 
+                 city={Amsterdam}, 
+                 country={The Netherlands}}
+
+\author{CV Radhakrishnan\fnref{fn2}}
+\ead{cvr@sayahna.org}
+ \affiliation[2]{organization={Sayahna Foundation},
+                 addressline={JWRA 34, Jagathy}, 
+                 city={Trivandrum}
+                 postcode={695014}, 
+                 country={India}}
+
+\author{CV Rajagopal\fnref{fn1,fn3}}
+\ead[url]{www.stmdocs.in}
+ \affiliation[3]{organization={STM Document Engineering 
+                               Pvt Ltd.},
+                 addressline={Mepukada, Malayinkil}, 
+                 city={Trivandrum}
+                 postcode={695571}, 
+                 country={India}}
+\end{vquote}
+
+\vspace*{-.5pc}
+
+\begin{vquote}
+\cortext[cor1]{Corresponding author}
+\fntext[fn1]{This is the first author footnote.}
+\fntext[fn2]{Another author footnote, this is a very long 
+  footnote and it should be a really long footnote. But this 
+  footnote is not yet sufficiently long enough to make two lines 
+  of footnote text.}
+\end{vquote}
+
+The output of the above \TeX{} source is given in Clip~\ref{clip3}.
+
+\def\rulecolor{blue!70}
+\src{Header of the title page..}
+\includeclip{1}{119 563 468 709}{1pseperateaug.pdf}%%{elstest-1p.pdf}%seperate author groups
+\def\rulecolor{orange}
+%\pagebreak
+
+Clip~\ref{clip4} shows the output after giving \verb+doubleblind+ class option. 
+
+\def\rulecolor{blue!70}
+\src{Double blind article}
+\includeclip{1}{124 567 477 670}{elstest-1pdoubleblind.pdf}%%{elstest-1p.pdf}%single author group%%doubleblind
+\def\rulecolor{orange}
+
+\vspace*{-.5pc}
+The frontmatter part has further environments such as abstracts and
+keywords.  These can be marked up in the following manner:
+
+\begin{vquote}
+ \begin{abstract}
+  In this work we demonstrate the formation of a new type of 
+  polariton on the interface between a ....
+ \end{abstract}
+\end{vquote} 
+
+\vspace*{-.5pc}
+\begin{vquote}
+ \begin{keyword}
+  quadruple exiton \sep polariton \sep WGM
+ \end{keyword}
+\end{vquote}
+
+\noindent Each keyword shall be separated by a \verb+\sep+ command.
+\textsc{msc} classifications shall be provided in 
+the keyword environment with the commands
+\verb+\MSC+. \verb+\MSC+ accepts an optional
+argument to accommodate future revisions.
+eg., \verb=\MSC[2008]=. The default is 2000.\looseness=-1
+
+\subsection{New page}
+Sometimes you may need to give a page-break and start a new page after
+title, author or abstract. Following commands can be used for this
+purpose.
+
+\begin{vquote}
+  \newpageafter{title}
+  \newpageafter{author}
+  \newpageafter{abstract}
+\end{vquote}
+
+
+\begin{itemize}
+\leftskip-2pc
+\item [] {\tt\color{verbcolor} \verb+\newpageafter{title}+} typeset the title alone on one page.
+
+\item [] {\tt\color{verbcolor} \verb+\newpageafter{author}+}  typeset the title
+and author details on one page.
+
+\item [] {\tt\color{verbcolor} \verb+\newpageafter{abstract}+}
+typeset the title,
+author details and abstract \& keywords one one page.
+
+\end{itemize}
+
+\section{Floats}
+{Figures} may be included using the command, \verb+\includegraphics+ in
+combination with or without its several options to further control
+graphic. \verb+\includegraphics+ is provided by \file{graphic[s,x].sty}
+which is part of any standard \LaTeX{} distribution.
+\file{graphicx.sty} is loaded by default. \LaTeX{} accepts figures in
+the postscript format while pdf\LaTeX{} accepts \file{*.pdf},
+\file{*.mps} (metapost), \file{*.jpg} and \file{*.png} formats. 
+pdf\LaTeX{} does not accept graphic files in the postscript format. 
+
+The \verb+table+ environment is handy for marking up tabular
+material. If users want to use \file{multirow.sty},
+\file{array.sty}, etc., to fine control/enhance the tables, they
+are welcome to load any package of their choice and
+\file{elsarticle.cls} will work in combination with all loaded
+packages.
+
+\section[Theorem and ...]{Theorem and theorem like environments}
+
+\file{elsarticle.cls} provides a few shortcuts to format theorems and
+theorem-like environments with ease. In all commands the options that
+are used with the \verb+\newtheorem+ command will work exactly in the same
+manner. \file{elsarticle.cls} provides three commands to format theorem or
+theorem-like environments: 
+
+\begin{vquote}
+ \newtheorem{thm}{Theorem}
+ \newtheorem{lem}[thm]{Lemma}
+ \newdefinition{rmk}{Remark}
+ \newproof{pf}{Proof}
+ \newproof{pot}{Proof of Theorem \ref{thm2}}
+\end{vquote}
+
+The \verb+\newtheorem+ command formats a
+theorem in \LaTeX's default style with italicized font, bold font
+for theorem heading and theorem number at the right hand side of the
+theorem heading.  It also optionally accepts an argument which
+will be printed as an extra heading in parentheses. 
+
+\begin{vquote}
+  \begin{thm} 
+   For system (8), consensus can be achieved with 
+   $\|T_{\omega z}$
+   ...
+     \begin{eqnarray}\label{10}
+     ....
+     \end{eqnarray}
+  \end{thm}
+\end{vquote}  
+
+Clip~\ref{clip5} will show you how some text enclosed between the
+above code\goodbreak \noindent looks like:
+
+\vspace*{6pt}
+\def\rulecolor{blue!70}
+\src{{\ttfamily\color{verbcolor}\bs newtheorem}}
+\includeclip{2}{1 1 453 120}{jfigs.pdf}
+\def\rulecolor{orange}
+
+The \verb+\newdefinition+ command is the same in
+all respects as its\linebreak \verb+\newtheorem+ counterpart except that
+the font shape is roman instead of italic.  Both
+\verb+\newdefinition+ and \verb+\newtheorem+ commands
+automatically define counters for the environments defined.
+
+\vspace*{6pt}
+\def\rulecolor{blue!70}
+\src{{\ttfamily\color{verbcolor}\bs newdefinition}}
+\includeclip{1}{1 1 453 105}{jfigs.pdf}
+\def\rulecolor{orange}
+
+The \verb+\newproof+ command defines proof environments with
+upright font shape.  No counters are defined. 
+
+\vspace*{6pt}
+\def\rulecolor{blue!70}
+\src{{\ttfamily\color{verbcolor}\bs newproof}}
+\includeclip{3}{1 1 453 65}{jfigs.pdf}
+\def\rulecolor{orange}
+
+Users can also make use of \verb+amsthm.sty+ which will override
+all the default definitions described above.
+
+\section[Enumerated ...]{Enumerated and Itemized Lists}
+\file{elsarticle.cls} provides an extended list processing macros
+which makes the usage a bit more user friendly than the default
+\LaTeX{} list macros.   With an optional argument to the
+\verb+\begin{enumerate}+ command, you can change the list counter
+type and its attributes.
+
+\begin{vquote}
+ \begin{enumerate}[1.]
+ \item The enumerate environment starts with an optional
+   argument `1.', so that the item counter will be suffixed
+   by a period.
+ \item You can use `a)' for alphabetical counter and '(i)' for
+   roman counter.
+  \begin{enumerate}[a)]
+    \item Another level of list with alphabetical counter.
+    \item One more item before we start another.
+\end{vquote}
+
+\def\rulecolor{blue!70}
+\src{List -- Enumerate}
+\includeclip{4}{1 1 453 185}{jfigs.pdf}
+\def\rulecolor{orange}
+
+Further, the enhanced list environment allows one to prefix a
+string like `step' to all the item numbers.  
+
+\begin{vquote}
+ \begin{enumerate}[Step 1.]
+  \item This is the first step of the example list.
+  \item Obviously this is the second step.
+  \item The final step to wind up this example.
+ \end{enumerate}
+\end{vquote}
+
+\def\rulecolor{blue!70}
+\src{List -- enhanced}
+\includeclip{5}{1 1 313 83}{jfigs.pdf}
+\def\rulecolor{orange}
+
+
+\section{Cross-references}
+In electronic publications, articles may be internally
+hyperlinked. Hyperlinks are generated from proper
+cross-references in the article.  For example, the words
+\textcolor{black!80}{Fig.~1} will never be more than simple text,
+whereas the proper cross-reference \verb+\ref{tiger}+ may be
+turned into a hyperlink to the figure itself:
+\textcolor{blue}{Fig.~1}.  In the same way,
+the words \textcolor{blue}{Ref.~[1]} will fail to turn into a
+hyperlink; the proper cross-reference is \verb+\cite{Knuth96}+.
+Cross-referencing is possible in \LaTeX{} for sections,
+subsections, formulae, figures, tables, and literature
+references.
+
+\section[Mathematical ...]{Mathematical symbols and formulae}
+
+Many physical/mathematical sciences authors require more
+mathematical symbols than the few that are provided in standard
+\LaTeX. A useful package for additional symbols is the
+\file{amssymb} package, developed by the American Mathematical
+Society. This package includes such oft-used symbols as
+$\lesssim$ (\verb+\lesssim+), $\gtrsim$ (\verb+\gtrsim+)  or 
+$\hbar$ (\verb+\hbar+). Note that your \TeX{}
+system should have the \file{msam} and \file{msbm} fonts installed. If
+you need only a few symbols, such as $\Box$ (\verb+\Box+), you might try the
+package \file{latexsym}.
+
+Another point which would require authors' attention is the
+breaking up of long equations.  When you use
+\file{elsarticle.cls} for formatting your submissions in the 
+\verb+preprint+ mode, the document is formatted in single column
+style with a text width of 384pt or 5.3in.  When this document is
+formatted for final print and if the journal happens to be a double column
+journal, the text width will be reduced to 224pt at for 3+
+double column and 5+ journals respectively. All the nifty 
+fine-tuning in equation breaking done by the author goes to waste in
+such cases.  Therefore, authors are requested to check this
+problem by typesetting their submissions in final format as well
+just to see if their equations are broken at appropriate places,
+by changing appropriate options in the document class loading
+command, which is explained in section~\ref{sec:usage},
+\nameref{sec:usage}. This allows authors to fix any equation breaking
+problem before submission for publication.
+\file{elsarticle.cls} supports formatting the author submission
+in different types of final format.  This is further discussed in
+section \ref{sec:final}, \nameref{sec:final}.
+
+\enlargethispage*{\baselineskip}
+
+\subsection*{Displayed equations and double column journals}
+
+Many Elsevier journals print their text in two columns. Since
+the preprint layout uses a larger line width than such columns,
+the formulae are too wide for the line width in print. Here is an
+example of an equation  (see equation 6) which is perfect in a
+single column preprint format:
+
+In normal course, articles are prepared and submitted in single column
+format even if the final printed article will come in a double column
+format journal. Here the problem is that when the article is typeset by
+the typesetters for paginating and fit within the single column width,
+they have to break the lengthy equations and align them properly. Even
+if most of the tasks in preparing your proof is automated, the equation
+breaking and aligning requires manual judgement, hence this task is manual.
+When there comes a manual operation that area is error prone. Author
+needs to check that equation pretty well. 
+
+However if authors themselves break the equation to the single column
+width typesetters need not want to touch these area and the proof authors
+get will be without any errors.
+
+%\bigskip
+\setlength\Sep{6pt}
+\src{See equation (6)}
+\def\rulecolor{blue!70}
+%\includeclip{<page>}{l b scale }{file.pdf}
+\includeclip{4}{105 500 500 700}{1psingleauthorgroup.pdf}
+\def\rulecolor{orange}
+                 	
+\noindent When this document is typeset for publication in a
+model 3+ journal with double columns, the equation will overlap
+the second column text matter if the equation is not broken at
+the appropriate location.
+
+\vspace*{6pt}
+\def\rulecolor{blue!70}
+\src{See equation (6) overprints into second column}
+\includeclip{3}{59 421 532 635}{elstest-3pd.pdf}
+\def\rulecolor{orange}
+\vspace*{6pt}
+
+\noindent The typesetter will try to break the equation which
+need not necessarily be to the liking of the author or as it
+happens, typesetter's break point may be semantically incorrect.
+Therefore, authors may check their submissions for the incidence
+of such long equations and break the equations at the correct
+places so that the final typeset copy will be as they wish.
+
+\section{Bibliography}
+
+Three bibliographic style files (\verb+*.bst+) are provided ---
+\file{elsarticle-num.bst}, \file{elsarticle-num-names.bst} and
+\file{elsarticle-harv.bst} --- the first one can be used for the
+numbered scheme, second one for numbered with new options of 
+\file{natbib.sty}. The third one is for the author year
+scheme.
+
+In \LaTeX{} literature, references are listed in the
+\verb+thebibliography+ environment.  Each reference is a
+\verb+\bibitem+ and each \verb+\bibitem+ is identified by a label,
+by which it can be cited in the text:
+
+\verb+\bibitem[Elson et al.(1996)]{ESG96}+ is cited as
+\verb+\citet{ESG96}+. 
+
+\noindent In connection with cross-referencing and
+possible future hyperlinking it is not a good idea to collect
+more that one literature item in one \verb+\bibitem+.  The
+so-called Harvard or author-year style of referencing is enabled
+by the \LaTeX{} package \file{natbib}. With this package the
+literature can be cited as follows:
+
+\begin{enumerate}[\textbullet]
+\item Parenthetical: \verb+\citep{WB96}+ produces (Wettig \& Brown, 1996).
+\item Textual: \verb+\citet{ESG96}+ produces Elson et al. (1996).
+\item An affix and part of a reference:
+\verb+\citep[e.g.][Ch. 2]{Gea97}+ produces (e.g. Governato et
+al., 1997, Ch. 2).
+\end{enumerate}
+
+In the numbered scheme of citation, \verb+\cite{<label>}+ is used,
+since \verb+\citep+ or \verb+\citet+ has no relevance in the numbered
+scheme.  \file{natbib} package is loaded by \file{elsarticle} with
+\verb+numbers+ as default option.  You can change this to author-year
+or harvard scheme by adding option \verb+authoryear+ in the class
+loading command.  If you want to use more options of the \file{natbib}
+package, you can do so with the \verb+\biboptions+ command, which is
+described in the section \ref{sec:usage}, \nameref{sec:usage}.  For
+details of various options of the \file{natbib} package, please take a
+look at the \file{natbib} documentation, which is part of any standard
+\LaTeX{} installation.
+
+In addition to the above standard \verb+.bst+ files, there are 10
+journal-specific \verb+.bst+ files also available.
+Instruction for using these \verb+.bst+ files can be found at 
+\href{http://support.stmdocs.in/wiki/index.php?title=Model-wise_bibliographic_style_files}
+{http://support.stmdocs.in}
+
+\section[Graphical ...]{Graphical abstract and highlights}
+A template for adding graphical abstract and highlights are available
+now. This will appear as the first two pages of the PDF before the
+article content begins.
+
+\pagebreak
+Please refer below to see how to code them.
+
+\begin{vquote}
+....
+....
+
+\end{abstract}
+
+%%Graphical abstract
+\begin{graphicalabstract}
+%\includegraphics{grabs}
+\end{graphicalabstract}
+
+%%Research highlights
+\begin{highlights}
+\item Research highlight 1
+\item Research highlight 2
+\end{highlights}
+
+\begin{keyword}
+%% keywords here, in the form: keyword \sep keyword
+....
+....
+\end{vquote}
+
+\section{Final print}\label{sec:final}
+
+The authors can format their submission to the page size and margins
+of their preferred journal.  \file{elsarticle} provides four
+class options for the same. But it does not mean that using these
+options you can emulate the exact page layout of the final print copy. 
+
+
+\lmrgn=3em
+\begin{description}
+\item [\texttt{1p}:] $1+$ journals with a text area of
+384pt $\times$ 562pt or 13.5cm $\times$ 19.75cm or 5.3in $\times$
+7.78in, single column style only.
+
+\item [\texttt{3p}:] $3+$ journals with a text area of 468pt
+$\times$ 622pt or 16.45cm $\times$ 21.9cm or 6.5in $\times$
+8.6in, single column style.
+
+\item [\texttt{twocolumn}:] should be used along with 3p option if the
+journal is $3+$ with the same text area as above, but double column
+style. 
+
+\item [\texttt{5p}:] $5+$ with text area of 522pt $\times$
+682pt or 18.35cm $\times$ 24cm or 7.22in $\times$ 9.45in,
+double column style only.
+\end{description}
+
+Following pages have the clippings of different parts of
+the title page of different journal models typeset in final
+format.
+
+Model $1+$ and $3+$  will have the same look and
+feel in the typeset copy when presented in this document. That is
+also the case with the double column $3+$ and $5+$ journal article
+pages. The only difference will be wider text width of
+higher models.  Here are the specimen single and double column journal 
+pages.
+
+%Therefore we will look at the
+%different portions of a typical single column journal page and
+%that of a double column article in the final format.
+
+
+\begin{comment}
+\begin{center}
+\hypertarget{bsc}{}
+\hyperlink{sc}{
+{\bf [Specimen single column article -- Click here]}
+}
+
+
+\hypertarget{bsc}{}
+\hyperlink{dc}{
+{\bf [Specimen double column article -- Click here]}
+}
+\end{center}
+\end{comment}
+
+\vspace*{-.5pc}
+
+\enlargethispage*{\baselineskip}
+
+\src{}\hypertarget{sc}{}
+\def\rulecolor{blue!70}
+\hyperlink{bsc}{\includeclip{1}{88 120 514 724}{elstest-1p.pdf}}
+\def\rulecolor{orange}
+
+\src{}\hypertarget{dc}{}
+\def\rulecolor{blue!70}
+\hyperlink{bsc}{\includeclip{1}{27 61 562 758}{elstest-5p.pdf}}
+\def\rulecolor{orange}
+
+~\hfill $\Box$
+
+\end{document}
+
diff --git a/papers/variational_smoother/doc/elstest-1p.pdf b/papers/variational_smoother/doc/elstest-1p.pdf
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diff --git a/papers/variational_smoother/doc/jfigs.pdf b/papers/variational_smoother/doc/jfigs.pdf
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diff --git a/papers/variational_smoother/doc/makefile b/papers/variational_smoother/doc/makefile
new file mode 100644
index 0000000..b573bb1
--- /dev/null
+++ b/papers/variational_smoother/doc/makefile
@@ -0,0 +1,38 @@
+# $Id: makefile 243 2024-04-06 10:34:40Z rishi $
+
+file=elsdoc
+
+
+all: pdf out 
+	make pdf
+	make pdf
+
+out:
+	if  [ -f $(file).out ] ; then cp $(file).out tmp.out; fi ;
+	sed 's/BOOKMARK/dtxmark/g;' tmp.out > x.out; mv x.out tmp.out ;
+
+pdf:
+	pdflatex $(file).tex
+
+index:
+	makeindex -s gind.ist -o $(file).ind $(file).idx 
+
+changes:
+	makeindex -s gglo.ist -o $(file).gls $(file).glo
+
+xview:
+#	xpdf -z 200 $(file).pdf &>/dev/null
+	open -a 'Skim.app' $(file).pdf 
+
+view:
+	open -a 'Adobe Reader.app' $(file).pdf
+
+ins:
+	latex $(file).ins 
+
+diff:
+	diff $(file).sty ../$(file).sty |less
+
+copy:
+	cp $(file).sty ../
+
diff --git a/papers/variational_smoother/doc/pdfwidgets.sty b/papers/variational_smoother/doc/pdfwidgets.sty
new file mode 100644
index 0000000..68d07a8
--- /dev/null
+++ b/papers/variational_smoother/doc/pdfwidgets.sty
@@ -0,0 +1,384 @@
+%%
+%% pdfwidgets.sty
+%%
+%% $Id: pdfwidgets.sty,v 1.2 2007-10-22 09:45:17 cvr Exp $
+%%    
+%% (c) C. V. Radhakrishnan <cvr@river-valley.org>
+%%
+%% This package may be distributed under the terms of the LaTeX Project 
+%% Public License, as described in lppl.txt in the base LaTeX distribution.
+%% Either version 1.0 or, at your option, any later version.
+%%
+%\RequirePackage[oldstyle]{minion}
+%\RequirePackage[scaled=.8]{prima}
+%\RequirePackage[scaled=.9]{lfr}
+\usepackage[dvipsnames,svgnames]{xcolor}
+\RequirePackage{graphicx}
+\RequirePackage{tikz}
+\usetikzlibrary{backgrounds}
+
+%\def\thesection{\ifnum\c@section<10
+%    \protect\phantom{0}\fi\arabic{section}}
+
+\newdimen\lmrgn
+\def\rulecolor{orange}
+\def\rulewidth{1pt}
+\pgfdeclareshape{filledbox}{%
+  \inheritsavedanchors[from=rectangle] % this is nearly a rectangle
+  \inheritanchorborder[from=rectangle]
+  \inheritanchor[from=rectangle]{center}
+  \inheritanchor[from=rectangle]{north}
+  \inheritanchor[from=rectangle]{south}
+  \inheritanchor[from=rectangle]{west}
+  \inheritanchor[from=rectangle]{east}
+  % ... and possibly more
+  \backgroundpath{% this is new
+    % store lower right in xa/ya and upper right in xb/yb
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    % compute corner of ``flipped page''
+    \pgf@xc=\pgf@xb \advance\pgf@xc by-5pt % this should be a parameter
+    \pgf@yc=\pgf@yb \advance\pgf@yc by-5pt
+    % construct main path
+    \pgfsetlinewidth{\rulewidth}
+    \pgfsetstrokecolor{\rulecolor}
+    \pgfpathmoveto{\pgfpoint{\pgf@xa}{\pgf@ya}}
+  \pgfsetcornersarced{\pgfpoint{9pt}{9pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xa}{\pgf@yb}}
+%  \pgfsetcornersarced{\pgforigin}
+  \pgfsetcornersarced{\pgfpoint{9pt}{9pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@yb}}
+  \pgfsetcornersarced{\pgfpoint{9pt}{9pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@ya}}
+  \pgfsetcornersarced{\pgforigin}
+    \pgfpathclose ;
+%  \draw(\pgf@xa,\pgf@ya) -- (\pgf@xa,\pgf@yb) ;
+ }%
+}
+\pgfdeclareshape{roundedbox}{%
+  \inheritsavedanchors[from=rectangle] % this is nearly a rectangle
+  \inheritanchorborder[from=rectangle]
+  \inheritanchor[from=rectangle]{center}
+  \inheritanchor[from=rectangle]{north}
+  \inheritanchor[from=rectangle]{south}
+  \inheritanchor[from=rectangle]{west}
+  \inheritanchor[from=rectangle]{east}
+  % ... and possibly more
+  \backgroundpath{% this is new
+    % store lower right in xa/ya and upper right in xb/yb
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    % compute corner of ``flipped page''
+    \pgf@xc=\pgf@xb \advance\pgf@xc by-5pt % this should be a parameter
+    \pgf@yc=\pgf@yb \advance\pgf@yc by-5pt
+    % construct main path
+    \pgfsetlinewidth{\rulewidth}
+    \pgfsetstrokecolor{\rulecolor}
+    \pgfpathmoveto{\pgfpoint{\pgf@xa}{\pgf@ya}}
+  \pgfsetcornersarced{\pgfpoint{4pt}{4pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xa}{\pgf@yb}}
+%  \pgfsetcornersarced{\pgforigin}
+  \pgfsetcornersarced{\pgfpoint{4pt}{4pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@yb}}
+  \pgfsetcornersarced{\pgfpoint{4pt}{4pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@ya}}
+%  \pgfsetcornersarced{\pgforigin}
+  \pgfsetcornersarced{\pgfpoint{4pt}{4pt}}
+    \pgfpathclose ;
+%  \draw(\pgf@xa,\pgf@ya) -- (\pgf@xa,\pgf@yb) ;
+ }%
+}
+
+
+
+
+\pgfdeclareshape{buttonbox}{%
+  \inheritsavedanchors[from=rectangle] % this is nearly a rectangle
+  \inheritanchorborder[from=rectangle]
+  \inheritanchor[from=rectangle]{center}
+  \inheritanchor[from=rectangle]{north}
+  \inheritanchor[from=rectangle]{south}
+  \inheritanchor[from=rectangle]{west}
+  \inheritanchor[from=rectangle]{east}
+  % ... and possibly more
+  \backgroundpath{% this is new
+    % store lower right in xa/ya and upper right in xb/yb
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    % compute corner of ``flipped page''
+    \pgf@xc=\pgf@xb \advance\pgf@xc by-5pt % this should be a parameter
+    \pgf@yc=\pgf@yb \advance\pgf@yc by-5pt
+    % construct main path
+    \pgfsetlinewidth{1pt}
+    \pgfsetstrokecolor{blue!10}
+    \pgfpathmoveto{\pgfpoint{\pgf@xa}{\pgf@ya}}
+  \pgfsetcornersarced{\pgfpoint{4pt}{4pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xa}{\pgf@yb}}
+%  \pgfsetcornersarced{\pgforigin}
+  \pgfsetcornersarced{\pgfpoint{4pt}{4pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@yb}}
+  \pgfsetcornersarced{\pgforigin}
+%  \pgfsetcornersarced{\pgfpoint{9pt}{9pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@ya}}
+  \pgfsetcornersarced{\pgforigin}
+    \pgfpathclose ;
+%  \draw(\pgf@xa,\pgf@ya) -- (\pgf@xa,\pgf@yb) ;
+ }%
+}
+\pgfdeclareshape{quotedbox}{%
+  \inheritsavedanchors[from=rectangle] % this is nearly a rectangle
+  \inheritanchorborder[from=rectangle]
+  \inheritanchor[from=rectangle]{center}
+  \inheritanchor[from=rectangle]{north}
+  \inheritanchor[from=rectangle]{south}
+  \inheritanchor[from=rectangle]{west}
+  \inheritanchor[from=rectangle]{east}
+  % ... and possibly more
+  \backgroundpath{% this is new
+    % store lower right in xa/ya and upper right in xb/yb
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    % compute corner of ``flipped page''
+    \pgf@xc=\pgf@xb \advance\pgf@xc by-5pt % this should be a parameter
+    \pgf@yc=\pgf@yb \advance\pgf@yc by-5pt
+    % construct main path
+    \pgfsetlinewidth{\rulewidth}
+    \pgfsetstrokecolor{\rulecolor}
+    \pgfpathmoveto{\pgfpoint{\pgf@xa}{\pgf@ya}}
+  \pgfsetcornersarced{\pgfpoint{9pt}{9pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xa}{\pgf@yb}}
+  \pgfsetcornersarced{\pgforigin}
+%  \pgfsetcornersarced{\pgfpoint{4pt}{4pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@yb}}
+  \pgfsetcornersarced{\pgforigin}
+%  \pgfsetcornersarced{\pgfpoint{9pt}{9pt}}
+    \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@ya}}
+  \pgfsetcornersarced{\pgforigin}
+    \pgfpathclose ;
+%  \draw(\pgf@xa,\pgf@ya) -- (\pgf@xa,\pgf@yb) ;
+ }%
+}
+
+\newcounter{clip}
+\newdimen\mywidth
+\mywidth=\linewidth
+
+\def\src#1{\gdef\@src{#1}}\let\@src\@empty
+\def\includeclip{\@ifnextchar[{\@includeclip}{\@includeclip[]}}
+\def\@includeclip[#1]#2#3#4{\par
+%    \vskip.75\baselineskip plus 3pt minus 1pt
+    \computeLinewidth{\mywidth}%
+    \begingroup\color{white}%
+     \noindent%
+     \begin{tikzpicture}
+      %\node[fill=black!10,draw,shape=filledbox,
+      \node[fill=black!10,%
+			draw,
+			shade,%
+			top color=blue!10,
+			bottom color=cyan!5,
+			shape=filledbox,
+      inner sep=\Sep,
+      text width=\Linewidth] (x)
+      {\parbox{\Linewidth}
+      {\ifx\@src\@empty\else\refstepcounter{clip}\label{clip\theclip}%
+			  {\par\vskip6pt\color{orange}\sffamily\small
+				 ~Clip \theclip:\space\@src.}%
+			 \par\vskip3pt\fi\normalcolor
+			 \includegraphics[width=\Linewidth,page={#2},%
+         viewport={#3},clip=true,#1]{#4}}
+       \hspace*{-10pt}};
+      \end{tikzpicture}
+     \endgroup
+%     \par\vskip.5\baselineskip
+%         plus 3pt minus 1pt
+				 }
+%%                                         
+%% include clippings from a pdf document:
+%% #1 => Optional argument for \includegraphics
+%% #2 => page number
+%% #3 => co-ordinates
+%% #4 => file name
+
+\newenvironment{quoted}{%\bigskip
+    \computeLinewidth{.95\linewidth}%
+    \global\setbox0=\hbox\bgroup
+	   \begin{minipage}{.95\linewidth}\color{brown}%
+		 \footnotesize\ttfamily\obeyspaces\obeylines}
+	{\end{minipage}\egroup
+   \vskip12pt plus 3pt minus 3pt\noindent\begin{tikzpicture}
+	  \node[fill=blue!10,draw,shade,top color=orange!10,
+		      bottom color=white,shape=filledbox,
+		 inner sep=8pt,text width=\Linewidth] (x) {\box0} ;
+ 	  \end{tikzpicture}%
+	 \vskip12pt plus 3pt minus 3pt}
+
+\newdimen\Linewidth
+\newdimen\Sep
+\def\computeLinewidth#1{\global\setlength\Linewidth{#1}%
+   \global\addtolength{\Linewidth}{-2\Sep}}
+
+\newdimen\npskip
+\npskip=0mm
+
+\long\def\NavigationPanel{%
+   \global\setbox0=\hbox\bgroup
+	   \begin{minipage}[t][.8125\panelheight][t]{.9\panelwidth}\color{brown}%
+     %\centering
+     \ifx\@pinclude\empty\relax\par\vfill\else
+		 \@pinclude\fi
+		 %River Valley Technologies
+	   \end{minipage}\egroup
+		 \Sep=.5cm
+		 \@tempdima=\panelwidth
+		 \advance\@tempdima-1cm
+		 \computeLinewidth{\@tempdima}%
+		 \def\rulewidth{.2pt}%
+	 \noindent\begin{tikzpicture}
+	  \node[fill=blue!10,draw,shade,bottom color=brown!30,
+		      top color=white,shape=filledbox,
+		 inner sep=\the\Sep,text width=\Linewidth] (x) 
+		 {\hspace*{\npskip}\box0} ;
+ 	  \end{tikzpicture}%
+		\vspace*{.0125\panelheight}
+}
+
+\long\def\pinclude#1{\gdef\@pinclude{#1}}
+\let\@pinclude\empty
+
+\def\Strut{\vrule depth 2pt height 10pt width 0pt}
+\def\pdfButton#1#2{\begin{tikzpicture}
+     \node[fill=blue!10,draw,shade,top color=blue!50,
+		       bottom color=white,shape=buttonbox,
+					 inner sep=2pt,text width=#1](x) 
+					 {\parbox{#1}{\centering\Strut#2}}; \end{tikzpicture}}
+
+\def\vpanel{\def\@linkcolor{blue}%
+            \def\@urlcolor{blue}%
+						\def\@menucolor{blue}%
+       \begin{minipage}[t][\vpanelheight][c]{\paperwidth}%
+       \normalsfcodes%
+   \hspace*{.25cm}
+	  \begin{minipage}[c][\vpanelheight][c]{17cm}
+		 \parbox[c][27mm][b]{15mm}%
+%		  {\includegraphics[width=15mm]{logo4.pdf}}\hfill%\hspace{1cm}
+     {\def\rulecolor{Goldenrod}%
+		  \def\rulewidth{1pt}%
+			\begin{tikzpicture}%
+      %\node[fill=black!10,draw,shape=filledbox,
+      \node[fill=white!10,%
+			 draw,
+%			 shade,%
+%			 top color=blue!10,
+%			 bottom color=white,
+			 shape=roundedbox,
+      inner sep=2mm,
+      text width=13mm] (x)
+      {\includegraphics[width=13mm]{els-logo.pdf}};
+			\end{tikzpicture}}\hfill
+%
+     \parbox[c][24mm][b]{145mm}%	
+	    {{\fontsize{30}{30}\selectfont\textsf{\color{white}elsarticle.cls}}
+			\quad{\fontsize{14}{14}\selectfont\sffamily\color{blue!50}
+			 A better way to format your submission}}
+    \end{minipage} 
+	 \hfill
+	 \begin{minipage}[c][\vpanelheight][b]{7.9cm}
+	  \sffamily\footnotesize
+	  \pdfButton{2cm}{\href{mailto:elsarticle@river-valley.com}{BUGS}}
+	  \pdfButton{2cm}{\href{http://support.river-valley.com}{SUPPORT}}
+	  \pdfButton{2cm}%
+		 {\href{http://www.elsevier.com/locate/latex}%
+		  {RESOURCES}}
+%		\pdfButton{2cm}{\Acrobatmenu{GoToPage}{GoTo}}
+	 \end{minipage}\\
+	 \rule{\paperwidth}{0.1pt}
+	 \end{minipage}%
+}
+
+\@ifundefined{backgroundcolor}%
+  {\def\backgroundcolor#1{\gdef\@backgroundcolor{#1}}}{}
+\colorlet{panelbackground}{orange!10}
+\backgroundcolor{orange!10}
+\def\@urlcolor{brown}
+\def\@linkcolor{brown}
+\def\@menucolor{brown}
+
+\RequirePackage{moreverb}
+
+\newenvironment{vquote}%
+    {\medskip
+		 \verbatimwrite{tmp.tex}}
+    {\endverbatimwrite
+		 \aftergroup\printBox}
+
+\def\printBox{\bgroup\def\rulecolor{orange}%
+    \def\rulewidth{.2pt}%
+		\noindent\begin{tikzpicture}
+	  \node[fill=blue!10,draw,shade,top color=white!10,
+		      bottom color=cyan!5,shape=quotedbox,
+		 inner sep=8pt,text width=.95\linewidth] 
+		 {\color{orange}\vspace*{-1pc}%
+     \verbatiminput{tmp.tex}%
+		 \vspace*{-\baselineskip}%
+		 } ;
+ 	  \end{tikzpicture}%
+		\egroup
+		\medskip
+}
+\def\red{\color{Sepia}}
+\def\verbatim@font{\red\normalfont\ttfamily}
+
+\def\verbatimcontinuewrite{%
+  \@bsphack
+%  \verbatim@out=#1
+  \let\do\@makeother\dospecials
+  \obeyspaces\catcode`\^^M\active \catcode`\^^I=12
+  \def\verbatim@processline{%
+    \immediate\write\verbatim@out
+      {\the\verbatim@line}}%
+  \verbatim@start}
+
+\def\@@@lbr{\expandafter\@gobble\string\{}
+\def\@@@rbr{\expandafter\@gobble\string\}}
+\def\@@@pcr{\expandafter\@gobble\string\%}
+
+
+%\immediate\write18{touch mytool.tex
+%  ^^J rm mytool.tex ^^J touch mytool.tex}
+
+\newenvironment{toolwrite}[1]%
+  {\@tempdima=#1
+	 \verbatimwrite{xx}}
+	{\endverbatimwrite
+	 \immediate\write18{echo 
+	 "\string\Clear\@@@lbr\the\@tempdima\@@@rbr\@@@lbr\@@@pcr">>mytool.tex^^J
+	   cat xx.tex >> mytool.tex ^^J
+		 echo "\@@@rbr" >> mytool.tex}}
+
+\tikzstyle{place}=[scale=.39,rectangle,draw=blue!90,fill=blue!30,thin,%
+                   minimum height=1mm,minimum width=13mm]
+\tikzstyle{trans}=[scale=.39,rectangle,draw=Olive,fill=Olive!20,thin,%
+                   minimum height=1mm,minimum width=13mm]
+\tikzstyle{past}=[scale=.39,rectangle,draw=Olive,fill=Olive!60,thin,%
+                   minimum height=1mm,minimum width=13mm]
+
+\def\printSq#1{\parbox{107mm}{\@tempcnta=1
+   \let\printfill\@empty
+   \loop\ifnum\@tempcnta<#1
+	  {\printfill\ifnum\c@page=\@tempcnta
+    	 \tikz\node at(0,0) [place]{};\else
+			\ifnum\c@page<\@tempcnta
+		   \hyperlink{page.\the\@tempcnta}{\tikz\node at(0,0)
+			 [trans]{};}%
+			\else
+		   \hyperlink{page.\the\@tempcnta}{\tikz\node at(0,0)
+			 [past]{};}%
+			\fi\fi}%
+		\advance\@tempcnta 1 \let\printfill\,\repeat}}	
+
+
+\endinput
+
+
+
diff --git a/papers/variational_smoother/doc/rvdtx.sty b/papers/variational_smoother/doc/rvdtx.sty
new file mode 100644
index 0000000..72d331b
--- /dev/null
+++ b/papers/variational_smoother/doc/rvdtx.sty
@@ -0,0 +1,478 @@
+%
+%
+%  File: rvdtx.sty
+%  
+%  Auxiliary package to format *.dtx documents.
+% 
+%  Copyright (c) 2008-2024 CV Radhakrishnan <cvr@stmdocs.in>,
+%                     
+%  This file may be distributed and/or modified under the conditions
+%  of the LaTeX Project Public License, either version 1.3 of this
+%  license or (at your option) any later version.  The latest version
+%  of this license is in:
+%   
+%    http://www.latex-project.org/lppl.txt
+%   
+%  and version 1.3 or later is part of all distributions of LaTeX
+%  version 1999/12/01 or later.
+%
+%
+\newcounter{colorscheme}
+
+\newif\if@xcolor \@xcolorfalse
+\newif\if@mylogo \@mylogofalse
+
+\DeclareOption{mylogo}{\global\@mylogotrue}
+\DeclareOption{green}{\setcounter{colorscheme}{1}}
+\DeclareOption{orange}{\setcounter{colorscheme}{0}}
+\DeclareOption{xcolor}{\global\@xcolortrue}
+\DeclareOption{qone}{\AtEndOfPackage{\global\let\dtxmark\dtxmarkone}}
+\DeclareOption{qtwo}{\AtEndOfPackage{\global\let\dtxmark\dtxmarktwo}}
+
+\ProcessOptions
+\def\loadXcolor{\if@xcolor\RequirePackage[dvipsnames,svgnames]{xcolor}\fi}
+
+\loadXcolor
+\ifcase\thecolorscheme
+%
+%  Orange color spec (default)
+%
+ \colorlet{itemcolor}{brown}
+ \colorlet{verbcolor}{Sepia}
+ \colorlet{botrulecolor}{orange!25}
+ \colorlet{botbgcolor}{orange!15}
+ \colorlet{botcolor}{orange!80}
+ \colorlet{pgrulecolor}{orange}
+ \colorlet{pgbgcolor}{white}
+
+ \colorlet{quicklinkrulecolor}{orange!40}
+ \colorlet{quicklinkcolor}{brown}
+ \colorlet{topverticalrule}{brown}
+ \colorlet{titlecolor}{brown}
+ \colorlet{hlinkcolor}{brown}
+ \colorlet{hlinktricolor}{orange!70}
+ \colorlet{linkcolor}{brown}
+ \colorlet{urlcolor}{brown}
+
+% \colorlet{arrayrulecolor}{olive!30}
+ \colorlet{seccolor}{brown}
+
+ \colorlet{toprulecolor}{orange!30}
+ \colorlet{topbgcolor}{orange!10}
+ \colorlet{topcolor}{brown!80}
+%
+%
+\or% Green color specs
+%
+%
+ \colorlet{itemcolor}{OliveGreen}
+ \colorlet{verbcolor}{OliveGreen}
+ \colorlet{botrulecolor}{GreenYellow!25}
+ \colorlet{botbgcolor}{GreenYellow!30}
+ \colorlet{botcolor}{Green!80}
+ \colorlet{pgrulecolor}{GreenYellow}
+ \colorlet{pgbgcolor}{white}
+
+ \colorlet{quicklinkrulecolor}{Green!40}
+ \colorlet{quicklinkcolor}{Green}
+ \colorlet{topverticalrule}{Green}
+ \colorlet{titlecolor}{DarkOliveGreen}
+ \colorlet{hlinkcolor}{DarkOliveGreen}
+ \colorlet{hlinktricolor}{Green!70}
+ \colorlet{linkcolor}{OliveGreen}
+ \colorlet{urlcolor}{OliveGreen}
+
+% \colorlet{arrayrulecolor}{olive!30}
+ \colorlet{seccolor}{OliveGreen}
+
+ \colorlet{toprulecolor}{GreenYellow!50}
+ \colorlet{topbgcolor}{GreenYellow!20}
+ \colorlet{topcolor}{GreenYellow!80}
+\fi
+
+\def\floatpagefraction{.99}
+\usepackage{geometry}
+\geometry{top=2in,
+  bottom=1in,
+  left=2in,
+  right=1in,
+  a4paper}
+
+%\DeclareRobustCommand{\LaTeX}{L\kern-.25em%
+%   {\sbox\z@ T%
+%     \vbox to\ht\z@{%
+%     {\check@mathfonts
+%     \fontsize\sf@size\z@
+%     \math@fontsfalse\selectfont
+%     A}%
+%    \vss}%
+%   }%-.10em%
+%  \TeX
+%}
+\DeclareRobustCommand{\LaTeX}{L\kern-.25em%
+  {\sbox\z@ T%
+         \vbox to\ht\z@{%
+           \hbox{%
+             \check@mathfonts
+              \fontsize\sf@size\z@
+              \math@fontsfalse\selectfont
+              A}%
+          \vss}%
+        }%
+   \kern-.10em%
+   \TeX}
+
+\RequirePackage{pdfwidgets}
+
+\RequirePackage{comment,xspace}
+\def\xml{\textsc{xml}\xspace}
+\def\latex{\LaTeX\xspace}
+\def\pdf{\textsc{pdf}\xspace}
+\def\pdfa{\textsc{pdf/a-1}b\xspace}
+\def\pdfx{\textsc{pdf/x-1}a\xspace}
+\def\xmp{\textsc{xmp}\xspace}
+\def\pdftex{\textsc{pdf\TeX}\xspace}
+\def\defmacro#1{\texttt{\@bsl#1}}
+\def\thanh{H\`an Th\^e Th\`anh\xspace}
+\def\gnulinux{\textsc{gnu/linux}\xspace}
+
+\let\@DRAFTout@Hook\@empty
+\newcommand{\DRAFTout}{\g@addto@macro\@DRAFTout@Hook}
+\newcommand{\@DRAFTout@Out}{%
+   \afterassignment\@DRAFTout@Test
+   \global\setbox\@cclv=
+   }
+\newcommand{\@DRAFTout@Test}{%
+   \ifvoid\@cclv\relax
+      \aftergroup\@DRAFTout@Output
+   \else
+      \@DRAFTout@Output
+   \fi%
+   }
+\newcommand{\@DRAFTout@Output}{%
+   \@DRAFTout@Hook%
+   \@DRAFTout@Org@Out\box\@cclv%
+   }
+\newcommand{\@DRAFTout@Org@Out}{}
+\newcommand*{\@DRAFTout@Init}{%
+   \let\@DRAFTout@Org@Out\shipout
+   \let\shipout\@DRAFTout@Out
+   }
+\newdimen\OHeight
+\setlength\OHeight{\textheight}
+\addtolength\OHeight{\headheight}
+\addtolength\OHeight{\headsep}
+\addtolength\OHeight{\footskip}
+
+
+\newif\ifoverlay\overlayfalse
+
+\AtBeginDocument{\@DRAFTout@Init}
+\newcommand{\@DraftOverlay@Hook}{}
+\newcommand{\AddToDraftOverlay}{\g@addto@macro\@DraftOverlay@Hook}
+\newcommand{\ClearDraftOverlay}{\let\@DraftOverlay@Hook\@empty}
+\newcommand{\@DraftOverlay}{%
+  \ifx\@DraftOverlay@Hook\@empty
+  \else
+    \bgroup
+      \@tempdima=1in
+      \@tempcnta=\@tempdima
+      \@tempcntb=-\@tempdima
+      \advance\@tempcntb\paperheight
+      \ifoverlay
+       \global\setbox\@cclv\vbox{%
+        \box\@cclv
+        \vbox{\let\protect\relax%
+         \unitlength=1pt%
+         \pictur@(0,0)(\strip@pt\@tempdima,\strip@pt\@tempdimb)%
+          \@DraftOverlay@Hook%
+         \endpicture}}%
+     \else
+       \global\setbox\@cclv\vbox{%
+        \vbox{\let\protect\relax%
+         \unitlength=1sp%
+         \pictur@(0,0)(\@tempcnta,\@tempcntb)%
+          \@DraftOverlay@Hook%
+         \endpicture}%
+         \box\@cclv}%
+     \fi 
+    \egroup
+  \fi
+}
+
+\definecolor{gray30}{gray}{.7}
+\definecolor{gray20}{gray}{.8}
+\definecolor{gray10}{gray}{.9}
+
+\DRAFTout{\@DraftOverlay}
+\long\def\puttext(#1)#2{\AddToDraftOverlay{%
+  \setlength{\unitlength}{1pt}\thinlines%
+  \put(#1){#2}}}
+
+\RequirePackage{shortvrb}
+\MakeShortVerb{\|}
+\RequirePackage{amsfonts,amssymb}
+\IfFileExists{pxfonts.sty}{\RequirePackage{pxfonts}}{}
+%\IfFileExists{charter.sty}{\RequirePackage{charter}}{}
+\IfFileExists{lfr.sty}{\RequirePackage[scaled=.85]{lfr}}{}
+%\IfFileExists{prima.sty}{\RequirePackage[scaled=.8]{prima}}{}
+
+\def\theCodelineNo{\reset@font\tiny\arabic{CodelineNo}}
+ 
+\def\@seccntformat#1{\llap{\csname the#1\endcsname.\hspace*{6pt}}}
+\def\section{\@startsection {section}{1}{\z@}%
+      {-3.5ex \@plus -1ex \@minus -.2ex}%
+      {2.3ex \@plus.2ex}%
+      {\normalfont\large\bfseries\color{seccolor}}}
+\def\subsection{\@startsection{subsection}{2}{\z@}%
+      {-2.25ex\@plus -1ex \@minus -.2ex}%
+      {1.5ex \@plus .2ex}%
+      {\normalfont\normalsize\bfseries\color{seccolor}}}
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}%
+      {-1.25ex\@plus -1ex \@minus -.2ex}%
+      {1.5ex \@plus .2ex}%
+      {\normalfont\normalsize\bfseries\color{seccolor}}}
+
+%\RequirePackage[draft]{pdfdraftcopy}
+% \draftstring{}
+ \puttext(0,36){\botstring}%
+ \puttext(0,840){\copy\topbox}
+\if@mylogo
+ \puttext(531,829){\cvrlogo}
+\fi
+
+\RequirePackage{colortbl}
+%\arrayrulecolor{arrayrulecolor}
+\let\shline\hline
+\def\hline{\noalign{\vskip3pt}\shline\noalign{\vskip4pt}}
+
+\RequirePackage[pdftex,colorlinks]{hyperref}
+\def\Hlink#1#2{\hyperlink{#2}{\color{hlinktricolor}%
+     $\blacktriangleright$~\color{hlinkcolor}#1}}
+ \def\@linkcolor{linkcolor}
+ \def\@urlcolor{urlcolor}
+
+\pagestyle{empty}
+\def\version#1{\gdef\@version{#1}}
+\def\@version{1.0}
+\def\contact#1{\gdef\@contact{#1}}
+\def\author#1{\gdef\@author{#1}}
+\def\@author{STM Document Engineering Pvt Ltd.}
+\def\@contact{\texttt{support@stmdocs.in}}
+\def\keywords#1{\gdef\@keywords{#1}}
+\def\@keywords{\LaTeX, \xml}
+
+\long\def\Hrule{\\\hspace*{-3em}%
+     {\color{quicklinkrulecolor}\rule{\linewidth}{.1pt}}\\}
+
+\long\def\dtxmarkone[#1][#2]#3#4#5{\def\next{#1}%
+     \ifcase\next\or\Hlink{#4}{#3}\Hrule \fi}
+
+\newcounter{dtx}
+
+\long\def\dtxmarktwo[#1][#2]#3#4#5{\def\next{#1}%
+%   \stepcounter{dtx}\parbox{.45\linewidth}%
+   \stepcounter{dtx}\parbox[][11pt][b]{.45\linewidth}%
+    {\ifcase\next\or\Hlink{#4}{#3}\fi}%
+   \ifodd\thedtx\relax\else\Hrule\fi}
+
+\let\dtxmark\dtxmarkone
+
+\newbox\topbox
+\long\def\maketitle{\global\setbox\topbox=\vbox{\hsize=\paperwidth
+    \parindent=0pt
+    \fcolorbox{toprulecolor}{topbgcolor}%
+    {\parbox[t][2in][c]{\paperwidth}%
+      {\hspace*{15mm}%
+       \parbox[c]{.35\paperwidth}{\fontsize{18pt}{20pt}%
+          \raggedright\normalfont\sffamily \selectfont
+          \color{titlecolor} \@title\\[6pt]
+          {\normalsize\rmfamily\scshape\@author}}%
+%          {\footnotesize\textsc{keywords:} \@keywords}}%
+        \hfill
+        \parbox[c][2in][c]{1mm}{\color{topverticalrule}%
+          \rule{.1pt}{2in}}%
+        \hfill
+        \parbox[c][2in][c]{.35\paperwidth}%
+        {\normalfont\footnotesize\sffamily\color{quicklinkcolor}%
+%          \advance\baselineskip-3pt%
+          \advance\baselineskip-5pt%
+           \vspace*{6pt} QUICK LINKS\Hrule
+            \IfFileExists{tmp.out}{\input tmp.out}{}%
+         }\hspace*{5mm}%
+      }%
+    }%
+  }%
+}
+\gdef\botstring{\fcolorbox{botrulecolor}{botbgcolor}%
+    {\parbox[t][.5in][t]{\paperwidth}%
+      {\normalfont\sffamily\footnotesize%
+        \color{botcolor}%
+        \hspace*{5mm}\parbox[c][.5in][c]{.45\paperwidth}%
+         {\raggedright \textcopyright\ \the\year, Elsevier Ltd.
+          Bugs, feature requests, suggestions and comments %\\
+          shall be mailed to \href{mailto:elsarticle@stmdocs.in}
+          {$<$elsarticle@stmdocs.in$>$}. 
+        }\hfill%
+       \parbox[c][.5in][c]{1cm}
+        {\centering\sffamily\mdseries
+          \fcolorbox{pgrulecolor}{pgbgcolor}{\thepage}%
+        }\hfill
+       \parbox[c][.5in][c]{.45\paperwidth}
+        {\raggedleft\begin{tabular}{rl}%
+          Version:&\@version\\
+          Date:&\@date\\
+          Contact:&\@contact
+         \end{tabular}\hspace*{5mm}%
+        }%
+      }%
+    }%
+  }
+
+\def\MacroFont{\fontencoding\encodingdefault
+        \fontfamily\ttdefault
+        \fontseries\mddefault
+        \fontshape\updefault
+        \color{verbcolor}\small}%
+
+\def\verbatim@font{\normalfont\color{verbcolor}\ttfamily}
+
+\def\verb{\relax\ifmmode\hbox\else\leavevmode\null\fi
+  \bgroup
+    \verb@eol@error \let\do\@makeother \dospecials
+    \verbatim@font\@noligs
+    \@ifstar\@sverb\@verb}
+
+
+\def\@lbr{\expandafter\@gobble\string\{}
+\def\@rbr{\expandafter\@gobble\string\}}
+\def\@bsl{\expandafter\@gobble\string\\}
+\def\@Bsl#1{\texttt{\@bsl#1}\xspace}
+\def\trics#1{\protect\@Bsl{#1}}
+\def\onecs#1{\protect\@Bsl{#1}}
+%\let\trics\onecs
+\@ifundefined{c@Glossary}{}{\c@GlossaryColumns=1
+  \c@IndexColumns=2}
+
+\def\index@prologue{\section{Index}%
+                 \markboth{Index}{Index}%
+%                  Numbers written in italic refer to the page
+%                  where the corresponding entry is described;
+%                  numbers underlined refer to the
+%                  \ifcodeline@index
+%                    code line of the
+%                  \fi
+%                  definition; numbers in roman refer to the
+%                  \ifcodeline@index
+%                    code lines
+%                  \else
+%                    pages
+%                  \fi
+%                  where the entry is used.
+                 }
+
+\@ifundefined{theglossary}{}{%
+\renewenvironment{theglossary}{%
+   \glossary@prologue%][\GlossaryMin]%
+    \GlossaryParms \let\item\@idxitem \ignorespaces}%
+   {}}
+
+\newenvironment{decl}[1][]%
+    {\par\small\addvspace{1.5ex plus 1ex}%
+     \vskip -\parskip
+     \ifx\relax#1\relax
+        \def\@decl@date{}%
+     \else
+        \def\@decl@date{\NEWfeature{#1}}%
+     \fi
+     \noindent%\hspace{-\leftmargini}%
+     \begin{tabular}{l}\hline\ignorespaces}%
+    {\\\hline\end{tabular}\nobreak\@decl@date\par\nobreak
+     \vspace{0.75ex}\vskip -\parskip\ignorespacesafterend\noindent}
+
+\newif\ifhave@multicol
+\newif\ifcodeline@index
+
+\IfFileExists{multicol.sty}{\have@multicoltrue
+                            \RequirePackage{multicol}%
+                           }{}
+
+\newdimen\IndexMin         \IndexMin       = 80pt
+\newcount\c@IndexColumns   \c@IndexColumns = 2
+\ifhave@multicol
+  \renewenvironment{theindex}
+    {\begin{multicols}\c@IndexColumns[\index@prologue][\IndexMin]%
+      \IndexParms \let\item\@idxitem \ignorespaces}%
+    {\end{multicols}}
+\else
+  \typeout{Can't find multicol.sty -- will use normal index layout if
+     necessary.}
+  \def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
+    \columnseprule \z@  \columnsep 35\p@
+    \twocolumn[\index@prologue]%
+    \IndexParms \let\item\@idxitem \ignorespaces}
+  \def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
+\fi
+\long\def\IndexPrologue#1{\@bsphack\def\index@prologue{#1}\@esphack}
+\@ifundefined{index@prologue}
+     {\def\index@prologue{\section{Index}%
+                 \markboth{Index}{Index}%
+%                  Numbers written in italic refer to the page
+%                  where the corresponding entry is described;
+%                  numbers underlined refer to the
+%                  \ifcodeline@index
+%                    code line of the
+%                  \fi
+%                  definition; numbers in roman refer to the
+%                  \ifcodeline@index
+%                    code lines
+%                  \else
+%                    pages
+%                  \fi
+%                  where the entry is used.
+                 }}{}
+\@ifundefined{IndexParms}
+    {\def\IndexParms{%
+       \parindent \z@
+       \columnsep 15pt
+       \parskip 0pt plus 1pt
+       \rightskip 15pt
+       \mathsurround \z@
+       \parfillskip=-15pt
+        \footnotesize
+       \def\@idxitem{\par\hangindent 30pt}%
+       \def\subitem{\@idxitem\hspace*{15pt}}%
+       \def\subsubitem{\@idxitem\hspace*{25pt}}%
+       \def\indexspace{\par\vspace{10pt plus 2pt minus 3pt}}%
+      }}{}
+\def\efill{\hfill\nopagebreak}%
+\def\dotfill{\leaders\hbox to.6em{\hss .\hss}\hskip\z@ plus  1fill}%
+\def\dotfil{\leaders\hbox to.6em{\hss .\hss}\hfil}%
+\def\pfill{\unskip~\dotfill\penalty500\strut\nobreak
+               \dotfil~\ignorespaces}%
+
+\let\scan@allowedfalse\relax
+
+\def\tlformat#1{\begingroup\Large
+  \parbox[c][1.25em][c]{1.25em}{\centering\fontfamily{phv}
+  \fontseries{m}%
+  \selectfont\color{white}\huge#1}%
+  \endgroup}
+\def\tlFormat#1{\begingroup\Large
+  \parbox[c][1.25em][c]{1.25em}{\centering\fontfamily{phv}
+  \fontseries{m}%
+  \selectfont\color{black}\huge#1}%
+  \endgroup}
+\def\cvrlogo{\begingroup\fboxsep=2pt
+  \colorbox{olive}{\tlformat{c}}%
+  \colorbox{blue}{\tlformat{v}}%
+  \colorbox{red}{\tlformat{r}}
+  \endgroup}
+
+
+\endinput
+
+%%
+%% End of file 'rvdtx.sty'
+%% 
+
diff --git a/papers/variational_smoother/elsarticle-harv.bst b/papers/variational_smoother/elsarticle-harv.bst
new file mode 100644
index 0000000..2228e3d
--- /dev/null
+++ b/papers/variational_smoother/elsarticle-harv.bst
@@ -0,0 +1,1598 @@
+%%
+%% This is file `elsarticle-harv.bst'  (Version 2.1),
+%% 
+%% Copyright 2009-2024 Elsevier Ltd
+%% 
+%% This file is part of the 'Elsarticle Bundle'.
+%% ---------------------------------------------
+%% 
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.3 of this license or (at your option) any
+%% later version.  The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%%
+%% $Id: elsarticle-harv.bst 255 2024-04-06 10:58:47Z rishi $
+%%
+%% $URL: https://lenova.river-valley.com/svn/elsarticle/trunk/elsarticle-harv.bst $
+%% 
+
+ENTRY
+  { address
+    archive
+    author
+    booktitle
+    chapter
+    collaboration
+    edition
+    editor
+    howpublished
+    institution
+    journal
+    key
+    month
+    note
+    number
+    organization
+    pages
+    publisher
+    school
+    series
+    title
+    type
+    volume
+    year
+    url
+    doi
+    eprint
+    pubmed
+  }
+  {}
+  { label extra.label sort.label short.list }
+
+INTEGERS { output.state before.all mid.sentence after.sentence after.block }
+
+STRINGS { urlprefix doiprefix eprintprefix pubmedprefix }
+
+FUNCTION {init.web.variables}
+{
+ "\URLprefix "     'urlprefix :=
+ "\DOIprefix"      'doiprefix :=
+ "\ArXivprefix  "   'eprintprefix :=
+ "\Pubmedprefix "  'pubmedprefix :=
+}
+
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+  #1 'mid.sentence :=
+  #2 'after.sentence :=
+  #3 'after.block :=
+}
+STRINGS { s t}
+FUNCTION {output.comma}
+{ ", " * write$}
+   
+FUNCTION {output.nonnull}
+{ 's :=
+  output.state mid.sentence =
+    { ". " * write$ }
+    { output.state after.block =
+        { add.period$ write$
+          newline$
+          "\newblock " write$
+        }
+        { output.state before.all =
+            'write$
+            { ", " * write$ }
+          if$
+        }
+      if$
+      mid.sentence 'output.state :=
+    }
+  if$
+  s
+}
+FUNCTION {output.commanull}
+{ 's :=
+  output.state mid.sentence =
+    { ", " * write$ }
+    { output.state after.block =
+        { ", " * write$
+          newline$
+          "\newblock " write$
+        }
+        { output.state before.all =
+            'write$
+            { add.period$ " " * write$ }
+          if$
+        }
+      if$
+      mid.sentence 'output.state :=
+    }
+  if$
+  s
+}
+FUNCTION {output}
+{ duplicate$ empty$
+    'pop$
+    'output.nonnull
+  if$
+}
+FUNCTION {output.check}
+{ 't :=
+  duplicate$ empty$
+    { pop$ "empty " t * " in " * cite$ * warning$ }
+    'output.nonnull
+  if$
+}
+FUNCTION {output.book.check}
+{ 't :=
+  duplicate$ empty$
+    { pop$ "empty " t * " in " * cite$ * warning$ }
+    'output.nonnull
+  if$
+}
+FUNCTION {fin.entry}
+{ add.period$
+  write$
+  newline$
+}
+
+FUNCTION {new.block}
+{ output.state before.all =
+    'skip$
+    { after.block 'output.state := }
+  if$
+}
+FUNCTION {new.sentence}
+{ output.state after.block =
+    'skip$
+    { output.state before.all =
+        'skip$
+        { after.sentence 'output.state := }
+      if$
+    }
+  if$
+}
+FUNCTION {add.blank}
+{  " " * before.all 'output.state :=
+}
+
+FUNCTION {date.block}
+{
+  new.block
+}
+
+FUNCTION {not}
+{   { #0 }
+    { #1 }
+  if$
+}
+FUNCTION {and}
+{   'skip$
+    { pop$ #0 }
+  if$
+}
+FUNCTION {or}
+{   { pop$ #1 }
+    'skip$
+  if$
+}
+FUNCTION {new.block.checkb}
+{ empty$
+  swap$ empty$
+  and
+    'skip$
+    'new.block
+  if$
+}
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+    { pop$ "" }
+    'skip$
+  if$
+}
+FUNCTION {emphasize}
+{ duplicate$ empty$
+    { pop$ "" }
+    { "\textit{" swap$ * "}" * }
+  if$
+}
+FUNCTION {tie.or.space.prefix}
+{ duplicate$ text.length$ #3 <
+    { "~" }
+    { " " }
+  if$
+  swap$
+}
+
+FUNCTION {capitalize}
+{ "u" change.case$ "t" change.case$ }
+
+FUNCTION {space.word}
+{ " " swap$ * " " * }
+ % Here are the language-specific definitions for explicit words.
+ % Each function has a name bbl.xxx where xxx is the English word.
+ % The language selected here is ENGLISH
+FUNCTION {bbl.and}
+{ "and"}
+
+FUNCTION {bbl.etal}
+{ "et~al." }
+
+FUNCTION {bbl.editors}
+{ "Eds." }
+
+FUNCTION {bbl.editor}
+{ "Ed." }
+
+FUNCTION {bbl.edby}
+{ "edited by" }
+
+FUNCTION {bbl.edition}
+{ "ed." }
+
+FUNCTION {bbl.volume}
+{ "volume" }
+
+FUNCTION {bbl.of}
+{ "of" }
+
+FUNCTION {bbl.number}
+{ "number" }
+
+FUNCTION {bbl.nr}
+{ "no." }
+
+FUNCTION {bbl.in}
+{ "in" }
+
+FUNCTION {bbl.pages}
+{ "pp." }
+
+FUNCTION {bbl.page}
+{ "p." }
+
+FUNCTION {bbl.chapter}
+{ "chapter" }
+
+FUNCTION {bbl.techrep}
+{ "Technical Report" }
+
+FUNCTION {bbl.mthesis}
+{ "Master's thesis" }
+
+FUNCTION {bbl.phdthesis}
+{ "Ph.D. thesis" }
+
+MACRO {jan} {"January"}
+
+MACRO {feb} {"February"}
+
+MACRO {mar} {"March"}
+
+MACRO {apr} {"April"}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"June"}
+
+MACRO {jul} {"July"}
+
+MACRO {aug} {"August"}
+
+MACRO {sep} {"September"}
+
+MACRO {oct} {"October"}
+
+MACRO {nov} {"November"}
+
+MACRO {dec} {"December"}
+
+MACRO {acmcs} {"ACM Comput. Surv."}
+
+MACRO {acta} {"Acta Inf."}
+
+MACRO {cacm} {"Commun. ACM"}
+
+MACRO {ibmjrd} {"IBM J. Res. Dev."}
+
+MACRO {ibmsj} {"IBM Syst.~J."}
+
+MACRO {ieeese} {"IEEE Trans. Software Eng."}
+
+MACRO {ieeetc} {"IEEE Trans. Comput."}
+
+MACRO {ieeetcad}
+ {"IEEE Trans. Comput. Aid. Des."}
+
+MACRO {ipl} {"Inf. Process. Lett."}
+
+MACRO {jacm} {"J.~ACM"}
+
+MACRO {jcss} {"J.~Comput. Syst. Sci."}
+
+MACRO {scp} {"Sci. Comput. Program."}
+
+MACRO {sicomp} {"SIAM J. Comput."}
+
+MACRO {tocs} {"ACM Trans. Comput. Syst."}
+
+MACRO {tods} {"ACM Trans. Database Syst."}
+
+MACRO {tog} {"ACM Trans. Graphic."}
+
+MACRO {toms} {"ACM Trans. Math. Software"}
+
+MACRO {toois} {"ACM Trans. Office Inf. Syst."}
+
+MACRO {toplas} {"ACM Trans. Progr. Lang. Syst."}
+
+MACRO {tcs} {"Theor. Comput. Sci."}
+
+FUNCTION {bibinfo.check}
+{ swap$
+  duplicate$ missing$
+    {
+      pop$ pop$
+      ""
+    }
+    { duplicate$ empty$
+        {
+          swap$ pop$
+        }
+        { swap$
+          "\bibinfo{" swap$ * "}{" * swap$ * "}" *
+        }
+      if$
+    }
+  if$
+}
+FUNCTION {bibinfo.warn}
+{ swap$
+  duplicate$ missing$
+    {
+      swap$ "missing " swap$ * " in " * cite$ * warning$ pop$
+      ""
+    }
+    { duplicate$ empty$
+        {
+          swap$ "empty " swap$ * " in " * cite$ * warning$
+        }
+        { swap$
+          pop$
+        }
+      if$
+    }
+  if$
+}
+
+STRINGS  { bibinfo}
+
+INTEGERS { nameptr namesleft numnames }
+
+FUNCTION {format.names}
+{ 'bibinfo :=
+  duplicate$ empty$ 'skip$ {
+  's :=
+  "" 't :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      "{vv~}{ll}{, jj}{, f{.}.}"
+      format.name$
+      bibinfo bibinfo.check
+      't :=
+      nameptr #1 >
+        {
+          namesleft #1 >
+            { ", " * t * }
+            {
+              "," *
+              s nameptr "{ll}" format.name$ duplicate$ "others" =
+                { 't := }
+                { pop$ }
+              if$
+              t "others" =
+                {
+                  " " * bbl.etal *
+                }
+                { " " * t * }
+              if$
+            }
+          if$
+        }
+        't
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+  } if$
+}
+FUNCTION {format.names.ed}
+{
+  format.names
+}
+FUNCTION {format.key}
+{ empty$
+    { key field.or.null }
+    { "" }
+  if$
+}
+
+FUNCTION {format.authors}
+{ author "author" format.names
+    duplicate$ empty$ 'skip$
+    { collaboration "collaboration" bibinfo.check
+      duplicate$ empty$ 'skip$
+        { " (" swap$ * ")" * }
+      if$
+      *
+    }
+  if$
+}
+
+FUNCTION {get.bbl.editor}
+{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ }
+
+FUNCTION {format.editors}
+{ editor "editor" format.names duplicate$ empty$ 'skip$
+    {
+      " " *
+      get.bbl.editor
+      capitalize
+   "(" swap$ * ")" *
+      *
+    }
+  if$
+}
+FUNCTION {format.note}
+{
+ note empty$
+    { "" }
+    { note #1 #1 substring$
+      duplicate$ "{" =
+        'skip$
+        { output.state mid.sentence =
+          { "l" }
+          { "u" }
+        if$
+        change.case$
+        }
+      if$
+      note #2 global.max$ substring$ * "note" bibinfo.check
+    }
+  if$
+}
+
+FUNCTION {format.title}
+{ title
+  duplicate$ empty$ 'skip$
+    { "t" change.case$ }
+  if$
+  "title" bibinfo.check
+}
+FUNCTION {format.full.names}
+{'s :=
+ "" 't :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      "{vv~}{ll}" format.name$
+      't :=
+      nameptr #1 >
+        {
+          namesleft #1 >
+            { ", " * t * }
+            {
+              s nameptr "{ll}" format.name$ duplicate$ "others" =
+                { 't := }
+                { pop$ }
+              if$
+              t "others" =
+                {
+                  " " * bbl.etal *
+                }
+                {
+                  bbl.and
+                  space.word * t *
+                }
+              if$
+            }
+          if$
+        }
+        't
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+}
+
+FUNCTION {author.editor.key.full}
+{ author empty$
+    { editor empty$
+        { key empty$
+            { cite$ #1 #3 substring$ }
+            'key
+          if$
+        }
+        { editor format.full.names }
+      if$
+    }
+    { author format.full.names }
+  if$
+}
+
+FUNCTION {author.key.full}
+{ author empty$
+    { key empty$
+         { cite$ #1 #3 substring$ }
+          'key
+      if$
+    }
+    { author format.full.names }
+  if$
+}
+
+FUNCTION {editor.key.full}
+{ editor empty$
+    { key empty$
+         { cite$ #1 #3 substring$ }
+          'key
+      if$
+    }
+    { editor format.full.names }
+  if$
+}
+
+FUNCTION {make.full.names}
+{ type$ "book" =
+  type$ "inbook" =
+  or
+    'author.editor.key.full
+    { type$ "proceedings" =
+        'editor.key.full
+        'author.key.full
+      if$
+    }
+  if$
+}
+
+FUNCTION {output.bibitem}
+{ newline$
+  "\bibitem[{" write$
+  label write$
+  ")" make.full.names duplicate$ short.list =
+     { pop$ }
+     { * }
+   if$
+  "}]{" * write$
+  cite$ write$
+  "}" write$
+  newline$
+  ""
+  before.all 'output.state :=
+}
+
+FUNCTION {n.dashify}
+{
+  't :=
+  ""
+    { t empty$ not }
+    { t #1 #1 substring$ "-" =
+        { t #1 #2 substring$ "--" = not
+            { "--" *
+              t #2 global.max$ substring$ 't :=
+            }
+            {   { t #1 #1 substring$ "-" = }
+                { "-" *
+                  t #2 global.max$ substring$ 't :=
+                }
+              while$
+            }
+          if$
+        }
+        { t #1 #1 substring$ *
+          t #2 global.max$ substring$ 't :=
+        }
+      if$
+    }
+  while$
+}
+
+FUNCTION {word.in}
+{ bbl.in %capitalize
+  ":" *
+  " " * }
+
+FUNCTION {format.date}
+{ year "year" bibinfo.check duplicate$ empty$
+    {
+    }
+    'skip$
+  if$
+  extra.label *
+  before.all 'output.state :=
+  ", " swap$ *
+}
+FUNCTION {format.btitle}
+{ title "title" bibinfo.check
+  duplicate$ empty$ 'skip$
+    {
+    }
+  if$
+}
+FUNCTION {either.or.check}
+{ empty$
+    'pop$
+    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+  if$
+}
+FUNCTION {format.bvolume}
+{ volume empty$
+    { "" }
+    { bbl.volume volume tie.or.space.prefix
+      "volume" bibinfo.check * *
+      series "series" bibinfo.check
+      duplicate$ empty$ 'pop$
+        { swap$ bbl.of space.word * swap$
+          emphasize * }
+      if$
+      "volume and number" number either.or.check
+    }
+  if$
+}
+FUNCTION {format.number.series}
+{ volume empty$
+    { number empty$
+        { series field.or.null }
+        { series empty$
+            { number "number" bibinfo.check }
+        { output.state mid.sentence =
+            { bbl.number }
+            { bbl.number capitalize }
+          if$
+          number tie.or.space.prefix "number" bibinfo.check * *
+          bbl.in space.word *
+          series "series" bibinfo.check *
+        }
+      if$
+    }
+      if$
+    }
+    { "" }
+  if$
+}
+
+FUNCTION {format.edition}
+{ edition duplicate$ empty$ 'skip$
+    {
+      output.state mid.sentence =
+        { "l" }
+        { "t" }
+      if$ change.case$
+      "edition" bibinfo.check
+      " " * bbl.edition *
+    }
+  if$
+}
+INTEGERS { multiresult }
+FUNCTION {multi.page.check}
+{ 't :=
+  #0 'multiresult :=
+    { multiresult not
+      t empty$ not
+      and
+    }
+    { t #1 #1 substring$
+      duplicate$ "-" =
+      swap$ duplicate$ "," =
+      swap$ "+" =
+      or or
+        { #1 'multiresult := }
+        { t #2 global.max$ substring$ 't := }
+      if$
+    }
+  while$
+  multiresult
+}
+%FUNCTION {format.pages}
+%{ pages duplicate$ empty$ 'skip$
+%    { duplicate$ multi.page.check
+%        {
+%          n.dashify
+%        }
+%        {
+%        }
+%      if$
+%      "pages" bibinfo.check
+%    }
+%  if$
+%}
+
+FUNCTION {format.pages}
+{ pages duplicate$ empty$ 'skip$
+    { duplicate$ multi.page.check
+        {
+          bbl.pages swap$
+          n.dashify
+        }
+        {
+          bbl.page swap$
+        }
+      if$
+      tie.or.space.prefix
+      "pages" bibinfo.check
+      * *
+    }
+  if$
+}
+
+FUNCTION {format.journal.pages}
+{ pages duplicate$ empty$ 'pop$
+    { swap$ duplicate$ empty$
+        { pop$ pop$ format.pages }
+        {
+          ", " *
+          swap$
+          n.dashify
+          "pages" bibinfo.check
+          *
+        }
+      if$
+    }
+  if$
+}
+FUNCTION {format.vol.num.pages}
+{ volume field.or.null
+  duplicate$ empty$ 'skip$
+    {
+      "volume" bibinfo.check
+    }
+  if$
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+    { "" }
+    { type empty$
+        { bbl.chapter }
+        { type "l" change.case$
+          "type" bibinfo.check
+        }
+      if$
+      chapter tie.or.space.prefix
+      "chapter" bibinfo.check
+      * *
+    }
+  if$
+}
+
+FUNCTION {format.booktitle}
+{
+  booktitle "booktitle" bibinfo.check
+}
+FUNCTION {format.in.ed.booktitle}
+{ format.booktitle duplicate$ empty$ 'skip$
+    {
+      editor "editor" format.names.ed duplicate$ empty$ 'pop$
+        {
+          " " *
+          get.bbl.editor
+          capitalize
+          "(" swap$ * "), " *
+          * swap$
+          * }
+      if$
+      word.in swap$ *
+    }
+  if$
+}
+FUNCTION {format.thesis.type}
+{ type duplicate$ empty$
+    'pop$
+    { swap$ pop$
+      "t" change.case$ "type" bibinfo.check
+    }
+  if$
+}
+FUNCTION {format.tr.number}
+{ number "number" bibinfo.check
+  type duplicate$ empty$
+    { pop$ bbl.techrep }
+    'skip$
+  if$
+  "type" bibinfo.check
+  swap$ duplicate$ empty$
+    { pop$ "t" change.case$ }
+    { tie.or.space.prefix * * }
+  if$
+}
+FUNCTION {format.article.crossref}
+{
+  word.in
+  " \cite{" * crossref * "}" *
+}
+FUNCTION {format.book.crossref}
+{ volume duplicate$ empty$
+    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
+      pop$ word.in
+    }
+    { bbl.volume
+      capitalize
+      swap$ tie.or.space.prefix "volume" bibinfo.check * * bbl.of space.word *
+    }
+  if$
+  " \cite{" * crossref * "}" *
+}
+FUNCTION {format.incoll.inproc.crossref}
+{
+  word.in
+  " \cite{" * crossref * "}" *
+}
+FUNCTION {format.org.or.pub}
+{ 't :=
+  ""
+  address empty$ t empty$ and
+    'skip$
+    {
+      t empty$
+        { address "address" bibinfo.check *
+        }
+        { t *
+          address empty$
+            'skip$
+            { ", " * address "address" bibinfo.check * }
+          if$
+        }
+      if$
+    }
+  if$
+}
+FUNCTION {format.publisher.address}
+{ publisher "publisher" bibinfo.check format.org.or.pub
+}
+
+FUNCTION {format.organization.address}
+{ organization "organization" bibinfo.check format.org.or.pub
+}
+
+FUNCTION {print.url}
+ {url duplicate$ empty$
+   { pop$ "" }
+   { new.sentence
+     urlprefix "\url{" * swap$  * "}" *
+   }
+   if$
+ }
+
+FUNCTION {print.doi}
+ {doi duplicate$ empty$
+   { pop$ "" }
+   { new.sentence
+     doiprefix "\doi{" * swap$  * "}" *
+   }
+   if$
+ }
+
+FUNCTION {print.eprint}
+ {eprint duplicate$ empty$
+   { pop$ "" }
+   { new.sentence
+     duplicate$ "\href{http://arxiv.org/abs/" swap$ * "}{{\tt arXiv:" * swap$ * "}}" *   }
+   if$
+ }
+
+FUNCTION {print.pubmed}
+ {pubmed duplicate$ empty$
+   { pop$ "" }
+   { new.sentence
+     pubmedprefix "\Pubmed{" * swap$  * "}" *
+   }
+   if$
+ }
+
+FUNCTION {webpage}
+{ "%Type = Webpage" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  author empty$
+  {
+    format.title "title" output.check
+    new.block
+    format.date "year" output.check
+    date.block
+  }
+  {
+    format.date "year" output.check
+    date.block
+    format.title "title" output.check
+    new.block
+}
+  if$
+  print.url output
+  fin.entry
+}
+
+
+FUNCTION {article}
+{ "%Type = Article" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.title "title" output.check
+  new.block
+  crossref missing$
+    {
+      journal
+      "journal" bibinfo.check
+      "journal" output.check
+      add.blank
+      format.vol.num.pages output
+    }
+    { format.article.crossref output.nonnull
+    }
+  if$
+  format.journal.pages
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {book}
+{ "%Type = Book" write$
+  output.bibitem
+  author empty$
+    { format.editors "author and editor" output.check
+      editor format.key output
+    }
+    { format.authors output.nonnull
+      crossref missing$
+        { "author and editor" editor either.or.check }
+        'skip$
+      if$
+    }
+  if$
+  format.date "year" output.check
+  date.block
+  format.btitle "title" output.check
+  crossref missing$
+    { format.bvolume output
+      new.block
+      format.number.series output
+      format.edition output
+      new.sentence
+      format.publisher.address output
+    }
+    {
+      new.block
+      format.book.crossref output.nonnull
+    }
+  if$
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {booklet}
+{ "%Type = Booklet" write$
+  output.bibitem
+  format.authors output
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.title "title" output.check
+  new.block
+  howpublished "howpublished" bibinfo.check output
+  address "address" bibinfo.check output
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {inbook}
+{ "%Type = Inbook" write$
+  output.bibitem
+  author empty$
+    { format.editors "author and editor" output.check
+      editor format.key output
+    }
+    { format.authors output.nonnull
+      crossref missing$
+        { "author and editor" editor either.or.check }
+        'skip$
+      if$
+    }
+  if$
+  format.date "year" output.check
+  date.block
+  format.btitle "title" output.check
+  format.edition output
+  crossref missing$
+    {
+      format.publisher.address output
+      format.bvolume output
+      format.chapter.pages "chapter and pages" output.check
+      new.block
+      format.number.series output
+      new.sentence
+    }
+    {
+      format.chapter.pages "chapter and pages" output.check
+      new.block
+      format.book.crossref output.nonnull
+    }
+  if$
+  format.pages "pages" output.check
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {incollection}
+{ "%Type = Incollection" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.title "title" output.book.check
+  new.sentence
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.book.check
+      format.edition output
+      format.publisher.address output
+      format.bvolume output
+      format.number.series output
+      format.chapter.pages output
+      new.sentence
+    }
+    { format.incoll.inproc.crossref output.nonnull
+      format.chapter.pages output
+    }
+  if$
+  format.pages "pages" output.check
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {inproceedings}
+{ "%Type = Inproceedings" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.title "title" output.book.check
+  new.sentence
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.check
+      new.sentence
+      publisher empty$
+        { format.organization.address output }
+        { organization "organization" bibinfo.check output
+          format.publisher.address output
+        }
+      if$
+%      format.bvolume output
+%      format.number.series output
+%      format.pages output
+    }
+    { format.incoll.inproc.crossref output.nonnull
+      format.pages output
+    }
+  if$
+  format.pages "pages" output.check
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {conference} { inproceedings }
+
+FUNCTION {manual}
+{ "%Type = Manual" write$
+  output.bibitem
+  format.authors output
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.btitle "title" output.check
+  format.edition output
+  organization address new.block.checkb
+  organization "organization" bibinfo.check output
+  address "address" bibinfo.check output
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {mastersthesis}
+{ "%Type = Masterthesis" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.btitle
+  "title" output.check
+  new.block
+  bbl.mthesis format.thesis.type output.nonnull
+  school "school" bibinfo.warn output
+  address "address" bibinfo.check output
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {misc}
+{ "%Type = Misc" write$
+  output.bibitem
+  format.authors output
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.title output
+  new.block
+  howpublished "howpublished" bibinfo.check output
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {phdthesis}
+{ "%Type = Phdthesis" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.btitle
+  "title" output.check
+  new.block
+  bbl.phdthesis format.thesis.type output.nonnull
+  school "school" bibinfo.warn output
+  address "address" bibinfo.check output
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {proceedings}
+{ "%Type = Proceedings" write$
+  output.bibitem
+  format.editors output
+  editor format.key output
+  format.date "year" output.check
+  date.block
+  format.btitle "title" output.check
+  format.bvolume output
+  format.number.series output
+  new.sentence
+  publisher empty$
+    { format.organization.address output }
+    { organization "organization" bibinfo.check output
+      format.publisher.address output
+    }
+  if$
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {techreport}
+{ "%Type = Techreport" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.btitle
+  "title" output.check
+  new.block
+  format.tr.number output.nonnull
+  institution "institution" bibinfo.warn output
+  address "address" bibinfo.check output
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {unpublished}
+{ "%Type = Unpublished" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.date "year" output.check
+  date.block
+  format.title "title" output.check
+  new.block
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note "note" output.check
+  fin.entry
+}
+
+FUNCTION {default.type} { misc }
+READ
+FUNCTION {sortify}
+{ purify$
+  "l" change.case$
+}
+INTEGERS { len }
+FUNCTION {chop.word}
+{ 's :=
+  'len :=
+  s #1 len substring$ =
+    { s len #1 + global.max$ substring$ }
+    's
+  if$
+}
+FUNCTION {format.lab.names}
+{ 's :=
+  "" 't :=
+  s #1 "{vv~}{ll}" format.name$
+  s num.names$ duplicate$
+  #2 >
+    { pop$
+      " " * bbl.etal *
+    }
+    { #2 <
+        'skip$
+        { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+            {
+              " " * bbl.etal *
+            }
+            { bbl.and space.word * s #2 "{vv~}{ll}" format.name$
+              * }
+          if$
+        }
+      if$
+    }
+  if$
+}
+
+FUNCTION {author.key.label}
+{ author empty$
+    { key empty$
+        { cite$ #1 #3 substring$ }
+        'key
+      if$
+    }
+    { author format.lab.names }
+  if$
+}
+
+FUNCTION {author.editor.key.label}
+{ author empty$
+    { editor empty$
+        { key empty$
+            { cite$ #1 #3 substring$ }
+            'key
+          if$
+        }
+        { editor format.lab.names }
+      if$
+    }
+    { author format.lab.names }
+  if$
+}
+
+FUNCTION {editor.key.label}
+{ editor empty$
+    { key empty$
+        { cite$ #1 #3 substring$ }
+        'key
+      if$
+    }
+    { editor format.lab.names }
+  if$
+}
+
+FUNCTION {calc.short.authors}
+{ type$ "book" =
+  type$ "inbook" =
+  or
+    'author.editor.key.label
+    { type$ "proceedings" =
+        'editor.key.label
+        'author.key.label
+      if$
+    }
+  if$
+  'short.list :=
+}
+
+FUNCTION {calc.label}
+{ calc.short.authors
+  short.list
+  "("
+  *
+  year duplicate$ empty$
+  short.list key field.or.null = or
+     { pop$ "" }
+     'skip$
+  if$
+  *
+  'label :=
+}
+
+FUNCTION {sort.format.names}
+{ 's :=
+  #1 'nameptr :=
+  ""
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      "{ll{ }}{  f{ }}{  jj{ }}"
+      format.name$ 't :=
+      nameptr #1 >
+        {
+          "   "  *
+          namesleft #1 = t "others" = and
+            { "zzzzz" * }
+            { t sortify * }
+          if$
+        }
+        { t sortify * }
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+}
+
+FUNCTION {sort.format.title}
+{ 't :=
+  "A " #2
+    "An " #3
+      "The " #4 t chop.word
+    chop.word
+  chop.word
+  sortify
+  #1 global.max$ substring$
+}
+FUNCTION {author.sort}
+{ author empty$
+    { key empty$
+        { "to sort, need author or key in " cite$ * warning$
+          ""
+        }
+        { key sortify }
+      if$
+    }
+    { author sort.format.names }
+  if$
+}
+FUNCTION {author.editor.sort}
+{ author empty$
+    { editor empty$
+        { key empty$
+            { "to sort, need author, editor, or key in " cite$ * warning$
+              ""
+            }
+            { key sortify }
+          if$
+        }
+        { editor sort.format.names }
+      if$
+    }
+    { author sort.format.names }
+  if$
+}
+FUNCTION {editor.sort}
+{ editor empty$
+    { key empty$
+        { "to sort, need editor or key in " cite$ * warning$
+          ""
+        }
+        { key sortify }
+      if$
+    }
+    { editor sort.format.names }
+  if$
+}
+FUNCTION {presort}
+{ calc.label
+  label sortify
+  "    "
+  *
+  type$ "book" =
+  type$ "inbook" =
+  or
+    'author.editor.sort
+    { type$ "proceedings" =
+        'editor.sort
+        'author.sort
+      if$
+    }
+  if$
+  #1 entry.max$ substring$
+  'sort.label :=
+  sort.label
+  *
+  "    "
+  *
+  title field.or.null
+  sort.format.title
+  *
+  #1 entry.max$ substring$
+  'sort.key$ :=
+}
+
+ITERATE {presort}
+SORT
+STRINGS { last.label next.extra }
+INTEGERS { last.extra.num number.label }
+FUNCTION {initialize.extra.label.stuff}
+{ #0 int.to.chr$ 'last.label :=
+  "" 'next.extra :=
+  #0 'last.extra.num :=
+  #0 'number.label :=
+}
+FUNCTION {forward.pass}
+{ last.label label =
+    { last.extra.num #1 + 'last.extra.num :=
+      last.extra.num int.to.chr$ 'extra.label :=
+    }
+    { "a" chr.to.int$ 'last.extra.num :=
+      "" 'extra.label :=
+      label 'last.label :=
+    }
+  if$
+  number.label #1 + 'number.label :=
+}
+FUNCTION {reverse.pass}
+{ next.extra "b" =
+    { "a" 'extra.label := }
+    'skip$
+  if$
+  extra.label 'next.extra :=
+  extra.label
+  duplicate$ empty$
+    'skip$
+%    { "{\natexlab{" swap$ * "}}" * }
+    { "" swap$ * "" * }
+  if$
+  'extra.label :=
+  label extra.label * 'label :=
+}
+EXECUTE {initialize.extra.label.stuff}
+ITERATE {forward.pass}
+REVERSE {reverse.pass}
+FUNCTION {bib.sort.order}
+{ sort.label
+  "    "
+  *
+  year field.or.null sortify
+  *
+  "    "
+  *
+  title field.or.null
+  sort.format.title
+  *
+  #1 entry.max$ substring$
+  'sort.key$ :=
+}
+ITERATE {bib.sort.order}
+SORT
+FUNCTION {begin.bib}
+{ preamble$ empty$
+    'skip$
+    { preamble$ write$ newline$ }
+  if$
+  "\begin{thebibliography}{" number.label int.to.str$ * "}" *
+  write$ newline$
+  "\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi"
+  write$ newline$
+  "\providecommand{\url}[1]{\texttt{#1}}"
+  write$ newline$
+  "\providecommand{\href}[2]{#2}"
+  write$ newline$
+  "\providecommand{\path}[1]{#1}"
+  write$ newline$
+  "\providecommand{\DOIprefix}{doi:}"
+  write$ newline$
+  "\providecommand{\ArXivprefix}{arXiv:}"
+  write$ newline$
+  "\providecommand{\URLprefix}{URL: }"
+  write$ newline$
+  "\providecommand{\Pubmedprefix}{pmid:}"
+  write$ newline$
+  "\providecommand{\doi}[1]{\href{http://dx.doi.org/#1}{\path{#1}}}"
+  write$ newline$
+  "\providecommand{\Pubmed}[1]{\href{pmid:#1}{\path{#1}}}"
+  write$ newline$
+  "\providecommand{\bibinfo}[2]{#2}"
+  write$ newline$
+	"\ifx\xfnm\relax \def\xfnm[#1]{\unskip,\space#1}\fi"
+  write$ newline$
+}
+EXECUTE {begin.bib}
+EXECUTE {init.state.consts}
+EXECUTE {init.web.variables} 
+ITERATE {call.type$}
+FUNCTION {end.bib}
+{ newline$
+  "\end{thebibliography}" write$ newline$
+}
+EXECUTE {end.bib}
+%% End of customized bst file
+%%
+%% End of file `elsarticle-harv.bst'.
+%%
+%% Change log:
+%% -----------
+%% 22.04.2011
+%%
+%% 10.08.2012
+%%   a. doi, url, eprint, pmid added
+%%   b. Bibtype `webpage' defined
+%%
+%% 30.08.2012
+%%   a. collaboration added.
+%%
+
+
diff --git a/papers/variational_smoother/elsarticle-num-names.bst b/papers/variational_smoother/elsarticle-num-names.bst
new file mode 100644
index 0000000..de32b37
--- /dev/null
+++ b/papers/variational_smoother/elsarticle-num-names.bst
@@ -0,0 +1,1535 @@
+%%
+%% This is file `elsarticle-num-names.bst'  (Version 2.1),
+%% 
+%% Copyright 2009-2024 Elsevier Ltd
+%% 
+%% This file is part of the 'Elsarticle Bundle'.
+%% ---------------------------------------------
+%% 
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.3 of this license or (at your option) any
+%% later version.  The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%%
+%% $Id: elsarticle-num-names.bst 253 2024-04-06 10:57:58Z rishi $
+%%
+%% $URL: https://lenova.river-valley.com/svn/elsarticle/trunk/elsarticle-num-names.bst $
+%%
+%%
+
+ENTRY
+  { address
+    author
+    booktitle
+    chapter
+    collaboration
+    edition
+    editor
+    howpublished
+    institution
+    journal
+    key
+    month
+    note
+    number
+    organization
+    pages
+    publisher
+    school
+    series
+    title
+    type
+    volume
+    year
+    url
+    doi
+    eprint
+    pubmed
+  }
+  {}
+  { label extra.label sort.label short.list }
+
+INTEGERS { output.state before.all mid.sentence after.sentence after.block }
+
+STRINGS { urlprefix doiprefix eprintprefix pubmedprefix }
+
+FUNCTION {init.web.variables}
+{
+ "\URLprefix "     'urlprefix :=
+ "\DOIprefix"      'doiprefix :=
+ "\ArXivprefix  "   'eprintprefix :=
+ "\Pubmedprefix "  'pubmedprefix :=
+}
+
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+  #1 'mid.sentence :=
+  #2 'after.sentence :=
+  #3 'after.block :=
+}
+STRINGS { s t}
+FUNCTION {output.nonnull}
+{ 's :=
+  output.state mid.sentence =
+    { ", " * write$ }
+    { output.state after.block =
+%        { add.period$ write$
+        { ", " * write$
+          newline$
+          "\newblock " write$
+        }
+        { output.state before.all =
+            'write$
+            { add.period$ " " * write$ }
+          if$
+        }
+      if$
+      mid.sentence 'output.state :=
+    }
+  if$
+  s
+}
+FUNCTION {output}
+{ duplicate$ empty$
+    'pop$
+    'output.nonnull
+  if$
+}
+FUNCTION {output.check}
+{ 't :=
+  duplicate$ empty$
+    { pop$ "empty " t * " in " * cite$ * warning$ }
+    'output.nonnull
+  if$
+}
+FUNCTION {fin.entry}
+{ add.period$
+  write$
+  newline$
+}
+
+FUNCTION {new.block}
+{ output.state before.all =
+    'skip$
+    { after.block 'output.state := }
+  if$
+}
+FUNCTION {new.sentence}
+{ output.state after.block =
+    'skip$
+    { output.state before.all =
+        'skip$
+        { after.sentence 'output.state := }
+      if$
+    }
+  if$
+}
+FUNCTION {add.blank}
+{  " " * before.all 'output.state :=
+}
+
+FUNCTION {date.block}
+{
+  skip$
+}
+
+FUNCTION {not}
+{   { #0 }
+    { #1 }
+  if$
+}
+FUNCTION {and}
+{   'skip$
+    { pop$ #0 }
+  if$
+}
+FUNCTION {or}
+{   { pop$ #1 }
+    'skip$
+  if$
+}
+FUNCTION {new.block.checkb}
+{ empty$
+  swap$ empty$
+  and
+    'skip$
+    'new.block
+  if$
+}
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+    { pop$ "" }
+    'skip$
+  if$
+}
+FUNCTION {emphasize}
+{ duplicate$ empty$
+    { pop$ "" }
+    { "\textit{" swap$ * "}" * }
+  if$
+}
+FUNCTION {tie.or.space.prefix}
+{ duplicate$ text.length$ #3 <
+    { "~" }
+    { " " }
+  if$
+  swap$
+}
+
+FUNCTION {capitalize}
+{ "u" change.case$ "t" change.case$ }
+
+FUNCTION {space.word}
+{ " " swap$ * " " * }
+ % Here are the language-specific definitions for explicit words.
+ % Each function has a name bbl.xxx where xxx is the English word.
+ % The language selected here is ENGLISH
+FUNCTION {bbl.and}
+{ "and"}
+
+FUNCTION {bbl.etal}
+{ "et~al." }
+
+FUNCTION {bbl.editors}
+{ "eds." }
+
+FUNCTION {bbl.editor}
+{ "ed." }
+
+FUNCTION {bbl.edby}
+{ "edited by" }
+
+FUNCTION {bbl.edition}
+{ "ed." }
+
+FUNCTION {bbl.volume}
+{ "volume" }
+
+FUNCTION {bbl.of}
+{ "of" }
+
+FUNCTION {bbl.number}
+{ "number" }
+
+FUNCTION {bbl.nr}
+{ "no." }
+
+FUNCTION {bbl.in}
+{ "in" }
+
+FUNCTION {bbl.pages}
+{ "pp." }
+
+FUNCTION {bbl.page}
+{ "p." }
+
+FUNCTION {bbl.chapter}
+{ "chapter" }
+
+FUNCTION {bbl.techrep}
+{ "Technical Report" }
+
+FUNCTION {bbl.mthesis}
+{ "Master's thesis" }
+
+FUNCTION {bbl.phdthesis}
+{ "Ph.D. thesis" }
+
+MACRO {jan} {"January"}
+
+MACRO {feb} {"February"}
+
+MACRO {mar} {"March"}
+
+MACRO {apr} {"April"}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"June"}
+
+MACRO {jul} {"July"}
+
+MACRO {aug} {"August"}
+
+MACRO {sep} {"September"}
+
+MACRO {oct} {"October"}
+
+MACRO {nov} {"November"}
+
+MACRO {dec} {"December"}
+
+MACRO {acmcs} {"ACM Comput. Surv."}
+
+MACRO {acta} {"Acta Inf."}
+
+MACRO {cacm} {"Commun. ACM"}
+
+MACRO {ibmjrd} {"IBM J. Res. Dev."}
+
+MACRO {ibmsj} {"IBM Syst.~J."}
+
+MACRO {ieeese} {"IEEE Trans. Software Eng."}
+
+MACRO {ieeetc} {"IEEE Trans. Comput."}
+
+MACRO {ieeetcad}
+ {"IEEE Trans. Comput. Aid. Des."}
+
+MACRO {ipl} {"Inf. Process. Lett."}
+
+MACRO {jacm} {"J.~ACM"}
+
+MACRO {jcss} {"J.~Comput. Syst. Sci."}
+
+MACRO {scp} {"Sci. Comput. Program."}
+
+MACRO {sicomp} {"SIAM J. Comput."}
+
+MACRO {tocs} {"ACM Trans. Comput. Syst."}
+
+MACRO {tods} {"ACM Trans. Database Syst."}
+
+MACRO {tog} {"ACM Trans. Graphic."}
+
+MACRO {toms} {"ACM Trans. Math. Software"}
+
+MACRO {toois} {"ACM Trans. Office Inf. Syst."}
+
+MACRO {toplas} {"ACM Trans. Progr. Lang. Syst."}
+
+MACRO {tcs} {"Theor. Comput. Sci."}
+
+FUNCTION {bibinfo.check}
+{ swap$
+  duplicate$ missing$
+    {
+      pop$ pop$
+      ""
+    }
+    { duplicate$ empty$
+        {
+          swap$ pop$
+        }
+        { swap$
+          "\bibinfo{" swap$ * "}{" * swap$ * "}" *
+        }
+      if$
+    }
+  if$
+}
+FUNCTION {bibinfo.warn}
+{ swap$
+  duplicate$ missing$
+    {
+      swap$ "missing " swap$ * " in " * cite$ * warning$ pop$
+      ""
+    }
+    { duplicate$ empty$
+        {
+          swap$ "empty " swap$ * " in " * cite$ * warning$
+        }
+        { swap$
+          pop$
+        }
+      if$
+    }
+  if$
+}
+STRINGS  { bibinfo}
+INTEGERS { nameptr namesleft numnames }
+
+FUNCTION {format.names}
+{ 'bibinfo :=
+  duplicate$ empty$ 'skip$ {
+  's :=
+  "" 't :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      "{f.~}{vv~}{ll}{, jj}"
+      format.name$
+      bibinfo bibinfo.check
+      't :=
+      nameptr #1 >
+        {
+          namesleft #1 >
+            { ", " * t * }
+            {
+              "," *
+              s nameptr "{ll}" format.name$ duplicate$ "others" =
+                { 't := }
+                { pop$ }
+              if$
+              t "others" =
+                {
+                  " " * bbl.etal *
+                }
+                { " " * t * }
+              if$
+            }
+          if$
+        }
+        't
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+  } if$
+}
+FUNCTION {format.names.ed}
+{
+  format.names
+}
+FUNCTION {format.key}
+{ empty$
+    { key field.or.null }
+    { "" }
+  if$
+}
+
+%FUNCTION {format.authors}
+%{ author "author" format.names
+%}
+
+FUNCTION {format.authors}
+{ author "author" format.names
+    duplicate$ empty$ 'skip$
+    { collaboration "collaboration" bibinfo.check
+      duplicate$ empty$ 'skip$
+        { " (" swap$ * ")" * }
+      if$
+      *
+    }
+  if$
+}
+
+FUNCTION {get.bbl.editor}
+{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ }
+
+FUNCTION {format.editors}
+{ editor "editor" format.names duplicate$ empty$ 'skip$
+    {
+      " " *
+      get.bbl.editor
+      capitalize
+   "(" swap$ * ")" *
+      *
+    }
+  if$
+}
+FUNCTION {format.note}
+{
+ note empty$
+    { "" }
+    { note #1 #1 substring$
+      duplicate$ "{" =
+        'skip$
+        { output.state mid.sentence =
+          { "l" }
+          { "u" }
+        if$
+        change.case$
+        }
+      if$
+      note #2 global.max$ substring$ * "note" bibinfo.check
+    }
+  if$
+}
+
+FUNCTION {format.title}
+{ title
+  duplicate$ empty$ 'skip$
+    { "t" change.case$ }
+  if$
+  "title" bibinfo.check
+}
+
+FUNCTION {format.full.names}
+{'s :=
+ "" 't :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+   { namesleft #0 > }
+   { s nameptr
+     "{vv~}{ll}" format.name$
+     't :=
+     nameptr #1 >
+       {
+         namesleft #1 >
+           { ", " * t * }
+           {
+             s nameptr "{ll}" format.name$ duplicate$ "others" =
+               { 't := }
+               { pop$ }
+             if$
+             t "others" =
+               {
+                 " " * bbl.etal *
+               }
+               {
+                 numnames #2 >
+                   { "," * }
+                   'skip$
+                 if$
+                 bbl.and
+                 space.word * t *
+               }
+             if$
+           }
+         if$
+       }
+       't
+     if$
+     nameptr #1 + 'nameptr :=
+     namesleft #1 - 'namesleft :=
+   }
+ while$
+}
+
+FUNCTION {author.editor.key.full}
+{ author empty$
+   { editor empty$
+       { key empty$
+           { cite$ #1 #3 substring$ }
+           'key
+         if$
+       }
+       { editor format.full.names }
+     if$
+   }
+   { author format.full.names }
+ if$
+}
+
+FUNCTION {author.key.full}
+{ author empty$
+   { key empty$
+        { cite$ #1 #3 substring$ }
+         'key
+     if$
+   }
+   { author format.full.names }
+ if$
+}
+
+FUNCTION {editor.key.full}
+{ editor empty$
+   { key empty$
+        { cite$ #1 #3 substring$ }
+         'key
+     if$
+   }
+   { editor format.full.names }
+ if$
+}
+
+FUNCTION {make.full.names}
+{ type$ "book" =
+ type$ "inbook" =
+ or
+   'author.editor.key.full
+   { type$ "proceedings" =
+       'editor.key.full
+       'author.key.full
+     if$
+   }
+ if$
+}
+
+FUNCTION {output.bibitem}
+{ newline$
+ "\bibitem[{" write$
+ label write$
+ ")" make.full.names duplicate$ short.list =
+    { pop$ }
+    { * }
+  if$
+ "}]{" * write$
+ cite$ write$
+ "}" write$
+ newline$
+ ""
+ before.all 'output.state :=
+}
+
+FUNCTION {n.dashify}
+{
+  't :=
+  ""
+    { t empty$ not }
+    { t #1 #1 substring$ "-" =
+        { t #1 #2 substring$ "--" = not
+            { "--" *
+              t #2 global.max$ substring$ 't :=
+            }
+            {   { t #1 #1 substring$ "-" = }
+                { "-" *
+                  t #2 global.max$ substring$ 't :=
+                }
+              while$
+            }
+          if$
+        }
+        { t #1 #1 substring$ *
+          t #2 global.max$ substring$ 't :=
+        }
+      if$
+    }
+  while$
+}
+
+FUNCTION {word.in}
+{ bbl.in
+  ":" *
+  " " * }
+
+FUNCTION {format.date}
+{ year "year" bibinfo.check duplicate$ empty$
+    {
+      "empty year in " cite$ * "; set to ????" * warning$
+       pop$ "????"
+    }
+    'skip$
+  if$
+  extra.label *
+}
+FUNCTION{format.year}
+{ year "year" bibinfo.check duplicate$ empty$
+    {  "empty year in " cite$ *
+       "; set to ????" *
+       warning$
+       pop$ "????"
+    }
+    {
+    }
+  if$
+  extra.label *
+  " (" swap$ * ")" *
+}
+FUNCTION {format.btitle}
+{ title "title" bibinfo.check
+  duplicate$ empty$ 'skip$
+    {
+    }
+  if$
+}
+FUNCTION {either.or.check}
+{ empty$
+    'pop$
+    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+  if$
+}
+FUNCTION {format.bvolume}
+{ volume empty$
+    { "" }
+    { bbl.volume volume tie.or.space.prefix
+      "volume" bibinfo.check * *
+      series "series" bibinfo.check
+      duplicate$ empty$ 'pop$
+        { swap$ bbl.of space.word * swap$
+          emphasize * }
+      if$
+      "volume and number" number either.or.check
+    }
+  if$
+}
+FUNCTION {format.number.series}
+{ volume empty$
+    { number empty$
+        { series field.or.null }
+        { series empty$
+            { number "number" bibinfo.check }
+        { output.state mid.sentence =
+            { bbl.number }
+            { bbl.number capitalize }
+          if$
+          number tie.or.space.prefix "number" bibinfo.check * *
+          bbl.in space.word *
+          series "series" bibinfo.check *
+        }
+      if$
+    }
+      if$
+    }
+    { "" }
+  if$
+}
+
+FUNCTION {format.edition}
+{ edition duplicate$ empty$ 'skip$
+    {
+      output.state mid.sentence =
+        { "l" }
+        { "t" }
+      if$ change.case$
+      "edition" bibinfo.check
+      " " * bbl.edition *
+    }
+  if$
+}
+INTEGERS { multiresult }
+FUNCTION {multi.page.check}
+{ 't :=
+  #0 'multiresult :=
+    { multiresult not
+      t empty$ not
+      and
+    }
+    { t #1 #1 substring$
+      duplicate$ "-" =
+      swap$ duplicate$ "," =
+      swap$ "+" =
+      or or
+        { #1 'multiresult := }
+        { t #2 global.max$ substring$ 't := }
+      if$
+    }
+  while$
+  multiresult
+}
+FUNCTION {format.pages}
+{ pages duplicate$ empty$ 'skip$
+    { duplicate$ multi.page.check
+        {
+          bbl.pages swap$
+          n.dashify
+        }
+        {
+          bbl.page swap$
+        }
+      if$
+      tie.or.space.prefix
+      "pages" bibinfo.check
+      * *
+    }
+  if$
+}
+FUNCTION {format.journal.pages}
+{ pages duplicate$ empty$ 'pop$
+    { swap$ duplicate$ empty$
+        { pop$ pop$ format.pages }
+        {
+          " " *
+          swap$
+          n.dashify
+          "pages" bibinfo.check
+          *
+        }
+      if$
+    }
+  if$
+}
+FUNCTION {format.vol.num.pages}
+{ volume field.or.null
+  duplicate$ empty$ 'skip$
+    {
+      "volume" bibinfo.check
+    }
+  if$
+  format.year *
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+    { "" }
+    { type empty$
+        { bbl.chapter }
+        { type "l" change.case$
+          "type" bibinfo.check
+        }
+      if$
+      chapter tie.or.space.prefix
+      "chapter" bibinfo.check
+      * *
+    }
+  if$
+}
+
+FUNCTION {format.booktitle}
+{
+  booktitle "booktitle" bibinfo.check
+}
+FUNCTION {format.in.ed.booktitle}
+{ format.booktitle duplicate$ empty$ 'skip$
+    {
+      editor "editor" format.names.ed duplicate$ empty$ 'pop$
+        {
+          " " *
+          get.bbl.editor
+          capitalize
+          "(" swap$ * "), " *
+          * swap$
+          * }
+      if$
+      word.in swap$ *
+    }
+  if$
+}
+FUNCTION {format.thesis.type}
+{ type duplicate$ empty$
+    'pop$
+    { swap$ pop$
+      "t" change.case$ "type" bibinfo.check
+    }
+  if$
+}
+FUNCTION {format.tr.number}
+{ number "number" bibinfo.check
+  type duplicate$ empty$
+    { pop$ bbl.techrep }
+    'skip$
+  if$
+  "type" bibinfo.check
+  swap$ duplicate$ empty$
+    { pop$ "t" change.case$ }
+    { tie.or.space.prefix * * }
+  if$
+}
+FUNCTION {format.article.crossref}
+{
+  word.in
+  " \cite{" * crossref * "}" *
+}
+FUNCTION {format.book.crossref}
+{ volume duplicate$ empty$
+    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
+      pop$ word.in
+    }
+    { bbl.volume
+      swap$ tie.or.space.prefix "volume" bibinfo.check * * bbl.of space.word *
+    }
+  if$
+  " \cite{" * crossref * "}" *
+}
+FUNCTION {format.incoll.inproc.crossref}
+{
+  word.in
+  " \cite{" * crossref * "}" *
+}
+FUNCTION {format.org.or.pub}
+{ 't :=
+  ""
+  address empty$ t empty$ and
+    'skip$
+    {
+      t empty$
+        { address "address" bibinfo.check *
+        }
+        { t *
+          address empty$
+            'skip$
+            { ", " * address "address" bibinfo.check * }
+          if$
+        }
+      if$
+    }
+  if$
+}
+FUNCTION {format.publisher.address}
+{ publisher "publisher" bibinfo.check format.org.or.pub
+}
+
+FUNCTION {format.organization.address}
+{ organization "organization" bibinfo.check format.org.or.pub
+}
+
+FUNCTION {print.url}
+ {url duplicate$ empty$
+   { pop$ "" }
+   { new.sentence
+     urlprefix "\url{" * swap$  * "}" *
+   }
+   if$
+ }
+
+FUNCTION {print.doi}
+ {doi duplicate$ empty$
+   { pop$ "" }
+   { new.sentence
+     doiprefix "\doi{" * swap$  * "}" *
+   }
+   if$
+ }
+
+FUNCTION {print.eprint}
+ {eprint duplicate$ empty$
+   { pop$ "" }
+   { new.sentence
+     duplicate$ "\href{http://arxiv.org/abs/" swap$ * "}{{\tt arXiv:" * swap$ * "}}" *
+   }
+   if$
+ }
+
+FUNCTION {print.pubmed}
+ {pubmed duplicate$ empty$
+   { pop$ "" }
+   { new.sentence
+     pubmedprefix "\Pubmed{" * swap$  * "}" *
+   }
+   if$
+ }
+
+FUNCTION {webpage}
+{ "%Type = Webpage" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  author empty$
+  {
+    format.title "title" output.check
+    new.block
+    format.date "year" output.check
+    date.block
+  }
+  {
+    format.date "year" output.check
+    date.block
+    format.title "title" output.check
+    new.block
+}
+  if$
+  print.url output
+  fin.entry
+}
+
+
+FUNCTION {article}
+{ "%Type = Article" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  new.block
+  format.title "title" output.check
+  new.block
+  crossref missing$
+    {
+      journal
+      "journal" bibinfo.check
+      "journal" output.check
+      add.blank
+      format.vol.num.pages output
+    }
+    { format.article.crossref output.nonnull
+    }
+  if$
+  format.journal.pages
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+FUNCTION {book}
+{ "%Type = Book" write$
+  output.bibitem
+  author empty$
+    { format.editors "author and editor" output.check
+      editor format.key output
+    }
+    { format.authors output.nonnull
+      crossref missing$
+        { "author and editor" editor either.or.check }
+        'skip$
+      if$
+    }
+  if$
+  format.btitle "title" output.check
+  crossref missing$
+    { format.bvolume output
+      format.number.series output
+      format.edition output
+      format.publisher.address output
+    }
+    {
+      format.book.crossref output.nonnull
+    }
+  if$
+  format.date "year" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+FUNCTION {booklet}
+{ "%Type = Booklet" write$
+  output.bibitem
+  format.authors output
+  author format.key output
+  format.title "title" output.check
+  howpublished "howpublished" bibinfo.check output
+  address "address" bibinfo.check output
+  format.date "year" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {inbook}
+{ "%Type = Inbook" write$
+  output.bibitem
+  author empty$
+    { format.editors "author and editor" output.check
+      editor format.key output
+    }
+    { format.authors output.nonnull
+      crossref missing$
+        { "author and editor" editor either.or.check }
+        'skip$
+      if$
+    }
+  if$
+  format.btitle "title" output.check
+  crossref missing$
+    {
+      format.bvolume output
+      format.number.series output
+      format.edition output
+      format.publisher.address output
+    }
+    {
+      format.book.crossref output.nonnull
+    }
+  if$
+  format.date "year" output.check
+  format.pages "pages" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {incollection}
+{ "%Type = Incollection" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  new.block
+  format.title "title" output.check
+  new.block
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.check
+      format.bvolume output
+      format.number.series output
+      format.edition output
+      format.publisher.address output
+    }
+    { format.incoll.inproc.crossref output.nonnull
+    }
+  if$
+  format.date "year" output.check
+  format.pages "pages" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+FUNCTION {inproceedings}
+{ "%Type = Inproceedings" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  new.block
+  format.title "title" output.check
+  new.block
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.check
+      format.bvolume output
+      format.number.series output
+      publisher empty$
+        { format.organization.address output }
+        { organization "organization" bibinfo.check output
+          format.publisher.address output
+        }
+      if$
+    }
+    { format.incoll.inproc.crossref output.nonnull
+    }
+  if$
+  format.date output
+  format.pages "pages" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+FUNCTION {conference} { inproceedings }
+FUNCTION {manual}
+{ "%Type = Manual" write$
+  output.bibitem
+  format.authors output
+  author format.key output
+  format.btitle "title" output.check
+  format.edition output
+  organization "organization" bibinfo.check output
+  address "address" bibinfo.check output
+  format.date "year" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {mastersthesis}
+{ "%Type = Masterthesis" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.btitle
+  "title" output.check
+  bbl.mthesis format.thesis.type output.nonnull
+  school "school" bibinfo.warn output
+  address "address" bibinfo.check output
+  format.date "year" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {misc}
+{ "%Type = Misc" write$
+  output.bibitem
+  format.authors output
+  author format.key output
+  format.title output
+  howpublished "howpublished" bibinfo.check output
+  format.date "year" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+FUNCTION {phdthesis}
+{ "%Type = Phdthesis" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.btitle
+  "title" output.check
+  bbl.phdthesis format.thesis.type output.nonnull
+  school "school" bibinfo.warn output
+  address "address" bibinfo.check output
+  format.date "year" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {proceedings}
+{ "%Type = Proceedings" write$
+  output.bibitem
+  format.editors output
+  editor format.key output
+  format.btitle "title" output.check
+  format.bvolume output
+  format.number.series output
+  publisher empty$
+    { format.organization.address output }
+    { organization "organization" bibinfo.check output
+      format.publisher.address output
+    }
+  if$
+  format.date "year" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {techreport}
+{ "%Type = Techreport" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.btitle
+  "title" output.check
+  format.tr.number output.nonnull
+  institution "institution" bibinfo.warn output
+  address "address" bibinfo.check output
+  format.date "year" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note output
+  fin.entry
+}
+
+FUNCTION {unpublished}
+{ "%Type = Unpublished" write$
+  output.bibitem
+  format.authors "author" output.check
+  author format.key output
+  format.title "title" output.check
+  format.date "year" output.check
+  new.sentence
+  print.url output
+  print.doi output
+  print.eprint output
+  print.pubmed output
+  format.note "note" output.check
+  fin.entry
+}
+
+FUNCTION {default.type} { misc }
+READ
+FUNCTION {sortify}
+{ purify$
+  "l" change.case$
+}
+INTEGERS { len }
+FUNCTION {chop.word}
+{ 's :=
+  'len :=
+  s #1 len substring$ =
+    { s len #1 + global.max$ substring$ }
+    's
+  if$
+}
+FUNCTION {format.lab.names}
+{ 's :=
+  "" 't :=
+  s #1 "{vv~}{ll}" format.name$
+  s num.names$ duplicate$
+  #2 >
+    { pop$
+      " " * bbl.etal *
+    }
+    { #2 <
+        'skip$
+        { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+            {
+              " " * bbl.etal *
+            }
+            { bbl.and space.word * s #2 "{vv~}{ll}" format.name$
+              * }
+          if$
+        }
+      if$
+    }
+  if$
+}
+
+FUNCTION {author.key.label}
+{ author empty$
+    { key empty$
+        { cite$ #1 #3 substring$ }
+        'key
+      if$
+    }
+    { author format.lab.names }
+  if$
+}
+
+FUNCTION {author.editor.key.label}
+{ author empty$
+    { editor empty$
+        { key empty$
+            { cite$ #1 #3 substring$ }
+            'key
+          if$
+        }
+        { editor format.lab.names }
+      if$
+    }
+    { author format.lab.names }
+  if$
+}
+
+FUNCTION {editor.key.label}
+{ editor empty$
+    { key empty$
+        { cite$ #1 #3 substring$ }
+        'key
+      if$
+    }
+    { editor format.lab.names }
+  if$
+}
+
+FUNCTION {calc.short.authors}
+{ type$ "book" =
+  type$ "inbook" =
+  or
+    'author.editor.key.label
+    { type$ "proceedings" =
+        'editor.key.label
+        'author.key.label
+      if$
+    }
+  if$
+  'short.list :=
+}
+
+FUNCTION {calc.label}
+{ calc.short.authors
+  short.list
+  "("
+  *
+  year duplicate$ empty$
+     { pop$ "????" }
+     { purify$ #-1 #4 substring$ }
+  if$
+  *
+  'label :=
+}
+
+FUNCTION {sort.format.names}
+{ 's :=
+  #1 'nameptr :=
+  ""
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      "{vv{ } }{ll{ }}{  f{ }}{  jj{ }}"
+      format.name$ 't :=
+      nameptr #1 >
+        {
+          "   "  *
+          namesleft #1 = t "others" = and
+            { "zzzzz" * }
+            { t sortify * }
+          if$
+        }
+        { t sortify * }
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+}
+
+FUNCTION {sort.format.title}
+{ 't :=
+  "A " #2
+    "An " #3
+      "The " #4 t chop.word
+    chop.word
+  chop.word
+  sortify
+  #1 global.max$ substring$
+}
+FUNCTION {author.sort}
+{ author empty$
+    { key empty$
+        { "to sort, need author or key in " cite$ * warning$
+          ""
+        }
+        { key sortify }
+      if$
+    }
+    { author sort.format.names }
+  if$
+}
+FUNCTION {author.editor.sort}
+{ author empty$
+    { editor empty$
+        { key empty$
+            { "to sort, need author, editor, or key in " cite$ * warning$
+              ""
+            }
+            { key sortify }
+          if$
+        }
+        { editor sort.format.names }
+      if$
+    }
+    { author sort.format.names }
+  if$
+}
+FUNCTION {editor.sort}
+{ editor empty$
+    { key empty$
+        { "to sort, need editor or key in " cite$ * warning$
+          ""
+        }
+        { key sortify }
+      if$
+    }
+    { editor sort.format.names }
+  if$
+}
+FUNCTION {presort}
+{ calc.label
+  label sortify
+  "    "
+  *
+  type$ "book" =
+  type$ "inbook" =
+  or
+    'author.editor.sort
+    { type$ "proceedings" =
+        'editor.sort
+        'author.sort
+      if$
+    }
+  if$
+  #1 entry.max$ substring$
+  'sort.label :=
+  sort.label
+  *
+  "    "
+  *
+  title field.or.null
+  sort.format.title
+  *
+  #1 entry.max$ substring$
+  'sort.key$ :=
+}
+
+ITERATE {presort}
+%SORT
+STRINGS { last.label next.extra }
+INTEGERS { last.extra.num number.label }
+FUNCTION {initialize.extra.label.stuff}
+{ #0 int.to.chr$ 'last.label :=
+  "" 'next.extra :=
+  #0 'last.extra.num :=
+  #0 'number.label :=
+}
+FUNCTION {forward.pass}
+{ last.label label =
+    { last.extra.num #1 + 'last.extra.num :=
+      last.extra.num int.to.chr$ 'extra.label :=
+    }
+    { "a" chr.to.int$ 'last.extra.num :=
+      "" 'extra.label :=
+      label 'last.label :=
+    }
+  if$
+  number.label #1 + 'number.label :=
+}
+FUNCTION {reverse.pass}
+{ next.extra "b" =
+    { "a" 'extra.label := }
+    'skip$
+  if$
+  extra.label 'next.extra :=
+  extra.label
+  duplicate$ empty$
+    'skip$
+    { "{\natexlab{" swap$ * "}}" * }
+  if$
+  'extra.label :=
+  label extra.label * 'label :=
+}
+EXECUTE {initialize.extra.label.stuff}
+ITERATE {forward.pass}
+REVERSE {reverse.pass}
+FUNCTION {bib.sort.order}
+{ sort.label
+  "    "
+  *
+  year field.or.null sortify
+  *
+  "    "
+  *
+  title field.or.null
+  sort.format.title
+  *
+  #1 entry.max$ substring$
+  'sort.key$ :=
+}
+ITERATE {bib.sort.order}
+%SORT
+FUNCTION {begin.bib}
+{ preamble$ empty$
+    'skip$
+    { preamble$ write$ newline$ }
+  if$
+  "\begin{thebibliography}{" number.label int.to.str$ * "}" *
+  write$ newline$
+  "\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi"
+  write$ newline$
+  "\providecommand{\url}[1]{\texttt{#1}}"
+  write$ newline$
+  "\providecommand{\href}[2]{#2}"
+  write$ newline$
+  "\providecommand{\path}[1]{#1}"
+  write$ newline$
+  "\providecommand{\DOIprefix}{doi:}"
+  write$ newline$
+  "\providecommand{\ArXivprefix}{arXiv:}"
+  write$ newline$
+  "\providecommand{\URLprefix}{URL: }"
+  write$ newline$
+  "\providecommand{\Pubmedprefix}{pmid:}"
+  write$ newline$
+  "\providecommand{\doi}[1]{\href{http://dx.doi.org/#1}{\path{#1}}}"
+  write$ newline$
+  "\providecommand{\Pubmed}[1]{\href{pmid:#1}{\path{#1}}}"
+  write$ newline$
+  "\providecommand{\bibinfo}[2]{#2}"
+  write$ newline$
+	"\ifx\xfnm\relax \def\xfnm[#1]{\unskip,\space#1}\fi"
+  write$ newline$
+}
+EXECUTE {begin.bib}
+EXECUTE {init.state.consts}
+EXECUTE {init.web.variables} 
+ITERATE {call.type$}
+FUNCTION {end.bib}
+{ newline$
+  "\end{thebibliography}" write$ newline$
+}
+EXECUTE {end.bib}
+%% End of customized bst file
+%%
+%% End of file `elsarticle-num-names.bst'.
+%%
+%%
+%% Change log:
+%% -----------
+%% 22.04.2011
+%%
+%% 10.08.2012
+%%   a. doi, url, eprint, pmid added
+%%   b. Bibtype `webpage' defined
+%%
+%% 30.08.2012
+%%   a. collaboration added.
+
+
diff --git a/papers/variational_smoother/elsarticle-num.bst b/papers/variational_smoother/elsarticle-num.bst
new file mode 100644
index 0000000..5e6b721
--- /dev/null
+++ b/papers/variational_smoother/elsarticle-num.bst
@@ -0,0 +1,1509 @@
+%%
+%% This is file `elsarticle-num.bst' (Version 2.1),
+%% 
+%% Copyright 2007-2024 Elsevier Ltd
+%% 
+%% This file is part of the 'Elsarticle Bundle'.
+%% ---------------------------------------------
+%% 
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.3 of this license or (at your option) any
+%% later version.  The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%% 
+%% 
+%% $Id: elsarticle-num.bst 254 2024-04-06 10:58:22Z rishi $
+%% 
+%% $URL: https://lenova.river-valley.com/svn/elsarticle/trunk/elsarticle-num.bst $
+%%
+%% ----------------------------------------
+
+ENTRY
+  { address
+    author
+    booktitle
+    chapter
+    edition
+    editor
+    howpublished
+    institution
+    journal
+    key
+    month
+    note
+    number
+    organization
+    pages
+    publisher
+    school
+    series
+    title
+    type
+    volume
+    year
+    eprint % urlbst
+    doi % urlbst
+    url % urlbst
+    lastchecked % urlbst
+  }
+  {}
+  { label }
+
+INTEGERS { output.state before.all mid.sentence after.sentence after.block }
+
+STRINGS { urlintro eprinturl eprintprefix doiprefix doiurl openinlinelink closeinlinelink } % urlbst...
+INTEGERS { hrefform inlinelinks makeinlinelink addeprints adddoiresolver }
+FUNCTION {init.urlbst.variables}
+{
+  "Available from: " 'urlintro := % prefix before URL
+  "http://arxiv.org/abs/" 'eprinturl := % prefix to make URL from eprint ref
+  "arXiv:" 'eprintprefix := % text prefix printed before eprint ref
+  "https://doi.org/" 'doiurl := % prefix to make URL from DOI
+  "doi:" 'doiprefix :=      % text prefix printed before DOI ref
+  #1 'addeprints :=         % 0=no eprints; 1=include eprints
+  #1 'adddoiresolver :=     % 0=no DOI resolver; 1=include it
+  #2 'hrefform :=           % 0=no crossrefs; 1=hypertex xrefs; 2=hyperref refs
+  #1 'inlinelinks :=        % 0=URLs explicit; 1=URLs attached to titles
+  % the following are internal state variables, not config constants
+  #0 'makeinlinelink :=     % state variable managed by setup.inlinelink
+  "" 'openinlinelink :=     % ditto
+  "" 'closeinlinelink :=    % ditto
+}
+INTEGERS {
+  bracket.state
+  outside.brackets
+  open.brackets
+  within.brackets
+  close.brackets
+}
+FUNCTION {init.state.consts}
+{ #0 'outside.brackets := % urlbst
+  #1 'open.brackets :=
+  #2 'within.brackets :=
+  #3 'close.brackets :=
+
+  #0 'before.all :=
+  #1 'mid.sentence :=
+  #2 'after.sentence :=
+  #3 'after.block :=
+}
+
+STRINGS { s t }
+
+FUNCTION {output.nonnull.original}
+{ 's :=
+  output.state mid.sentence =
+    { ", " * write$ }
+    { output.state after.block =
+        { add.period$ write$
+          newline$
+          "\newblock " write$
+        }
+        { output.state before.all =
+            'write$
+            { add.period$ " " * write$ }
+          if$
+        }
+      if$
+      mid.sentence 'output.state :=
+    }
+  if$
+  s
+}
+
+FUNCTION {setup.inlinelink}
+{ makeinlinelink
+    { hrefform #1 = % hypertex
+        { "\special {html:<a href=" quote$ * url * quote$ * "> }{" * 'openinlinelink :=
+          "\special {html:</a>}" 'closeinlinelink :=
+          }
+        { hrefform #2 = % hyperref
+            { "\href{" url * "}{" * 'openinlinelink :=
+              "}" 'closeinlinelink :=
+              }
+            'skip$
+          if$ % hrefform #2 =
+        }
+      if$ % hrefform #1 =
+      #0 'makeinlinelink :=
+    }
+    'skip$
+ if$ % makeinlinelink
+}
+FUNCTION {add.inlinelink}
+{ openinlinelink empty$
+    'skip$
+    { openinlinelink swap$ * closeinlinelink *
+      "" 'openinlinelink :=
+      }
+  if$
+}
+FUNCTION {output.nonnull}
+{ % Save the thing we've been asked to output
+  's :=
+  % If the bracket-state is close.brackets, then add a close-bracket to
+  % what is currently at the top of the stack, and set bracket.state
+  % to outside.brackets
+  bracket.state close.brackets =
+    { "]" *
+      outside.brackets 'bracket.state :=
+    }
+    'skip$
+  if$
+  bracket.state outside.brackets =
+    { % We're outside all brackets -- this is the normal situation.
+      % Write out what's currently at the top of the stack, using the
+      % original output.nonnull function.
+      s
+      add.inlinelink
+      output.nonnull.original % invoke the original output.nonnull
+    }
+    { % Still in brackets.  Add open-bracket or (continuation) comma, add the
+      % new text (in s) to the top of the stack, and move to the close-brackets
+      % state, ready for next time (unless inbrackets resets it).  If we come
+      % into this branch, then output.state is carefully undisturbed.
+      bracket.state open.brackets =
+        { " [" * }
+        { ", " * } % bracket.state will be within.brackets
+      if$
+      s *
+      close.brackets 'bracket.state :=
+    }
+  if$
+}
+
+FUNCTION {inbrackets}
+{ bracket.state close.brackets =
+    { within.brackets 'bracket.state := } % reset the state: not open nor closed
+    { open.brackets 'bracket.state := }
+  if$
+}
+
+FUNCTION {format.lastchecked}
+{ lastchecked empty$
+    { "" }
+    { inbrackets "cited " lastchecked * }
+  if$
+}
+
+FUNCTION {output}
+{ duplicate$ empty$
+    'pop$
+    'output.nonnull
+  if$
+}
+
+FUNCTION {output.check}
+{ 't :=
+  duplicate$ empty$
+    { pop$ "empty " t * " in " * cite$ * warning$ }
+    'output.nonnull
+  if$
+}
+
+FUNCTION {fin.entry.original}
+{ add.period$
+  write$
+  newline$
+}
+
+FUNCTION {new.block}
+{ output.state before.all =
+    'skip$
+    { after.block 'output.state := }
+  if$
+}
+
+FUNCTION {new.sentence}
+{ output.state after.block =
+    'skip$
+    { output.state before.all =
+        'skip$
+        { after.sentence 'output.state := }
+      if$
+    }
+  if$
+}
+
+FUNCTION {add.blank}
+{  " " * before.all 'output.state :=
+}
+
+FUNCTION {date.block}
+{
+  add.blank
+}
+
+FUNCTION {not}
+{   { #0 }
+    { #1 }
+  if$
+}
+
+FUNCTION {and}
+{   'skip$
+    { pop$ #0 }
+  if$
+}
+
+FUNCTION {or}
+{   { pop$ #1 }
+    'skip$
+  if$
+}
+
+FUNCTION {new.block.checka}
+{ empty$
+    'skip$
+    'new.block
+  if$
+}
+
+FUNCTION {new.block.checkb}
+{ empty$
+  swap$ empty$
+  and
+    'skip$
+    'new.block
+  if$
+}
+
+FUNCTION {new.sentence.checka}
+{ empty$
+    'skip$
+    'new.sentence
+  if$
+}
+
+FUNCTION {new.sentence.checkb}
+{ empty$
+  swap$ empty$
+  and
+    'skip$
+    'new.sentence
+  if$
+}
+
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+    { pop$ "" }
+    'skip$
+  if$
+}
+
+FUNCTION {emphasize}
+{ skip$ }
+
+FUNCTION {capitalize}
+{ "u" change.case$ "t" change.case$ }
+
+FUNCTION {space.word}
+{ " " swap$ * " " * }
+
+ % Here are the language-specific definitions for explicit words.
+ % Each function has a name bbl.xxx where xxx is the English word.
+ % The language selected here is ENGLISH
+FUNCTION {bbl.and}
+{ "and"}
+
+FUNCTION {bbl.etal}
+{ "et~al." }
+
+FUNCTION {bbl.editors}
+{ "Eds." }
+
+FUNCTION {bbl.editor}
+{ "Ed." }
+
+FUNCTION {bbl.edby}
+{ "edited by" }
+
+FUNCTION {bbl.edition}
+{ "Edition" }
+
+FUNCTION {bbl.volume}
+{ "Vol." }
+
+FUNCTION {bbl.of}
+{ "of" }
+
+FUNCTION {bbl.number}
+{ "no." }
+
+FUNCTION {bbl.nr}
+{ "no." }
+
+FUNCTION {bbl.in}
+{ "in" }
+
+FUNCTION {bbl.pages}
+{ "pp." }
+
+FUNCTION {bbl.page}
+{ "p." }
+
+FUNCTION {bbl.chapter}
+{ "Ch." }
+
+FUNCTION {bbl.techrep}
+{ "Tech. Rep." }
+
+FUNCTION {bbl.mthesis}
+{ "Master's thesis" }
+
+FUNCTION {bbl.phdthesis}
+{ "Ph.D. thesis" }
+
+FUNCTION {bbl.first}
+{ "1st" }
+
+FUNCTION {bbl.second}
+{ "2nd" }
+
+FUNCTION {bbl.third}
+{ "3rd" }
+
+FUNCTION {bbl.fourth}
+{ "4th" }
+
+FUNCTION {bbl.fifth}
+{ "5th" }
+
+FUNCTION {bbl.st}
+{ "st" }
+
+FUNCTION {bbl.nd}
+{ "nd" }
+
+FUNCTION {bbl.rd}
+{ "rd" }
+
+FUNCTION {bbl.th}
+{ "th" }
+
+MACRO {jan} {"Jan."}
+
+MACRO {feb} {"Feb."}
+
+MACRO {mar} {"Mar."}
+
+MACRO {apr} {"Apr."}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"Jun."}
+
+MACRO {jul} {"Jul."}
+
+MACRO {aug} {"Aug."}
+
+MACRO {sep} {"Sep."}
+
+MACRO {oct} {"Oct."}
+
+MACRO {nov} {"Nov."}
+
+MACRO {dec} {"Dec."}
+
+FUNCTION {eng.ord}
+{ duplicate$ "1" swap$ *
+  #-2 #1 substring$ "1" =
+     { bbl.th * }
+     { duplicate$ #-1 #1 substring$
+       duplicate$ "1" =
+         { pop$ bbl.st * }
+         { duplicate$ "2" =
+             { pop$ bbl.nd * }
+             { "3" =
+                 { bbl.rd * }
+                 { bbl.th * }
+               if$
+             }
+           if$
+          }
+       if$
+     }
+   if$
+}
+
+MACRO {acmcs} {"ACM Comput. Surv."}
+
+MACRO {acta} {"Acta Inf."}
+
+MACRO {cacm} {"Commun. ACM"}
+
+MACRO {ibmjrd} {"IBM J. Res. Dev."}
+
+MACRO {ibmsj} {"IBM Syst.~J."}
+
+MACRO {ieeese} {"IEEE Trans. Softw. Eng."}
+
+MACRO {ieeetc} {"IEEE Trans. Comput."}
+
+MACRO {ieeetcad}
+ {"IEEE Trans. Comput.-Aided Design Integrated Circuits"}
+
+MACRO {ipl} {"Inf. Process. Lett."}
+
+MACRO {jacm} {"J.~ACM"}
+
+MACRO {jcss} {"J.~Comput. Syst. Sci."}
+
+MACRO {scp} {"Sci. Comput. Programming"}
+
+MACRO {sicomp} {"SIAM J. Comput."}
+
+MACRO {tocs} {"ACM Trans. Comput. Syst."}
+
+MACRO {tods} {"ACM Trans. Database Syst."}
+
+MACRO {tog} {"ACM Trans. Gr."}
+
+MACRO {toms} {"ACM Trans. Math. Softw."}
+
+MACRO {toois} {"ACM Trans. Office Inf. Syst."}
+
+MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."}
+
+MACRO {tcs} {"Theoretical Comput. Sci."}
+
+FUNCTION {write.url}
+{ url empty$
+    { skip$ }
+    { "\newline\urlprefix\url{" url * "}" * write$ newline$ }
+  if$
+}
+
+INTEGERS { nameptr namesleft numnames }
+
+FUNCTION {format.names}
+{ 's :=
+  #1 'nameptr :=
+  s num.names$ 'numnames :=
+  numnames 'namesleft :=
+    { namesleft #0 > }
+    { s nameptr
+      "{f.~}{vv~}{ll}{, jj}" format.name$
+    't :=
+      nameptr #1 >
+        {
+          namesleft #1 >
+            { ", " * t * }
+            {
+              "," *
+              s nameptr "{ll}" format.name$ duplicate$ "others" =
+                { 't := }
+                { pop$ }
+              if$
+              t "others" =
+                {
+                  " " * bbl.etal *
+                }
+                { " " * t * }
+              if$
+            }
+          if$
+        }
+        't
+      if$
+      nameptr #1 + 'nameptr :=
+      namesleft #1 - 'namesleft :=
+    }
+  while$
+}
+FUNCTION {format.names.ed}
+{ format.names }
+FUNCTION {format.authors}
+{ author empty$
+    { "" }
+    { author format.names }
+  if$
+}
+
+FUNCTION {format.editors}
+{ editor empty$
+    { "" }
+    { editor format.names
+      editor num.names$ #1 >
+        { " (" * bbl.editors * ")" * }
+        { " (" * bbl.editor * ")" * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.in.editors}
+{ editor empty$
+    { "" }
+    { editor format.names.ed
+      editor num.names$ #1 >
+        { " (" * bbl.editors * ")" * }
+        { " (" * bbl.editor * ")" * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.note}
+{
+ note empty$
+    { "" }
+    { note #1 #1 substring$
+      duplicate$ "{" =
+        'skip$
+        { output.state mid.sentence =
+          { "l" }
+          { "u" }
+        if$
+        change.case$
+        }
+      if$
+      note #2 global.max$ substring$ *
+    }
+  if$
+}
+
+FUNCTION {format.title}
+{ title empty$
+    { "" }
+    { title "t" change.case$
+    }
+  if$
+}
+
+FUNCTION {output.bibitem.original}
+{ newline$
+  "\bibitem{" write$
+  cite$ write$
+  "}" write$
+  newline$
+  ""
+  before.all 'output.state :=
+}
+
+FUNCTION {n.dashify}
+{
+  't :=
+  ""
+    { t empty$ not }
+    { t #1 #1 substring$ "-" =
+        { t #1 #2 substring$ "--" = not
+            { "--" *
+              t #2 global.max$ substring$ 't :=
+            }
+            {   { t #1 #1 substring$ "-" = }
+                { "-" *
+                  t #2 global.max$ substring$ 't :=
+                }
+              while$
+            }
+          if$
+        }
+        { t #1 #1 substring$ *
+          t #2 global.max$ substring$ 't :=
+        }
+      if$
+    }
+  while$
+}
+
+FUNCTION {word.in}
+{ bbl.in
+  ":" *
+  " " * }
+
+FUNCTION {format.date}
+{ year empty$
+    { month empty$
+        { "" }
+        { "there's a month but no year in " cite$ * warning$
+          month
+        }
+      if$
+    }
+    { month empty$
+        'year
+        { month " " * year * }
+      if$
+    }
+  if$
+  duplicate$ empty$
+    'skip$
+    {
+      before.all 'output.state :=
+    " (" swap$ * ")" *
+    }
+  if$
+}
+
+FUNCTION{format.year}
+{ year duplicate$ empty$
+    { "empty year in " cite$ * warning$ pop$ "" }
+    { "(" swap$ * ")" * }
+  if$
+}
+
+FUNCTION {format.btitle}
+{ title
+}
+
+FUNCTION {tie.or.space.connect}
+{ duplicate$ text.length$ #3 <
+    { "~" }
+    { " " }
+  if$
+  swap$ * *
+}
+
+FUNCTION {either.or.check}
+{ empty$
+    'pop$
+    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+  if$
+}
+
+FUNCTION {format.bvolume}
+{ volume empty$
+    { "" }
+    { bbl.volume volume tie.or.space.connect
+      series empty$
+        'skip$
+        { bbl.of space.word * series emphasize * }
+      if$
+      "volume and number" number either.or.check
+    }
+  if$
+}
+
+FUNCTION {format.number.series}
+{ volume empty$
+    { number empty$
+        { series field.or.null }
+        { output.state mid.sentence =
+            { bbl.number }
+            { bbl.number capitalize }
+          if$
+          number tie.or.space.connect
+          series empty$
+            { "there's a number but no series in " cite$ * warning$ }
+            { bbl.in space.word * series * }
+          if$
+        }
+      if$
+    }
+    { "" }
+  if$
+}
+
+FUNCTION {is.num}
+{ chr.to.int$
+  duplicate$ "0" chr.to.int$ < not
+  swap$ "9" chr.to.int$ > not and
+}
+
+FUNCTION {extract.num}
+{ duplicate$ 't :=
+  "" 's :=
+  { t empty$ not }
+  { t #1 #1 substring$
+    t #2 global.max$ substring$ 't :=
+    duplicate$ is.num
+      { s swap$ * 's := }
+      { pop$ "" 't := }
+    if$
+  }
+  while$
+  s empty$
+    'skip$
+    { pop$ s }
+  if$
+}
+
+FUNCTION {convert.edition}
+{ edition extract.num "l" change.case$ 's :=
+  s "first" = s "1" = or
+    { bbl.first 't := }
+    { s "second" = s "2" = or
+        { bbl.second 't := }
+        { s "third" = s "3" = or
+            { bbl.third 't := }
+            { s "fourth" = s "4" = or
+                { bbl.fourth 't := }
+                { s "fifth" = s "5" = or
+                    { bbl.fifth 't := }
+                    { s #1 #1 substring$ is.num
+                        { s eng.ord 't := }
+                        { edition 't := }
+                      if$
+                    }
+                  if$
+                }
+              if$
+            }
+          if$
+        }
+      if$
+    }
+  if$
+  t
+}
+
+FUNCTION {format.edition}
+{ edition empty$
+    { "" }
+    { output.state mid.sentence =
+        { convert.edition "l" change.case$ " " * bbl.edition * }
+        { convert.edition "t" change.case$ " " * bbl.edition * }
+      if$
+    }
+  if$
+}
+
+INTEGERS { multiresult }
+
+FUNCTION {multi.page.check}
+{ 't :=
+  #0 'multiresult :=
+    { multiresult not
+      t empty$ not
+      and
+    }
+    { t #1 #1 substring$
+      duplicate$ "-" =
+      swap$ duplicate$ "," =
+      swap$ "+" =
+      or or
+        { #1 'multiresult := }
+        { t #2 global.max$ substring$ 't := }
+      if$
+    }
+  while$
+  multiresult
+}
+
+FUNCTION {format.pages}
+{ pages empty$
+    { "" }
+    { pages multi.page.check
+        { bbl.pages pages n.dashify tie.or.space.connect }
+        { bbl.page pages tie.or.space.connect }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.journal.pages}
+{ pages empty$
+    'skip$
+    { duplicate$ empty$
+        { pop$ format.pages }
+        {
+          " " *
+          format.year * " " *
+          pages n.dashify *
+        }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.vol.num.pages}
+{
+  % volume field.or.null
+  " "
+  volume empty$
+    { pop$ "" }
+    { volume * }
+  if$
+  number empty$
+    'skip$
+    {
+      "~(" number * ")" * *
+      volume empty$
+        { "there's a number but no volume in " cite$ * warning$ }
+        'skip$
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+    { "" }
+    { type empty$
+        { bbl.chapter }
+        { type "l" change.case$ }
+      if$
+      chapter tie.or.space.connect
+    }
+  if$
+}
+
+FUNCTION {format.in.ed.booktitle}
+{ booktitle empty$
+    { "" }
+    { editor empty$
+        { word.in booktitle * }
+        { word.in format.in.editors * ", " *
+          booktitle * }
+      if$
+    }
+  if$
+}
+
+FUNCTION {empty.misc.check}
+{ author empty$ title empty$ howpublished empty$
+  month empty$ year empty$ note empty$
+  and and and and and
+    { "all relevant fields are empty in " cite$ * warning$ }
+    'skip$
+  if$
+}
+
+FUNCTION {format.thesis.type}
+{ type empty$
+    'skip$
+    { pop$
+      type "t" change.case$
+    }
+  if$
+}
+
+FUNCTION {format.tr.number}
+{ type empty$
+    { bbl.techrep }
+    'type
+  if$
+  number empty$
+    { "t" change.case$ }
+    { number tie.or.space.connect }
+  if$
+}
+
+FUNCTION {format.article.crossref}
+{
+  key empty$
+    { journal empty$
+        { "need key or journal for " cite$ * " to crossref " * crossref *
+          warning$
+          ""
+        }
+        { word.in journal emphasize * }
+      if$
+    }
+    { word.in key * " " *}
+  if$
+  " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.crossref.editor}
+{ editor #1 "{vv~}{ll}" format.name$
+  editor num.names$ duplicate$
+  #2 >
+    { pop$
+      " " * bbl.etal *
+    }
+    { #2 <
+        'skip$
+        { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+            {
+              " " * bbl.etal *
+            }
+            { bbl.and space.word * editor #2 "{vv~}{ll}" format.name$
+              * }
+          if$
+        }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.book.crossref}
+{ volume empty$
+    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
+      word.in
+    }
+    { bbl.volume volume tie.or.space.connect
+      bbl.of space.word *
+    }
+  if$
+  editor empty$
+  editor field.or.null author field.or.null =
+  or
+    { key empty$
+        { series empty$
+            { "need editor, key, or series for " cite$ * " to crossref " *
+              crossref * warning$
+              "" *
+            }
+            { series emphasize * }
+          if$
+        }
+        { key * }
+      if$
+    }
+    { format.crossref.editor * }
+  if$
+  " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.incoll.inproc.crossref}
+{
+  editor empty$
+  editor field.or.null author field.or.null =
+  or
+    { key empty$
+        { booktitle empty$
+            { "need editor, key, or booktitle for " cite$ * " to crossref " *
+              crossref * warning$
+              ""
+            }
+            { word.in booktitle * }
+          if$
+        }
+        { word.in key * " " *}
+      if$
+    }
+    { word.in format.crossref.editor * " " *}
+  if$
+  " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.org.or.pub}
+{ 't :=
+  ""
+  year empty$
+    { "empty year in " cite$ * warning$ }
+    'skip$
+  if$
+  address empty$ t empty$ and
+  year empty$ and
+    'skip$
+    {
+      t empty$
+        { address empty$
+          'skip$
+          { address * }
+          if$
+        }
+        { t *
+          address empty$
+            'skip$
+            { ", " * address * }
+          if$
+        }
+      if$
+      year empty$
+        'skip$
+        { t empty$ address empty$ and
+            'skip$
+            { ", " * }
+          if$
+          year *
+        }
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.publisher.address}
+{ publisher empty$
+    { "empty publisher in " cite$ * warning$
+      ""
+    }
+    { publisher }
+  if$
+  format.org.or.pub
+}
+
+FUNCTION {format.organization.address}
+{ organization empty$
+    { "" }
+    { organization }
+  if$
+  format.org.or.pub
+}
+
+FUNCTION {make.href.null}
+{
+  pop$
+}
+FUNCTION {make.href.hypertex}
+{
+  "\special {html:<a href=" quote$ *
+  swap$ * quote$ * "> }" * swap$ *
+  "\special {html:</a>}" *
+}
+FUNCTION {make.href.hyperref}
+{
+  "\href {" swap$ * "} {\path{" * swap$ * "}}" *
+}
+FUNCTION {make.href}
+{ hrefform #2 =
+    'make.href.hyperref      % hrefform = 2
+    { hrefform #1 =
+        'make.href.hypertex  % hrefform = 1
+        'make.href.null      % hrefform = 0 (or anything else)
+      if$
+    }
+  if$
+}
+
+FUNCTION {format.url}
+{ inlinelinks #1 = url empty$ or
+   { "" }
+   { hrefform #1 =
+       { % special case -- add HyperTeX specials
+         urlintro "\url{" url * "}" * url make.href.hypertex * }
+       { urlintro "\url{" * url * "}" * }
+     if$
+   }
+  if$
+}
+
+FUNCTION {format.eprint}
+{ eprint empty$
+    { "" }
+    { eprintprefix eprint * eprinturl eprint * make.href }
+  if$
+}
+
+FUNCTION {format.doi}
+{ doi empty$
+    { "" }
+    { doiprefix doi * doiurl doi * make.href }
+  if$
+}
+
+FUNCTION {output.url}
+{ url empty$
+    'skip$
+    { new.block
+      format.url output
+      format.lastchecked output
+    }
+  if$
+}
+
+FUNCTION {output.web.refs}
+{
+  new.block
+  output.url
+  addeprints eprint empty$ not and
+    { format.eprint output.nonnull }
+    'skip$
+  if$
+  adddoiresolver doi empty$ not and
+    { format.doi output.nonnull }
+    'skip$
+  if$
+}
+
+FUNCTION {output.bibitem}
+{ outside.brackets 'bracket.state :=
+  output.bibitem.original
+  inlinelinks url empty$ not and
+    { #1 'makeinlinelink := }
+    { #0 'makeinlinelink := }
+  if$
+}
+
+FUNCTION {fin.entry}
+{ output.web.refs  % urlbst
+  makeinlinelink       % ooops, it appears we didn't have a title for inlinelink
+    { setup.inlinelink % add some artificial link text here, as a fallback
+      "[link]" output.nonnull }
+    'skip$
+  if$
+  bracket.state close.brackets = % urlbst
+    { "]" * }
+    'skip$
+  if$
+  fin.entry.original
+}
+
+FUNCTION {webpage}
+{ output.bibitem
+  author empty$
+    { editor empty$
+        'skip$  % author and editor both optional
+        { format.editors output.nonnull }
+      if$
+    }
+    { editor empty$
+        { format.authors output.nonnull }
+        { "can't use both author and editor fields in " cite$ * warning$ }
+      if$
+    }
+  if$
+  new.block
+  title empty$ 'skip$ 'setup.inlinelink if$
+  format.title "title" output.check
+  inbrackets "online" output
+  new.block
+  year empty$
+    'skip$
+    { format.date "year" output.check }
+  if$
+  % We don't need to output the URL details ('lastchecked' and 'url'),
+  % because fin.entry does that for us, using output.web.refs.  The only
+  % reason we would want to put them here is if we were to decide that
+  % they should go in front of the rather miscellaneous information in 'note'.
+  new.block
+  note output
+  fin.entry
+}
+
+FUNCTION {article}
+{ output.bibitem
+  format.authors "author" output.check
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.title "title" output.check
+  crossref missing$
+    { journal
+      "journal" output.check
+      % add.blank
+  before.all 'output.state :=
+      format.vol.num.pages output
+    }
+    { format.article.crossref output.nonnull
+      format.pages output
+    }
+  if$
+  format.journal.pages
+  format.note output
+  pages empty$  
+	  { format.date "year" output.check }
+    'skip$ 
+  if$
+  fin.entry
+  write.url
+}
+
+FUNCTION {book}
+{ output.bibitem
+  author empty$
+    { format.editors "author and editor" output.check
+    }
+    { format.authors output.nonnull
+      crossref missing$
+        { "author and editor" editor either.or.check }
+        'skip$
+      if$
+    }
+  if$
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.btitle "title" output.check
+  crossref missing$
+    { format.edition output
+      format.bvolume output
+      format.number.series output
+      format.publisher.address output
+    }
+    {
+      format.book.crossref output.nonnull
+    }
+  if$
+  format.note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {booklet}
+{ output.bibitem
+  format.authors output
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.title "title" output.check
+  howpublished output
+  address output
+  format.note output
+  format.date "year" output.check
+  fin.entry
+  write.url
+}
+
+FUNCTION {inbook}
+{ output.bibitem
+  author empty$
+    { format.editors "author and editor" output.check
+    }
+    { format.authors output.nonnull
+      crossref missing$
+        { "author and editor" editor either.or.check }
+        'skip$
+      if$
+    }
+  if$
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.btitle "title" output.check
+  crossref missing$
+    {
+      format.edition output
+      format.bvolume output
+      format.number.series output
+      format.publisher.address output
+      format.chapter.pages "chapter and pages" output.check
+    }
+    {
+      format.chapter.pages "chapter and pages" output.check
+      format.book.crossref output.nonnull
+    }
+  if$
+  format.pages "pages" output.check
+  format.note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {incollection}
+{ output.bibitem
+  format.authors "author" output.check
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.title "title" output.check
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.check
+      format.edition output
+      format.bvolume output
+      format.number.series output
+      format.publisher.address output
+      format.chapter.pages output
+    }
+    { format.incoll.inproc.crossref output.nonnull
+      format.chapter.pages output
+    }
+  if$
+  format.pages "pages" output.check
+  format.note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {inproceedings}
+{ output.bibitem
+  format.authors "author" output.check
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.title "title" output.check
+  crossref missing$
+    { format.in.ed.booktitle "booktitle" output.check
+      format.edition output
+      format.bvolume output
+      format.number.series output
+      publisher empty$
+        { format.organization.address output }
+        { organization output
+          format.publisher.address output
+        }
+      if$
+    }
+    { format.incoll.inproc.crossref output.nonnull
+    }
+  if$
+  format.pages "pages" output.check
+  format.note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {conference} { inproceedings }
+
+FUNCTION {manual}
+{ output.bibitem
+  author empty$
+    { organization empty$
+        'skip$
+        { organization output.nonnull
+          address output
+        }
+      if$
+    }
+    { format.authors output.nonnull }
+  if$
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.btitle "title" output.check
+  author empty$
+    { organization empty$
+    {
+          address output
+        }
+        'skip$
+      if$
+    }
+    {
+      organization output
+      address output
+    }
+  if$
+  format.edition output
+  format.note output
+  format.date "year" output.check
+  fin.entry
+  write.url
+}
+
+FUNCTION {mastersthesis}
+{ output.bibitem
+  format.authors "author" output.check
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.title "title" output.check
+  bbl.mthesis format.thesis.type output.nonnull
+  school "school" output.check
+  address output
+  format.note output
+  format.date "year" output.check
+  fin.entry
+  write.url
+}
+
+FUNCTION {misc}
+{ output.bibitem
+  format.authors output
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.title output
+  howpublished output
+  format.note output
+  format.date "year" output.check
+  fin.entry
+  write.url
+  empty.misc.check
+}
+
+FUNCTION {phdthesis}
+{ output.bibitem
+  format.authors "author" output.check
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.title "title" output.check
+  bbl.phdthesis format.thesis.type output.nonnull
+  school "school" output.check
+  address output
+  format.note output
+  format.date "year" output.check
+  fin.entry
+  write.url
+}
+
+FUNCTION {proceedings}
+{ output.bibitem
+  editor empty$
+    { organization output }
+    { format.editors output.nonnull }
+  if$
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.btitle "title" output.check
+  format.bvolume output
+  format.number.series output
+  editor empty$
+    { publisher empty$
+        'skip$
+        {
+          format.publisher.address output
+        }
+      if$
+    }
+    { publisher empty$
+        {
+          format.organization.address output }
+        {
+          organization output
+          format.publisher.address output
+        }
+      if$
+     }
+  if$
+  format.note output
+  fin.entry
+  write.url
+}
+
+FUNCTION {techreport}
+{ output.bibitem
+  format.authors "author" output.check
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.title "title" output.check
+  format.tr.number output.nonnull
+  institution "institution" output.check
+  address output
+  format.note output
+  format.date "year" output.check
+  fin.entry
+  write.url
+}
+
+FUNCTION {unpublished}
+{ output.bibitem
+  format.authors "author" output.check
+  title empty$ 'skip$ 'setup.inlinelink if$ % urlbst
+  format.title "title" output.check
+  format.note "note" output.check
+  format.date "year" output.check
+  fin.entry
+  write.url
+}
+
+FUNCTION {default.type} { misc }
+
+READ
+
+STRINGS { longest.label }
+
+INTEGERS { number.label longest.label.width }
+
+FUNCTION {initialize.longest.label}
+{ "" 'longest.label :=
+  #1 'number.label :=
+  #0 'longest.label.width :=
+}
+
+FUNCTION {longest.label.pass}
+{ number.label int.to.str$ 'label :=
+  number.label #1 + 'number.label :=
+  label width$ longest.label.width >
+    { label 'longest.label :=
+      label width$ 'longest.label.width :=
+    }
+    'skip$
+  if$
+}
+
+EXECUTE {initialize.longest.label}
+
+ITERATE {longest.label.pass}
+
+FUNCTION {begin.bib}
+{ preamble$ empty$
+    'skip$
+    { preamble$ write$ newline$ }
+  if$
+  "\begin{thebibliography}{"  longest.label  * "}" *
+  write$ newline$
+  "\expandafter\ifx\csname url\endcsname\relax"
+  write$ newline$
+  "  \def\url#1{\texttt{#1}}\fi"
+  write$ newline$
+  "\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi"
+  write$ newline$
+  "\expandafter\ifx\csname href\endcsname\relax"
+  write$ newline$
+  "  \def\href#1#2{#2} \def\path#1{#1}\fi"
+  write$ newline$
+}
+
+EXECUTE {begin.bib}
+
+EXECUTE {init.urlbst.variables}
+EXECUTE {init.state.consts}
+
+ITERATE {call.type$}
+
+FUNCTION {end.bib}
+{ newline$
+  "\end{thebibliography}" write$ newline$
+}
+
+EXECUTE {end.bib}
+%% End of customized bst file
+%%
+%% End of file `elsarticle-num.bst'.
+
+
diff --git a/papers/variational_smoother/elsarticle-template-harv.tex b/papers/variational_smoother/elsarticle-template-harv.tex
new file mode 100644
index 0000000..5a9e013
--- /dev/null
+++ b/papers/variational_smoother/elsarticle-template-harv.tex
@@ -0,0 +1,286 @@
+%% 
+%% Copyright 2007-2024 Elsevier Ltd
+%% 
+%% This file is part of the 'Elsarticle Bundle'.
+%% ---------------------------------------------
+%% 
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.3 of this license or (at your option) any
+%% later version.  The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%% 
+%% The list of all files belonging to the 'Elsarticle Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%% Template article for Elsevier's document class `elsarticle'
+%% with harvard style bibliographic references
+
+\documentclass[preprint,12pt,authoryear]{elsarticle}
+
+%% Use the option review to obtain double line spacing
+%% \documentclass[authoryear,preprint,review,12pt]{elsarticle}
+
+%% Use the options 1p,twocolumn; 3p; 3p,twocolumn; 5p; or 5p,twocolumn
+%% for a journal layout:
+%% \documentclass[final,1p,times,authoryear]{elsarticle}
+%% \documentclass[final,1p,times,twocolumn,authoryear]{elsarticle}
+%% \documentclass[final,3p,times,authoryear]{elsarticle}
+%% \documentclass[final,3p,times,twocolumn,authoryear]{elsarticle}
+%% \documentclass[final,5p,times,authoryear]{elsarticle}
+%% \documentclass[final,5p,times,twocolumn,authoryear]{elsarticle}
+
+%% For including figures, graphicx.sty has been loaded in
+%% elsarticle.cls. If you prefer to use the old commands
+%% please give \usepackage{epsfig}
+
+%% The amssymb package provides various useful mathematical symbols
+\usepackage{amssymb}
+%% The amsmath package provides various useful equation environments.
+\usepackage{amsmath}
+%% The amsthm package provides extended theorem environments
+%% \usepackage{amsthm}
+
+%% The lineno packages adds line numbers. Start line numbering with
+%% \begin{linenumbers}, end it with \end{linenumbers}. Or switch it on
+%% for the whole article with \linenumbers.
+%% \usepackage{lineno}
+
+\journal{Nuclear Physics B}
+
+\begin{document}
+
+\begin{frontmatter}
+
+%% Title, authors and addresses
+
+%% use the tnoteref command within \title for footnotes;
+%% use the tnotetext command for theassociated footnote;
+%% use the fnref command within \author or \affiliation for footnotes;
+%% use the fntext command for theassociated footnote;
+%% use the corref command within \author for corresponding author footnotes;
+%% use the cortext command for theassociated footnote;
+%% use the ead command for the email address,
+%% and the form \ead[url] for the home page:
+%% \title{Title\tnoteref{label1}}
+%% \tnotetext[label1]{}
+%% \author{Name\corref{cor1}\fnref{label2}}
+%% \ead{email address}
+%% \ead[url]{home page}
+%% \fntext[label2]{}
+%% \cortext[cor1]{}
+%% \affiliation{organization={},
+%%            addressline={}, 
+%%            city={},
+%%            postcode={}, 
+%%            state={},
+%%            country={}}
+%% \fntext[label3]{}
+
+\title{} %% Article title
+
+%% use optional labels to link authors explicitly to addresses:
+%% \author[label1,label2]{}
+%% \affiliation[label1]{organization={},
+%%             addressline={},
+%%             city={},
+%%             postcode={},
+%%             state={},
+%%             country={}}
+%%
+%% \affiliation[label2]{organization={},
+%%             addressline={},
+%%             city={},
+%%             postcode={},
+%%             state={},
+%%             country={}}
+
+\author{} %% Author name
+
+%% Author affiliation
+\affiliation{organization={},%Department and Organization
+            addressline={}, 
+            city={},
+            postcode={}, 
+            state={},
+            country={}}
+
+%% Abstract
+\begin{abstract}
+%% Text of abstract
+Abstract text.
+\end{abstract}
+
+%%Graphical abstract
+\begin{graphicalabstract}
+%\includegraphics{grabs}
+\end{graphicalabstract}
+
+%%Research highlights
+\begin{highlights}
+\item Research highlight 1
+\item Research highlight 2
+\end{highlights}
+
+%% Keywords
+\begin{keyword}
+%% keywords here, in the form: keyword \sep keyword
+
+%% PACS codes here, in the form: \PACS code \sep code
+
+%% MSC codes here, in the form: \MSC code \sep code
+%% or \MSC[2008] code \sep code (2000 is the default)
+
+\end{keyword}
+
+\end{frontmatter}
+
+%% Add \usepackage{lineno} before \begin{document} and uncomment 
+%% following line to enable line numbers
+%% \linenumbers
+
+%% main text
+%%
+
+%% Use \section commands to start a section
+\section{Example Section}
+\label{sec1}
+%% Labels are used to cross-reference an item using \ref command.
+
+Section text. See Subsection \ref{subsec1}.
+
+%% Use \subsection commands to start a subsection.
+\subsection{Example Subsection}
+\label{subsec1}
+
+Subsection text.
+
+%% Use \subsubsection, \paragraph, \subparagraph commands to 
+%% start 3rd, 4th and 5th level sections.
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Document_Structure#Sectioning_commands
+
+\subsubsection{Mathematics}
+%% Inline mathematics is tagged between $ symbols.
+This is an example for the symbol $\alpha$ tagged as inline mathematics.
+
+%% Displayed equations can be tagged using various environments. 
+%% Single line equations can be tagged using the equation environment.
+\begin{equation}
+f(x) = (x+a)(x+b)
+\end{equation}
+
+%% Unnumbered equations are tagged using starred versions of the environment.
+%% amsmath package needs to be loaded for the starred version of equation environment.
+\begin{equation*}
+f(x) = (x+a)(x+b)
+\end{equation*}
+
+%% align or eqnarray environments can be used for multi line equations.
+%% & is used to mark alignment points in equations.
+%% \\ is used to end a row in a multiline equation.
+\begin{align}
+ f(x) &= (x+a)(x+b) \\
+      &= x^2 + (a+b)x + ab
+\end{align}
+
+\begin{eqnarray}
+ f(x) &=& (x+a)(x+b) \nonumber\\ %% If equation numbering is not needed for a row use \nonumber.
+      &=& x^2 + (a+b)x + ab
+\end{eqnarray}
+
+%% Unnumbered versions of align and eqnarray
+\begin{align*}
+ f(x) &= (x+a)(x+b) \\
+      &= x^2 + (a+b)x + ab
+\end{align*}
+
+\begin{eqnarray*}
+ f(x)&=& (x+a)(x+b) \\
+     &=& x^2 + (a+b)x + ab
+\end{eqnarray*}
+
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Mathematics
+%% https://en.wikibooks.org/wiki/LaTeX/Advanced_Mathematics
+
+%% Use a table environment to create tables.
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Tables
+\begin{table}[t]%% placement specifier
+%% Use tabular environment to tag the tabular data.
+%% https://en.wikibooks.org/wiki/LaTeX/Tables#The_tabular_environment
+\centering%% For centre alignment of tabular.
+\begin{tabular}{l c r}%% Table column specifiers
+%% Tabular cells are separated by &
+  1 & 2 & 3 \\ %% A tabular row ends with \\
+  4 & 5 & 6 \\
+  7 & 8 & 9 \\
+\end{tabular}
+%% Use \caption command for table caption and label.
+\caption{Table Caption}\label{fig1}
+\end{table}
+
+
+%% Use figure environment to create figures
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Floats,_Figures_and_Captions
+\begin{figure}[t]%% placement specifier
+%% Use \includegraphics command to insert graphic files. Place graphics files in 
+%% working directory.
+\centering%% For centre alignment of image.
+\includegraphics{example-image-a}
+%% Use \caption command for figure caption and label.
+\caption{Figure Caption}\label{fig1}
+%% https://en.wikibooks.org/wiki/LaTeX/Importing_Graphics#Importing_external_graphics
+\end{figure}
+
+
+%% The Appendices part is started with the command \appendix;
+%% appendix sections are then done as normal sections
+\appendix
+\section{Example Appendix Section}
+\label{app1}
+
+Appendix text.
+
+%% For citations use: 
+%%       \citet{<label>} ==> Lamport (1994)
+%%       \citep{<label>} ==> (Lamport, 1994)
+%%
+Example citation, See \citet{lamport94}.
+
+%% If you have bib database file and want bibtex to generate the
+%% bibitems, please use
+%%
+%%  \bibliographystyle{elsarticle-harv} 
+%%  \bibliography{<your bibdatabase>}
+
+%% else use the following coding to input the bibitems directly in the
+%% TeX file.
+
+%% Refer following link for more details about bibliography and citations.
+%% https://en.wikibooks.org/wiki/LaTeX/Bibliography_Management
+
+\begin{thebibliography}{00}
+
+%% For authoryear reference style
+%% \bibitem[Author(year)]{label}
+%% Text of bibliographic item
+
+\bibitem[Lamport(1994)]{lamport94}
+  Leslie Lamport,
+  \textit{\LaTeX: a document preparation system},
+  Addison Wesley, Massachusetts,
+  2nd edition,
+  1994.
+
+\end{thebibliography}
+\end{document}
+
+\endinput
+%%
+%% End of file `elsarticle-template-harv.tex'.
+
+
diff --git a/papers/variational_smoother/elsarticle-template-num-names.tex b/papers/variational_smoother/elsarticle-template-num-names.tex
new file mode 100644
index 0000000..9237a59
--- /dev/null
+++ b/papers/variational_smoother/elsarticle-template-num-names.tex
@@ -0,0 +1,284 @@
+%% 
+%% Copyright 2007-2024 Elsevier Ltd
+%% 
+%% This file is part of the 'Elsarticle Bundle'.
+%% ---------------------------------------------
+%% 
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.3 of this license or (at your option) any
+%% later version.  The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%% 
+%% The list of all files belonging to the 'Elsarticle Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%% Template article for Elsevier's document class `elsarticle'
+%% with harvard style bibliographic references
+
+\documentclass[preprint,12pt]{elsarticle}
+
+%% Use the option review to obtain double line spacing
+%% \documentclass[preprint,review,12pt]{elsarticle}
+
+%% Use the options 1p,twocolumn; 3p; 3p,twocolumn; 5p; or 5p,twocolumn
+%% for a journal layout:
+%% \documentclass[final,1p,times]{elsarticle}
+%% \documentclass[final,1p,times,twocolumn]{elsarticle}
+%% \documentclass[final,3p,times]{elsarticle}
+%% \documentclass[final,3p,times,twocolumn]{elsarticle}
+%% \documentclass[final,5p,times]{elsarticle}
+%% \documentclass[final,5p,times,twocolumn]{elsarticle}
+
+%% For including figures, graphicx.sty has been loaded in
+%% elsarticle.cls. If you prefer to use the old commands
+%% please give \usepackage{epsfig}
+
+%% The amssymb package provides various useful mathematical symbols
+\usepackage{amssymb}
+%% The amsmath package provides various useful equation environments.
+\usepackage{amsmath}
+%% The amsthm package provides extended theorem environments
+%% \usepackage{amsthm}
+
+%% The lineno packages adds line numbers. Start line numbering with
+%% \begin{linenumbers}, end it with \end{linenumbers}. Or switch it on
+%% for the whole article with \linenumbers.
+%% \usepackage{lineno}
+
+\journal{Nuclear Physics B}
+
+\begin{document}
+
+\begin{frontmatter}
+
+%% Title, authors and addresses
+
+%% use the tnoteref command within \title for footnotes;
+%% use the tnotetext command for theassociated footnote;
+%% use the fnref command within \author or \affiliation for footnotes;
+%% use the fntext command for theassociated footnote;
+%% use the corref command within \author for corresponding author footnotes;
+%% use the cortext command for theassociated footnote;
+%% use the ead command for the email address,
+%% and the form \ead[url] for the home page:
+%% \title{Title\tnoteref{label1}}
+%% \tnotetext[label1]{}
+%% \author{Name\corref{cor1}\fnref{label2}}
+%% \ead{email address}
+%% \ead[url]{home page}
+%% \fntext[label2]{}
+%% \cortext[cor1]{}
+%% \affiliation{organization={},
+%%             addressline={},
+%%             city={},
+%%             postcode={},
+%%             state={},
+%%             country={}}
+%% \fntext[label3]{}
+
+\title{} %% Article title
+
+%% use optional labels to link authors explicitly to addresses:
+%% \author[label1,label2]{}
+%% \affiliation[label1]{organization={},
+%%             addressline={},
+%%             city={},
+%%             postcode={},
+%%             state={},
+%%             country={}}
+%%
+%% \affiliation[label2]{organization={},
+%%             addressline={},
+%%             city={},
+%%             postcode={},
+%%             state={},
+%%             country={}}
+
+\author{} %% Author name
+
+%% Author affiliation
+\affiliation{organization={},%Department and Organization
+            addressline={}, 
+            city={},
+            postcode={}, 
+            state={},
+            country={}}
+
+%% Abstract
+\begin{abstract}
+%% Text of abstract
+Abstract text.
+\end{abstract}
+
+%%Graphical abstract
+\begin{graphicalabstract}
+%\includegraphics{grabs}
+\end{graphicalabstract}
+
+%%Research highlights
+\begin{highlights}
+\item Research highlight 1
+\item Research highlight 2
+\end{highlights}
+
+%% Keywords
+\begin{keyword}
+%% keywords here, in the form: keyword \sep keyword
+
+%% PACS codes here, in the form: \PACS code \sep code
+
+%% MSC codes here, in the form: \MSC code \sep code
+%% or \MSC[2008] code \sep code (2000 is the default)
+
+\end{keyword}
+
+\end{frontmatter}
+
+%% Add \usepackage{lineno} before \begin{document} and uncomment 
+%% following line to enable line numbers
+%% \linenumbers
+
+%% main text
+%%
+
+%% Use \section commands to start a section
+\section{Example Section}
+\label{sec1}
+%% Labels are used to cross-reference an item using \ref command.
+
+Section text. See Subsection \ref{subsec1}.
+
+%% Use \subsection commands to start a subsection.
+\subsection{Example Subsection}
+\label{subsec1}
+
+Subsection text.
+
+%% Use \subsubsection, \paragraph, \subparagraph commands to 
+%% start 3rd, 4th and 5th level sections.
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Document_Structure#Sectioning_commands
+
+\subsubsection{Mathematics}
+%% Inline mathematics is tagged between $ symbols.
+This is an example for the symbol $\alpha$ tagged as inline mathematics.
+
+%% Displayed equations can be tagged using various environments. 
+%% Single line equations can be tagged using the equation environment.
+\begin{equation}
+f(x) = (x+a)(x+b)
+\end{equation}
+
+%% Unnumbered equations are tagged using starred versions of the environment.
+%% amsmath package needs to be loaded for the starred version of equation environment.
+\begin{equation*}
+f(x) = (x+a)(x+b)
+\end{equation*}
+
+%% align or eqnarray environments can be used for multi line equations.
+%% & is used to mark alignment points in equations.
+%% \\ is used to end a row in a multiline equation.
+\begin{align}
+ f(x) &= (x+a)(x+b) \\
+      &= x^2 + (a+b)x + ab
+\end{align}
+
+\begin{eqnarray}
+ f(x) &=& (x+a)(x+b) \nonumber\\ %% If equation numbering is not needed for a row use \nonumber.
+      &=& x^2 + (a+b)x + ab
+\end{eqnarray}
+
+%% Unnumbered versions of align and eqnarray
+\begin{align*}
+ f(x) &= (x+a)(x+b) \\
+      &= x^2 + (a+b)x + ab
+\end{align*}
+
+\begin{eqnarray*}
+ f(x)&=& (x+a)(x+b) \\
+     &=& x^2 + (a+b)x + ab
+\end{eqnarray*}
+
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Mathematics
+%% https://en.wikibooks.org/wiki/LaTeX/Advanced_Mathematics
+
+%% Use a table environment to create tables.
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Tables
+\begin{table}[t]%% placement specifier
+%% Use tabular environment to tag the tabular data.
+%% https://en.wikibooks.org/wiki/LaTeX/Tables#The_tabular_environment
+\centering%% For centre alignment of tabular.
+\begin{tabular}{l c r}%% Table column specifiers
+%% Tabular cells are separated by &
+  1 & 2 & 3 \\ %% A tabular row ends with \\
+  4 & 5 & 6 \\
+  7 & 8 & 9 \\
+\end{tabular}
+%% Use \caption command for table caption and label.
+\caption{Table Caption}\label{fig1}
+\end{table}
+
+
+%% Use figure environment to create figures
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Floats,_Figures_and_Captions
+\begin{figure}[t]%% placement specifier
+%% Use \includegraphics command to insert graphic files. Place graphics files in 
+%% working directory.
+\centering%% For centre alignment of image.
+\includegraphics{example-image-a}
+%% Use \caption command for figure caption and label.
+\caption{Figure Caption}\label{fig1}
+%% https://en.wikibooks.org/wiki/LaTeX/Importing_Graphics#Importing_external_graphics
+\end{figure}
+
+
+%% The Appendices part is started with the command \appendix;
+%% appendix sections are then done as normal sections
+\appendix
+\section{Example Appendix Section}
+\label{app1}
+
+Appendix text.
+
+%% For citations use: 
+%%       \citet{<label>} ==> Lamport [21]
+%%       \citep{<label>} ==> [21]
+%%
+Example citation, See \citet{lamport94}.
+
+%% If you have bib database file and want bibtex to generate the
+%% bibitems, please use
+%%
+%%  \bibliographystyle{elsarticle-num-names} 
+%%  \bibliography{<your bibdatabase>}
+
+%% else use the following coding to input the bibitems directly in the
+%% TeX file.
+
+%% Refer following link for more details about bibliography and citations.
+%% https://en.wikibooks.org/wiki/LaTeX/Bibliography_Management
+
+\begin{thebibliography}{00}
+
+%% For authoryear reference style
+%% \bibitem[Author(year)]{label}
+%% Text of bibliographic item
+
+\bibitem[Lamport(1994)]{lamport94}
+  Leslie Lamport,
+  \textit{\LaTeX: a document preparation system},
+  Addison Wesley, Massachusetts,
+  2nd edition,
+  1994.
+
+\end{thebibliography}
+\end{document}
+
+\endinput
+%%
+%% End of file `elsarticle-template-num-names.tex'.
diff --git a/papers/variational_smoother/elsarticle.dtx b/papers/variational_smoother/elsarticle.dtx
new file mode 100644
index 0000000..a0c2b2e
--- /dev/null
+++ b/papers/variational_smoother/elsarticle.dtx
@@ -0,0 +1,1526 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 2007-2024 by Elsevier Ltd
+% -----------------------------------------------
+% 
+% This file may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in:
+%
+%    http://www.latex-project.org/lppl.txt
+%
+% and version 1.3 or later is part of all distributions of LaTeX 
+% version 1999/12/01 or later.
+%
+% \fi
+% \CheckSum{3279}
+%
+% $Id: elsarticle.dtx 259 2024-04-06 12:00:41Z rishi $
+% $URL: https://lenova.river-valley.com/svn/elsarticle/trunk/elsarticle.dtx $
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\EnableCrossrefs         
+\CodelineIndex
+\RecordChanges
+\usepackage{comment}
+\begin{document}
+  \DocInput{elsarticle.dtx}
+  \PrintChanges
+  \PrintIndex
+\end{document}
+%</driver>
+% \fi
+%
+% \CharacterTable
+%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%   Digits        \0\1\2\3\4\5\6\7\8\9
+%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%   Dollar        \$     Percent       \%     Ampersand     \&
+%   Acute accent  \'     Left paren    \(     Right paren   \)
+%   Asterisk      \*     Plus          \+     Comma         \,
+%   Minus         \-     Point         \.     Solidus       \/
+%   Colon         \:     Semicolon     \;     Less than     \<
+%   Equals        \=     Greater than  \>     Question mark \?
+%   Commercial at \@     Left bracket  \[     Backslash     \\
+%   Right bracket \]     Circumflex    \^     Underscore    \_
+%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%   Right brace   \}     Tilde         \~}
+%
+%
+% \changes{v1.1}{2008/09/25}{Initial version}
+%
+%
+% \changes{v1.2}{2009/09/17}{Documentation, templates, and *.bst
+%    has been seperated from this .dtx. Incompatibility problems
+%    with amsref.sty, fncylab.sty have been fixed. Some bugs related
+%    to author/affiliation part have been fixed.}
+%
+%
+% \changes{v3.3}{2020/11/20}{Defined \string\affiliation command for structured
+%    address tagging.}
+%
+% \changes{v3.4}{2022/11/26}{A bug fix. Accented characters produced errors. So loaded fontenc package.}
+%
+% \GetFileInfo{elsarticle.dtx}
+%
+% \DoNotIndex{\newcommand,\newenvironment}
+% 
+%
+% \title{The \textsf{elsarticle.cls} -- Implimentation}
+% \author{Elsevier Ltd}
+%
+% \maketitle
+%
+% \StopEventually{}
+%
+% \section{Implementation}
+%
+%    \begin{macrocode}
+%<*class>
+%% 
+%% 
+%%
+ \def\RCSfile{elsarticle}%
+ \def\RCSversion{3.4}%
+ \def\RCSdate{2024/04/04}%
+ \def\@shortjnl{\relax}
+ \def\@journal{Elsevier Ltd} 
+ \def\@company{Elsevier Ltd}
+ \def\@issn{000-0000}
+ \def\@shortjid{elsarticle}
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\ProvidesClass{\@shortjid}[\RCSdate, \RCSversion: \@journal]
+\def\ABD{\AtBeginDocument}
+\newif\ifpreprint \preprintfalse
+\newif\ifnonatbib \nonatbibfalse
+\newif\iflongmktitle \longmktitlefalse
+\newif\ifnopreprintline \nopreprintlinefalse
+\newif\ifdoubleblind \doubleblindfalse
+
+\newif\ifuseexplthreefunctions \useexplthreefunctionsfalse
+
+\RequirePackage[T1]{fontenc}
+
+\IfFileExists{expl3.sty}{%
+  \global\useexplthreefunctionstrue%
+  \RequirePackage{expl3}}{}
+\ifuseexplthreefunctions\relax%
+	\IfFileExists{xparse.sty}{\RequirePackage{xparse}}{}
+	\IfFileExists{etoolbox.sty}{\RequirePackage{etoolbox}}{}
+\fi
+
+\def\@blstr{1}
+\newdimen\@bls
+\@bls=\baselineskip
+
+\def\@finalWarning{%
+  *****************************************************\MessageBreak
+   This document is typeset in the CRC style which\MessageBreak
+   is not suitable for submission.\MessageBreak
+   \MessageBreak
+   Please typeset again using 'preprint' option\MessageBreak
+   for creating PDF suitable for submission.\MessageBreak
+  ******************************************************\MessageBreak
+}
+
+\DeclareOption{preprint}{\global\preprinttrue
+  \gdef\@blstr{1}\xdef\jtype{0}%
+   \AtBeginDocument{\@twosidefalse\@mparswitchfalse}}
+\DeclareOption{nopreprintline}{\global\nopreprintlinetrue}
+\DeclareOption{final}{\gdef\@blstr{1}\global\preprintfalse}
+\DeclareOption{review}{\global\preprinttrue\gdef\@blstr{1.5}}
+\DeclareOption{authoryear}{\xdef\@biboptions{round,authoryear}}
+\DeclareOption{number}{\xdef\@biboptions{numbers}}
+\DeclareOption{numbers}{\xdef\@biboptions{numbers}}
+\DeclareOption{nonatbib}{\global\nonatbibtrue}
+\DeclareOption{longtitle}{\global\longmktitletrue}
+\DeclareOption{5p}{\xdef\jtype{5}\global\preprintfalse
+  \ExecuteOptions{twocolumn}}
+  \def\jtype{0}
+\DeclareOption{3p}{\xdef\jtype{3}\global\preprintfalse}
+\DeclareOption{1p}{\xdef\jtype{1}\global\preprintfalse
+  \AtBeginDocument{\@twocolumnfalse}}
+\DeclareOption{times}{\IfFileExists{txfonts.sty}%
+  {\AtEndOfClass{\RequirePackage{txfonts}%
+  \gdef\ttdefault{cmtt}%
+  \let\iint\relax
+  \let\iiint\relax
+  \let\iiiint\relax
+  \let\idotsint\relax
+  \let\openbox\relax}}{\AtEndOfClass{\RequirePackage{times}}}}
+
+\DeclareOption{endfloat}{\IfFileExists{endfloat.sty}
+   {\AtEndOfClass{\RequirePackage[markers]{endfloat}}}{}}
+\DeclareOption{endfloats}{\IfFileExists{endfloat.sty}
+   {\AtEndOfClass{\RequirePackage[markers]{endfloat}}}{}}
+\DeclareOption{numafflabel}
+   {\AtBeginDocument{\def\theaffn{\arabic{affn}}}} %*%
+\DeclareOption{lefttitle}
+   {\AtBeginDocument{\def\elsarticletitlealign{flushleft}}} %*%
+\DeclareOption{centertitle}
+   {\AtBeginDocument{\def\elsarticletitlealign{center}}} %*%
+\DeclareOption{reversenotenum}
+   {\AtBeginDocument{\def\theaffn{\arabic{affn}}
+    \def\thefnote{\alph{fnote}}}}
+\DeclareOption{doubleblind}{\doubleblindtrue}
+
+\ExecuteOptions{a4paper,10pt,oneside,onecolumn,number,preprint,centertitle}
+\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}
+\ProcessOptions
+\LoadClass{article}
+\RequirePackage{graphicx}
+%    \end{macrocode}
+% 
+% \section{Preamble}
+%
+%    \begin{macrocode}
+\let\comma\@empty
+\let\tnotesep\@empty
+\let\@title\@empty
+
+\def\useelstitle{}
+
+\def\title#1{\g@addto@macro\@title{#1%
+       \global\let\tnoteref\@gobble}%
+       \g@addto@macro\useelstitle{#1}}
+
+\def\elsLabel#1{\@bsphack\protected@write\@auxout{}%
+         {\string\Newlabel{#1}{\@currentlabel}}\@esphack}
+\def\Newlabel#1#2{\expandafter\xdef\csname X@#1\endcsname{#2}}
+
+\def\elsRef#1{\@ifundefined{X@#1}{0}{\csname X@#1\endcsname}}
+
+\let\@tnotemark\@empty
+
+\ifdoubleblind
+  \def\tnotemark[#1]{}
+\else
+  \def\tnotemark[#1]{\@for\mytmark:=#1\do{%
+%       \expandafter\ifcase\csname X@\mytmark\endcsname\or$^{\star}$\or
+        \expandafter\ifcase\elsRef{\mytmark}\or$^{\star}$\or
+       $^{,\star\star}$\fi
+    }%
+}
+\fi
+
+\def\tnoteref#1{\tnotemark[{#1}]}
+\let\@tnotes\@empty
+\newcounter{tnote}
+\def\tnotetext[#1]#2{\g@addto@macro\@tnotes{%
+  \stepcounter{tnote}\elsLabel{#1}%
+    \def\thefootnote{\ifcase\c@tnote\or$\star$\or$\star\star$\fi}%
+    \footnotetext{#2}}}
+
+\let\@nonumnotes\@empty
+\def\nonumnote#1{\g@addto@macro\@nonumnotes{%
+     \let\thefootnote\relax\footnotetext{#1}}}
+
+\newcounter{fnote}
+\def\thefnote{\arabic{fnote}}
+\def\fnmark[#1]{\let\comma\@empty
+    \def\@fnmark{\@for\@@fnmark:=#1\do{%
+    \edef\fnotenum{\@ifundefined{X@\@@fnmark}{1}{\elsRef{\@@fnmark}}}%
+  \unskip\comma\fnotenum\let\comma,}}%
+}
+
+\def\fnref#1{\fnmark[#1]}
+
+\let\@fnotes\@empty\let\@fnmark\@empty
+\def\fntext[#1]#2{\g@addto@macro\@fnotes{%
+   \refstepcounter{fnote}\elsLabel{#1}%
+   \def\thefootnote{\thefnote}%
+   \global\setcounter{footnote}{\c@fnote}%
+   \footnotetext{#2}}}
+
+\def\cormark[#1]{\edef\cnotenum{\elsRef{#1}}%
+    \unskip\textsuperscript{\sep\ifcase\cnotenum\or
+       $\ast$\or$\ast\ast$\fi\hspace{-1pt}}\let\sep=,}
+
+\let\@cormark\@empty
+\let\@cornotes\@empty
+\newcounter{cnote}
+\def\cortext[#1]#2{\g@addto@macro\@cornotes{%
+    \refstepcounter{cnote}\elsLabel{#1}%
+    \def\thefootnote{\ifcase\thecnote\or$\ast$\or
+    $\ast\ast$\fi}%
+    \footnotetext{#2}}}
+
+\let\@corref\@empty
+\def\corref#1{\edef\cnotenum{\elsRef{#1}}%
+    \edef\@corref{\ifcase\cnotenum\or
+         $\ast$\or$\ast\ast$\fi\hskip-1pt}}
+
+\def\resetTitleCounters{\c@cnote=0
+   \c@fnote=0 \c@tnote=0 \c@footnote=0}
+
+\let\eadsep\@empty
+\def\@elseads{}
+\let\@elsuads\@empty
+\let\@cormark\@empty
+\def\hashchar{\expandafter\@gobble\string\~}
+\def\underscorechar{\expandafter\@gobble\string\_}
+\def\lbracechar{\expandafter\@gobble\string\{}
+\def\rbracechar{\expandafter\@gobble\string\}}
+
+\gdef\ead{\@ifnextchar[{\@uad}{\@ead}}
+\gdef\@ead#1{\bgroup
+   \def\_{\underscorechar}%
+   \def\{{\lbracechar}%
+   \def~{\hashchar}%
+   \def\}{\rbracechar}%
+   \edef\tmp{\the\@eadauthor}%
+   \immediate\write\@auxout{\string\emailauthor
+     {#1}{\expandafter\strip@prefix\meaning\tmp}}%
+   \egroup
+}
+\newcounter{ead}
+\gdef\emailauthor#1#2{\stepcounter{ead}%
+     \g@addto@macro\@elseads{\raggedright%
+      \let\corref\@gobble\def\@@tmp{#1}%
+      \eadsep{\ttfamily\expandafter\strip@prefix\meaning\@@tmp}
+      (#2)\def\eadsep{\unskip,\space}}%
+}
+\gdef\@uad[#1]#2{\bgroup
+   \def~{\hashchar}%
+   \def\_{\underscorechar}%
+   \def~{\hashchar}%
+   \def\}{\rbracechar}%
+   \edef\tmp{\the\@eadauthor}
+   \immediate\write\@auxout{\string\urlauthor
+     {#2}{\expandafter\strip@prefix\meaning\tmp}}%
+  \egroup
+}
+\gdef\urlauthor#1#2{\g@addto@macro\@elsuads{\let\corref\@gobble%
+     \def\@@tmp{#1}\raggedright\eadsep
+     {\ttfamily\expandafter\strip@prefix\meaning\@@tmp}\space(#2)%
+     \def\eadsep{\unskip,\space}}%
+}
+
+\def\elsauthors{}
+\def\useauthors{}
+\def\elsprelimauthors{}
+
+\def\pprinttitle{}
+\let\authorsep\@empty
+\let\prelimauthorsep\@empty
+\let\sep\@empty
+\newcounter{author}
+\def\author{\@ifnextchar[{\@@author}{\@author}}
+
+\newtoks\@eadauthor
+\def\@@author[#1]#2{%
+    \g@addto@macro\elsprelimauthors{%
+     \prelimauthorsep#2%
+     \def\prelimauthorsep{\unskip,\space}}%
+    \g@addto@macro\elsauthors{%
+    \def\baselinestretch{1}%
+    \authorsep#2\unskip\textsuperscript{%#1%
+      \@for\@@affmark:=#1\do{%
+       \edef\affnum{\@ifundefined{X@\@@affmark}{1}{\elsRef{\@@affmark}}}%
+     \unskip\sep\affnum\let\sep=,}%
+      \ifx\@fnmark\@empty\else\unskip\sep\@fnmark\let\sep=,\fi
+      \ifx\@corref\@empty\else\unskip\sep\@corref\let\sep=,\fi
+      }%
+    \def\authorsep{\unskip,\space}%
+    \global\let\sep\@empty\global\let\@corref\@empty
+    \global\let\@fnmark\@empty}%
+    \@eadauthor={#2}%
+    \g@addto@macro\useauthors{#2; }%
+}
+
+\def\@author#1{%
+    \g@addto@macro\elsprelimauthors{%
+     \prelimauthorsep#1%
+     \def\prelimauthorsep{\unskip,\space}}%
+    \g@addto@macro\elsauthors{\normalsize%
+    \def\baselinestretch{1}%
+    \upshape\authorsep#1\unskip\textsuperscript{%
+      \ifx\@fnmark\@empty\else\unskip\sep\@fnmark\let\sep=,\fi
+      \ifx\@corref\@empty\else\unskip\sep\@corref\let\sep=,\fi
+      }%
+    \def\authorsep{\unskip,\space}%
+    \global\let\@fnmark\@empty
+    \global\let\@corref\@empty    \global\let\sep\@empty}%
+    \@eadauthor={#1}%
+    \g@addto@macro\useauthors{#1; }%
+}
+
+\AtBeginDocument{%
+  \@ifpackageloaded{hyperref}{%
+    \expandafter\gdef\csname Hy@title\endcsname{\useelstitle}%
+    \expandafter\gdef\csname Hy@author\endcsname{\useauthors}%
+   }{}
+}
+
+\def\elsaddress{}
+\def\addsep{\par\vskip6pt}
+
+\def\@alph#1{%
+  \ifcase#1\or a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or k\or
+  l\or m\or n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or
+  y\or z%
+  \or aa\or ab\or ac\or ad\or ae\or af\or ag\or ah\or ai\or aj\or
+  ak\or al\or am\or an\or ao\or ap\or aq\or ar\or as\or at\or au\or
+  av\or aw\or ax\or ay\or az%
+  \or ba\or bb\or bc\or bd\or be\or bf\or bg\or bh\or bi\or bj\or
+  bk\or bl\or bm\or bn\or bo\or bp\or bq\or br\or bs\or bt\or bu\or
+  bv\or bw\or bx\or by\or bz%
+  \or ca\or cb\or cc\or cd\or ce\or cf\or cg\or ch\or ci\or cj\or
+  ck\or cl\or cm\or cn\or co\or cp\or cq\or cr\or cs\or ct\or cu\or
+  cv\or cw\or cx\or cy\or cz%
+  \or da\or db\or dc\or dd\or de\or df\or dg\or dh\or di\or dj\or
+  dk\or dl\or dm\or dn\or do\or dp\or dq\or dr\or ds\or dt\or du\or
+  dv\or dw\or dx\or dy\or dz%
+  \or ea\or eb\or ec\or ed\or ee\or ef\or eg\or eh\or ei\or ej\or
+  ek\or el\or em\or en\or eo\or ep\or eq\or er\or es\or et\or eu\or
+  ev\or ew\or ex\or ey\or ez%
+  \or fa\or fb\or fc\or fd\or fe\or ff\or fg\or fh\or fi\or fj\or
+  fk\or fl\or fm\or fn\or fo\or fp\or fq\or fr\or fs\or ft\or fu\or
+  fv\or fw\or fx\or fy\or fz%
+  \or ga\or gb\or gc\or gd\or ge\or gf\or gg\or gh\or gi\or gj\or
+  gk\or gl\or gm\or gn\or go\or gp\or gq\or gr\or gs\or gt\or gu\or
+  gv\or gw\or gx\or gy\or gz%
+  \else\@ctrerr\fi}
+
+\newcounter{affn}
+\renewcommand\theaffn{\alph{affn}}
+
+\ifuseexplthreefunctions\relax%
+  \ExplSyntaxOn
+  \def\ca_affitem_postskip{\mbox{~}\unskip\ignorespaces}
+  %%Author Address
+  \DeclareDocumentCommand \ca_organization { O{,} m }
+    {
+  %    #2 #1\mbox{~}\unskip\ignorespaces
+      \csgappto { ca_affiliation_values } { #2 #1\ca_affitem_postskip }
+    }
+  \DeclareDocumentCommand \ca_postal_code { O{,} m }
+    {
+  %    #2 #1\mbox{~}\unskip\ignorespaces
+      \csgappto { ca_affiliation_values } { #2 #1\ca_affitem_postskip }
+    }
+  \DeclareDocumentCommand \ca_aff_city { O{,}  m }
+    {
+  %    #2 #1\mbox{~}\unskip\ignorespaces
+      \csgappto { ca_affiliation_values } { #2 #1\ca_affitem_postskip }
+    }
+  \DeclareDocumentCommand \ca_address_line { O{,}m }
+    {
+  %    #2 #1\mbox{~}\unskip\ignorespaces
+      \csgappto { ca_affiliation_values } { #2 #1\ca_affitem_postskip }
+    }
+  \DeclareDocumentCommand \ca_state { O{,} m }
+    {
+  %    #2 #1\mbox{~}\unskip\ignorespaces
+      \csgappto { ca_affiliation_values } { #2 #1\ca_affitem_postskip }
+    }
+  \DeclareDocumentCommand \ca_country { O{ } m }
+    {
+  %    #2 #1
+      \csgappto { ca_affiliation_values } { #2 #1 }
+    }
+
+  \DeclareDocumentCommand \ca_stm_organization { O{,} m }
+    {
+      #2 #1\ca_affitem_postskip
+    }
+  \DeclareDocumentCommand \ca_stm_postal_code { O{,} m }
+    {
+      #2 #1\ca_affitem_postskip
+    }
+  \DeclareDocumentCommand \ca_stm_aff_city { O{,}  m }
+    {
+      #2 #1\ca_affitem_postskip
+    }
+  \DeclareDocumentCommand \ca_stm_aff_address_line { O{,}m }
+    {
+      #2 #1\ca_affitem_postskip
+    }
+  \DeclareDocumentCommand \ca_stm_state { O{,} m }
+    {
+      #2 #1\ca_affitem_postskip
+    }
+  \DeclareDocumentCommand \ca_stm_country { O{ } m }
+    {
+      #2 #1
+    }
+
+  \keys_define:nn { stm / affiliation }
+    {
+      op   .tl_set_x:N   = \l_organization_punc_tl,
+      oraganizationsep   .tl_set_x:N   = \l_organization_punc_tl,
+      oraganisationsep   .tl_set_x:N   = \l_organization_punc_tl,
+      ap   .tl_set_x:N   = \l_address_line_punc_tl,
+      addresslinesep   .tl_set_x:N   = \l_address_line_punc_tl,
+      cp   .tl_set_x:N   = \l_city_punc_tl,
+      citysep   .tl_set_x:N   = \l_city_punc_tl,
+      pp   .tl_set_x:N   = \l_postal_code_punc_tl,
+      postcodesep   .tl_set_x:N   = \l_postal_code_punc_tl,
+      sp   .tl_set_x:N   = \l_state_punc_tl,
+      statesep   .tl_set_x:N   = \l_state_punc_tl,
+      o    .code:n       = { \ca_organization[\l_organization_punc_tl]{#1} },
+      organization    .code:n       = { \ca_organization[\l_organization_punc_tl]{#1} },
+      organisation    .code:n       = { \ca_organization[\l_organization_punc_tl]{#1} },
+      a    .code:n       = { \ca_address_line[\l_address_line_punc_tl]{#1} },
+      addressline    .code:n       = { \ca_address_line[\l_address_line_punc_tl]{#1} },
+      c    .code:n       = { \ca_aff_city[\l_city_punc_tl]{#1} },
+      city .code:n       = { \ca_aff_city[\l_city_punc_tl]{#1} },
+      p    .code:n       = { \ca_postal_code[\l_postal_code_punc_tl]{#1} },
+      postcode    .code:n       = { \ca_postal_code[\l_postal_code_punc_tl]{#1} },
+      s    .code:n       = { \ca_state[\l_state_punc_tl]{#1} },
+      state    .code:n       = { \ca_state[\l_state_punc_tl]{#1} },
+      orp  .tl_set_x:N   = \l_organization_punc_tl,
+      adp  .tl_set_x:N   = \l_address_line_punc_tl,
+      cip  .tl_set_x:N   = \l_city_punc_tl,
+      pcp  .tl_set_x:N   = \l_postal_code_punc_tl,
+      stp  .tl_set_x:N   = \l_state_punc_tl,
+      cyp  .tl_set_x:N   = \l_country_punc_tl,
+      or   .code:n       = { \ca_organization[\l_organization_punc_tl]{#1} },
+      ad   .code:n       = { \ca_address_line[\l_address_line_punc_tl]{#1} },
+      ci   .code:n       = { \ca_aff_city[\l_city_punc_tl]{#1} },
+      pc   .code:n       = { \ca_postal_code[\l_postal_code_punc_tl]{#1} },
+      st   .code:n       = { \ca_state[\l_state_punc_tl]{#1} },
+      cy   .code:n       = { \ca_country[\l_country_punc_tl]{#1} },
+      country   .code:n  = { \ca_country[\l_country_punc_tl]{#1} },
+      unknown   .code:n  = {
+                             \ifstrempty { #1 } {
+                                  \csxappto { ca_affiliation_values }
+                                       { {\l_keys_key_tl}~ }
+                                } {
+                                  \csxappto { ca_affiliation_values }
+                                       { {#1}~ }
+                                }
+                           }
+    }
+
+  \cs_set:Npn \__reset_affiliation:
+  {
+    \tl_gset:Nn \l_organization_punc_tl { , }
+    \tl_gset:Nn \l_address_line_punc_tl { , }
+    \tl_gset:Nn \l_city_punc_tl { , }
+    \tl_gset:Nn \l_postal_code_punc_tl { , }
+    \tl_gset:Nn \l_state_punc_tl { , }
+    \tl_gset:Nn \l_country_punc_tl { }
+  }
+
+  \DeclareDocumentCommand\affiliation{ o m }{
+    \__reset_affiliation:
+    \csgdef { ca_affiliation_values } { }
+    \IfNoValueTF { #2 }
+      { }
+      {
+       \keys_set:nn { stm / affiliation } { #2 }
+      }
+     \IfNoValueTF { #1 }
+      { 
+        \csgappto{elsauthors}{%
+          \par\vspace*{6pt}\noindent
+          \bgroup\def\baselinestretch{1}%
+           \footnotesize\itshape%
+           \unskip\ignorespaces}
+        \csxappto{elsauthors}{\csuse { ca_affiliation_values }}
+        \csgappto{elsauthors}{\par\vspace*{6pt}
+          \noindent\unskip\ignorespaces
+          \gdef\authorsep{}
+        \egroup}
+      }
+      { 
+        \csgappto{elsaddress}{
+        \def\baselinestretch{1}%
+        \refstepcounter{affn}
+        \xdef\@currentlabel{\theaffn}
+        \IfNoValueTF { #1 }
+          { }
+          { \elsLabel{#1} }
+        \textsuperscript{\theaffn}}
+        \csxappto{elsaddress}{
+          \csuse { ca_affiliation_values }
+          \par
+        }
+      }
+  }
+  \ExplSyntaxOff
+  \else%
+  \def\caaffitempostskip{\space}
+
+  \DeclareRobustCommand\caorganization[2][,]{%
+     \g@addto@macro\caaffiliationvalues{#2#1\caaffitempostskip}%
+  }
+  \DeclareRobustCommand\capostalcode[2][,]{%
+     \g@addto@macro\caaffiliationvalues{#2#1\caaffitempostskip}%
+  }
+  \DeclareRobustCommand\caaffcity[2][,]{%
+     \g@addto@macro\caaffiliationvalues{#2#1\caaffitempostskip}%
+  }
+  \DeclareRobustCommand\caaddressline[2][,]{%
+     \g@addto@macro\caaffiliationvalues{#2#1\caaffitempostskip}%
+  }
+  \DeclareRobustCommand\castate[2][,]{%
+     \g@addto@macro\caaffiliationvalues{#2#1\caaffitempostskip}%
+  }
+  \DeclareRobustCommand\cacountry[2][,]{%
+     \g@addto@macro\caaffiliationvalues{#2#1\caaffitempostskip}%
+  }
+  \DeclareRobustCommand\castmorganization[2][,]{%
+     #2#1\caaffitempostskip%
+  }
+  \DeclareRobustCommand\castmpostalcode[2][,]{%
+     #2#1\caaffitempostskip%
+  }
+  \DeclareRobustCommand\castmaffcity[2][,]{%
+     #2#1\caaffitempostskip%
+  }
+  \DeclareRobustCommand\castmaddressline[2][,]{%
+     #2#1\caaffitempostskip%
+  }
+  \DeclareRobustCommand\castmstate[2][,]{%
+     #2#1\caaffitempostskip%
+  }
+  \DeclareRobustCommand\castmcountry[2][,]{%
+     #2#1\caaffitempostskip%
+  }
+
+  \define@key{affiliation}{op}{\xdef\@organizationpunc{#1}}
+  \define@key{affiliation}{orp}{\xdef\@organizationpunc{#1}}
+  \define@key{affiliation}{organizationsep}{\xdef\@organizationpunc{#1}}
+  \define@key{affiliation}{ap}{\xdef\@addresslinepunc{#1}}
+  \define@key{affiliation}{adp}{\xdef\@addresslinepunc{#1}}
+  \define@key{affiliation}{addresslinesep}{\xdef\@addresslinepunc{#1}}
+  \define@key{affiliation}{cp}{\xdef\@citypunc{#1}}
+  \define@key{affiliation}{cip}{\xdef\@citypunc{#1}}
+  \define@key{affiliation}{cyp}{\xdef\@countrypunc{#1}}
+  \define@key{affiliation}{citysep}{\xdef\@citypunc{#1}}
+  \define@key{affiliation}{pp}{\xdef\@postcodepunc{#1}}
+  \define@key{affiliation}{pop}{\xdef\@postcodepunc{#1}}
+  \define@key{affiliation}{postcodesep}{\xdef\@postcodepunc{#1}}
+  \define@key{affiliation}{sp}{\xdef\@statepunc{#1}}
+  \define@key{affiliation}{stp}{\xdef\@statepunc{#1}}
+  \define@key{affiliation}{statesep}{\xdef\@statepunc{#1}}
+  \define@key{affiliation}{countrysep}{\xdef\@countrypunc{#1}}
+
+  \define@key{affiliation}{organization}{%
+  	\caorganization[\@organizationpunc]{#1}}
+  \define@key{affiliation}{addressline}{%
+  	\caaddressline[\@addresslinepunc]{#1}}
+  \define@key{affiliation}{city}{%
+  	\caaffcity[\@citypunc]{#1}}
+  \define@key{affiliation}{postcode}{%
+  	\capostalcode[\@postcodepunc]{#1}}
+  \define@key{affiliation}{state}{%
+  	\castate[\@statepunc]{#1}}
+  \define@key{affiliation}{or}{%
+  	\caorganization[\@organizationpunc]{#1}}
+  \define@key{affiliation}{ad}{%
+  	\caaddressline[\@addresslinepunc]{#1}}
+  \define@key{affiliation}{ci}{%
+  	\caaffcity[\@citypunc]{#1}}
+  \define@key{affiliation}{po}{%
+  	\capostalcode[\@postcodepunc]{#1}}
+  \define@key{affiliation}{st}{%
+  	\castate[\@statepunc]{#1}}
+  \define@key{affiliation}{o}{%
+  	\caorganization[\@organizationpunc]{#1}}
+  \define@key{affiliation}{a}{%
+  	\caaddressline[\@addresslinepunc]{#1}}
+  \define@key{affiliation}{c}{%
+  	\cacity[\@citypunc]{#1}}
+  \define@key{affiliation}{p}{%
+  	\capostcode[\@postcodepunc]{#1}}
+  \define@key{affiliation}{s}{%
+  	\castate[\@statepunc]{#1}}
+  \define@key{affiliation}{cy}{%
+  	\cacountry[\@countrypunc]{#1}}
+  \define@key{affiliation}{country}{%
+  	\cacountry[\@countrypunc]{#1}}
+
+
+  \gdef\@resetaffiliation{%
+    \gdef\@organizationpunc{,}%
+    \gdef\@addresslinepunc{,}%
+    \gdef\@citypunc{,}%
+    \gdef\@statepunc{,}%
+    \gdef\@postcodepunc{,}%
+    \gdef\@countrypunc{}%
+  }
+
+  \def\affiliation{\@ifnextchar[{\@@affiliation}{\@affiliation}}
+
+  \newcommand*{\newstmrobustcmd}{}
+  \protected\def\newstmrobustcmd{\@star@or@long\stmetb@new@command}
+
+  \def\stmetb@new@command#1{\@testopt{\stmetb@newcommand#1}0}
+
+  \def\stmetb@newcommand#1[#2]{%
+    \@ifnextchar[%]
+      {\stmetb@xargdef#1[#2]}
+      {\ifx\l@ngrel@x\relax
+         \let\l@ngrel@x\protected
+       \else
+         \protected\def\l@ngrel@x{\protected\long}%
+       \fi
+       \@argdef#1[#2]}}
+
+  \long\def\stmetb@xargdef#1[#2][#3]#4{%
+    \@ifdefinable#1{%
+      \expandafter\protected
+      \expandafter\def
+      \expandafter#1%
+      \expandafter{%
+        \expandafter\@testopt
+        \csname\string#1\endcsname{#3}}%
+      \expandafter\@yargdef\csname\string#1\endcsname\tw@{#2}{#4}}}
+  %
+  \newcommand{\ifstmundef}[1]{%
+    \ifdefined#1%
+      \ifx#1\relax
+        \expandafter\expandafter
+        \expandafter\@firstoftwo
+      \else
+        \expandafter\expandafter
+        \expandafter\@secondoftwo
+      \fi
+    \else
+      \expandafter\@firstoftwo
+    \fi}
+  \newcommand{\stmexpandonce}[1]{%
+    \unexpanded\expandafter{#1}}
+  \newstmrobustcmd{\gstmappto}[2]{%
+    \ifundef{#1}
+      {\xdef#1{\unexpanded{#2}}}
+      {\xdef#1{\stmexpandonce#1\unexpanded{#2}}}}
+  \newstmrobustcmd{\xstmappto}[2]{%
+    \ifstmundef{#1}
+      {\xdef#1{#2}}
+      {\xdef#1{\stmexpandonce#1#2}}}
+
+
+  \long\def\@@affiliation[#1]#2{%
+      \@resetaffiliation%
+      \gdef\caaffiliationvalues{}%
+      \elsLabel{#1}%
+      \setkeys{affiliation}{#2}%
+      \g@addto@macro\elsaddress{%
+      \def\baselinestretch{1}%
+      \refstepcounter{affn}%
+      \xdef\@currentlabel{\theaffn}%
+      \elsLabel{#1}%
+      \textsuperscript{\theaffn}}
+      \xstmappto\elsaddress{\caaffiliationvalues\par}}
+
+  \long\def\@affiliation#1{%
+      \@resetaffiliation%
+      \gdef\caaffiliationvalues{}%
+      \setkeys{affiliation}{#1}%
+      \g@addto@macro\elsauthors{%
+      \def\baselinestretch{1}}%
+      \xstmappto\elsaddress{\caaffiliationvalues\par}}
+\fi
+
+\def\address{\@ifnextchar[{\@@address}{\@address}}
+
+\long\def\@@address[#1]#2{\g@addto@macro\elsaddress{%
+    \def\baselinestretch{1}%
+     \refstepcounter{affn}
+     \xdef\@currentlabel{\theaffn}
+     \elsLabel{#1}%
+    \textsuperscript{\theaffn}#2\par}}
+
+\long\def\@address#1{\g@addto@macro\elsauthors{%
+    \def\baselinestretch{1}%
+    \addsep\footnotesize\itshape#1\def\addsep{\par\vskip6pt}%
+    \def\authorsep{\par\vskip8pt}}}
+
+\newbox\absbox
+\let\@elsarticleabstitle\@empty %*%
+\def\abstracttitle#1{\gdef\@elsarticleabstitle{#1}} %*%
+\abstracttitle{Abstract} %*%
+\renewenvironment{abstract}{\global\setbox\absbox=\vbox\bgroup
+  \hsize=\textwidth\def\baselinestretch{1}%
+  \noindent\unskip\textbf{\@elsarticleabstitle} %*%
+ \par\medskip\noindent\unskip\ignorespaces}
+ {\egroup}
+   
+\newbox\elsarticlehighlightsbox
+\newbox\elsarticlegrabsbox  
+\def\@elsarticlehighlightstitle{Highlights}
+\def\@elsarticlegrabstitle{Graphical Abstract}
+\newif\ifelsprelimpagegrabs\global\elsprelimpagegrabsfalse
+\newif\ifelsprelimpagehl\global\elsprelimpagehlfalse
+\def\elsarticleprelims{%
+ \ifelsprelimpagegrabs\relax%
+   \thispagestyle{empty}%
+   \unvbox\elsarticlegrabsbox%
+   \pagebreak\clearpage%
+ \fi%
+ \ifelsprelimpagehl\relax%
+   \thispagestyle{empty}
+   \unvbox\elsarticlehighlightsbox%
+   \pagebreak\clearpage%   
+   \setcounter{page}{1}%
+ \fi%
+}
+\newenvironment{highlights}{%
+  \global\elsprelimpagehltrue%  
+  \global\setbox\elsarticlehighlightsbox=\vbox\bgroup
+  \hsize=\textwidth\def\baselinestretch{1}%
+  \noindent\unskip{\Large\@elsarticlehighlightstitle}%*%
+  \par\vskip12pt\noindent\unskip\ignorespaces\textbf{\@title}%
+  \ifx\elsprelimauthors\@empty\relax\else%
+    \par\vskip6pt\noindent\unskip\ignorespaces%
+    \ifdoubleblind%
+      \vspace*{2pc}
+    \else%
+      \elsprelimauthors%
+    \fi%
+  \fi%
+  \par\medskip\noindent\unskip\ignorespaces
+ \begin{itemize}
+ }
+ {\end{itemize}
+  \egroup}
+\newenvironment{graphicalabstract}{%
+  \global\elsprelimpagegrabstrue%
+  \global\setbox\elsarticlegrabsbox=\vbox\bgroup
+  \hsize=\textwidth\def\baselinestretch{1}%
+  \noindent\unskip{\Large\@elsarticlegrabstitle}%*%
+  \par\vskip12pt\noindent\unskip\ignorespaces\textbf{\@title}%
+  \ifx\elsprelimauthors\@empty\relax\else%
+    \par\vskip6pt\noindent\unskip\ignorespaces%
+    \ifdoubleblind%
+      \vspace*{2pc}
+    \else%
+      \elsprelimauthors%
+    \fi%
+  \fi%  
+ \par\medskip\noindent\unskip\ignorespaces}
+ {\egroup} 
+
+\newbox\keybox
+\let\@elsarticlekwdtitle\@empty %*%
+\def\keywordtitle#1{\gdef\@elsarticlekwdtitle{#1}} %*%
+\def\keywordtitlesep#1{\gdef\@elsarticlekeywordtitlesep{#1}} %*%
+\keywordtitle{Keywords} %*%
+\keywordtitlesep{:\ }
+\def\keyword{%
+  \def\sep{\unskip, }%
+ \def\MSC{\@ifnextchar[{\@MSC}{\@MSC[2000]}}
+  \def\@MSC[##1]{\par\leavevmode\hbox {\it ##1~MSC:\space}}%
+  \def\PACS{\par\leavevmode\hbox {\it PACS:\space}}%
+  \def\JEL{\par\leavevmode\hbox {\it JEL:\space}}%
+  \global\setbox\keybox=\vbox\bgroup\hsize=\textwidth
+  \normalsize\normalfont\def\baselinestretch{1}
+  \parskip\z@
+  \noindent\textit{\@elsarticlekwdtitle\@elsarticlekeywordtitlesep}
+  \raggedright                         % Keywords are not justified.
+  \ignorespaces}
+\def\endkeyword{\par \egroup}
+
+\newdimen\Columnwidth
+\Columnwidth=\columnwidth
+
+\def\printFirstPageNotes{%
+  \iflongmktitle
+    \let\columnwidth=\textwidth
+  \fi
+\ifdoubleblind
+\else
+  \ifx\@tnotes\@empty\else\@tnotes\fi
+  \ifx\@nonumnotes\@empty\else\@nonumnotes\fi
+  \ifx\@cornotes\@empty\else\@cornotes\fi
+  \ifx\@elseads\@empty\relax\else
+   \let\thefootnote\relax
+   \footnotetext{\ifnum\theead=1\relax
+      \textit{Email address:\space}\else
+      \textit{Email addresses:\space}\fi
+     \@elseads}\fi
+  \ifx\@elsuads\@empty\relax\else
+   \let\thefootnote\relax
+   \footnotetext{\textit{URL:\space}%
+     \@elsuads}\fi
+\fi
+  \ifx\@fnotes\@empty\else\@fnotes\fi
+  \iflongmktitle\if@twocolumn
+   \let\columnwidth=\Columnwidth\fi\fi
+}
+
+%% Pushing text to begin on newpage %*%
+\def\newpage@after@title{title}
+\def\newpage@after@author{author}
+\def\newpage@after@abstract{abstract}
+\def\newpageafter#1%
+    {\gdef\@elsarticlenewpageafter{#1}}
+
+\long\def\pprintMaketitle{\clearpage
+  \iflongmktitle\if@twocolumn\let\columnwidth=\textwidth\fi\fi
+  \resetTitleCounters
+  \def\baselinestretch{1}%
+  \printFirstPageNotes
+  \begin{\elsarticletitlealign}%
+ \thispagestyle{pprintTitle}%
+   \def\baselinestretch{1}%
+    \Large\@title\par\vskip18pt%
+    \ifx\@elsarticlenewpageafter\newpage@after@title% %*%
+      \newpage
+    \fi%
+    \ifdoubleblind
+      \vspace*{2pc}
+    \else
+      \normalsize\elsauthors\par\vskip10pt
+      \footnotesize\itshape\elsaddress\par\vskip36pt
+    \fi
+    \ifx\@elsarticlenewpageafter\newpage@after@author% %*%
+      \newpage
+    \fi%
+    \hrule\vskip12pt
+    \ifvoid\absbox\else\unvbox\absbox\par\vskip10pt\fi
+    \ifvoid\keybox\else\unvbox\keybox\par\vskip10pt\fi
+    \hrule\vskip12pt
+    \ifx\@elsarticlenewpageafter\newpage@after@abstract% %*%
+      \newpage
+    \fi%
+    \end{\elsarticletitlealign}%
+    \gdef\thefootnote{\arabic{footnote}}%
+  }
+
+\def\printWarning{%
+     \mbox{}\par\vfill\par\bgroup
+     \fboxsep12pt\fboxrule1pt
+     \hspace*{.18\textwidth}
+     \fcolorbox{gray50}{gray10}{\box\warnbox}
+     \egroup\par\vfill\thispagestyle{empty}
+     \setcounter{page}{0}
+     \clearpage}
+
+\long\def\finalMaketitle{%
+  \resetTitleCounters
+  \def\baselinestretch{1}%
+   \MaketitleBox
+   \thispagestyle{pprintTitle}%
+  \gdef\thefootnote{\arabic{footnote}}%
+  }
+
+\long\def\MaketitleBox{%
+  \resetTitleCounters
+  \def\baselinestretch{1}%
+  \begin{\elsarticletitlealign}%
+   \def\baselinestretch{1}%
+    \Large\@title\par\vskip18pt
+  \ifdoubleblind
+    \vspace*{2pc}
+  \else
+    \normalsize\elsauthors\par\vskip10pt
+    \footnotesize\itshape\elsaddress\par\vskip36pt
+  \fi
+    \hrule\vskip12pt
+    \ifvoid\absbox\else\unvbox\absbox\par\vskip10pt\fi
+    \ifvoid\keybox\else\unvbox\keybox\par\vskip10pt\fi
+    \hrule\vskip12pt
+    \end{\elsarticletitlealign}%
+}
+
+\def\FNtext#1{\par\bgroup\footnotesize#1\egroup}
+\newdimen\space@left
+\def\alarm#1{\typeout{******************************}%
+             \typeout{#1}%
+             \typeout{******************************}%
+}
+
+\def\titlespancalculator#1#2#3#4{%
+  % break count
+  \@tempcnta=#4\relax%
+  % pagebreakcount increment
+  \advance\@tempcnta by 1\relax%
+  % title page height
+  \@tempdima=#1\relax%
+  % Page height - title page notes height (only for first break)
+  % Page height - textheight (for remaining breaks)
+  % Page height - title page notes height
+  \@tempdimb=#2\relax%
+  % Remaining title page height
+  \advance\@tempdima -\the\@tempdimb%
+  % Checks if remaining title page
+  % height less than textheight
+  \ifdim\the\@tempdima>#3\relax%
+     \titlespancalculator%
+      {\the\@tempdima}{#3}{#3}{\the\@tempcnta}%Break again
+  \else%
+  % Save break count and exit.
+     \xdef\savetitlepagespan{\the\@tempcnta}%
+  \fi%
+}%
+
+\long\def\myfor#1#2#3{%
+  \@tempcnta=#1\relax%
+  \ifnum#1<#2\relax%
+    \advance\@tempcnta by 1\relax%
+    #3%
+    \myfor{\the\@tempcnta}{#2}{#3}%
+  \fi}
+
+\long\def\getSpaceLeft{%\global\@twocolumnfalse%
+   \global\setbox0=\vbox{\hsize=\textwidth\MaketitleBox}%
+   \global\setbox1=\vbox{\hsize=\textwidth
+    \let\footnotetext\FNtext
+    \printFirstPageNotes}%
+    \xdef\noteheight{\the\ht1}%
+    \xdef\titleheight{\the\ht0}%
+    \@tempdima=\vsize
+    \advance\@tempdima-\noteheight
+    \advance\@tempdima-1\baselineskip
+    \xdef\savefpageheight{\the\@tempdima}%
+    \setbox2=\vbox{\titlespancalculator{\titleheight}%
+       {\savefpageheight}{\textheight}{0}}%
+}
+
+  \skip\footins=24pt
+
+\newbox\els@boxa
+\newbox\els@boxb
+
+\ifpreprint
+  \def\maketitle{\elsarticleprelims\pprintMaketitle}
+  \else
+   \ifnum\jtype=1
+    \def\maketitle{%
+      \elsarticleprelims%
+      \iflongmktitle\getSpaceLeft
+        \ifdim\noteheight>0pt%
+    \advance\@tempdima-1.35\baselineskip
+        \fi%
+       \global\setbox\els@boxa=\vsplit0 to \@tempdima
+       \box\els@boxa\par\resetTitleCounters
+       \thispagestyle{pprintTitle}%
+       \printFirstPageNotes
+       \ifnum\savetitlepagespan>1\relax%
+       \myfor{2}{\savetitlepagespan}{%
+       \global\setbox\els@boxb=\vsplit0 to \textheight%\@tempdima
+       \box\els@boxb}
+       \else%
+       \fi%
+       \box0%
+      \else
+       \finalMaketitle\printFirstPageNotes
+      \fi
+    \gdef\thefootnote{\arabic{footnote}}}%
+  \else
+ \ifnum\jtype=5
+    \def\maketitle{%
+      \elsarticleprelims%
+      \iflongmktitle\getSpaceLeft
+        \ifdim\noteheight>0pt%
+    \advance\@tempdima-1.35\baselineskip
+        \fi%
+       \global\setbox\els@boxa=\vsplit0 to \@tempdima
+       \box\els@boxa\par\resetTitleCounters
+       \thispagestyle{pprintTitle}%
+       \printFirstPageNotes
+       \ifnum\savetitlepagespan>1\relax%
+       \myfor{2}{\savetitlepagespan}{%
+       \global\setbox\els@boxb=\vsplit0 to \textheight%\@tempdima
+       \twocolumn[\box\els@boxb]}
+       \else%
+       \fi%
+       \twocolumn[\box0]%\printFirstPageNotes
+      \else
+       \twocolumn[\finalMaketitle]\printFirstPageNotes
+     \fi
+     \gdef\thefootnote{\arabic{footnote}}}
+  \else
+  \if@twocolumn
+    \def\maketitle{%
+        \elsarticleprelims%
+        \iflongmktitle\getSpaceLeft
+          \ifdim\noteheight>0pt%
+    \advance\@tempdima-1.35\baselineskip
+        \fi%
+       \global\setbox\els@boxa=\vsplit0 to \@tempdima
+       \box\els@boxa\par\resetTitleCounters
+       \thispagestyle{pprintTitle}%
+       \printFirstPageNotes
+       \ifnum\savetitlepagespan>1\relax%
+       \myfor{2}{\savetitlepagespan}{%
+       \global\setbox\els@boxb=\vsplit0 to \textheight%\@tempdima
+       \twocolumn[\box\els@boxb]}
+       \else%
+       \fi%
+       \twocolumn[\box0]%
+      \else
+       \twocolumn[\finalMaketitle]\printFirstPageNotes
+      \fi
+     \gdef\thefootnote{\arabic{footnote}}}%
+   \else
+    \def\maketitle{%
+      \elsarticleprelims%
+      \iflongmktitle\getSpaceLeft
+        \ifdim\noteheight>0pt%
+    \advance\@tempdima-1.35\baselineskip
+        \fi%
+       \global\setbox\els@boxa=\vsplit0 to \@tempdima
+       \box\els@boxa\par\resetTitleCounters
+       \thispagestyle{pprintTitle}%
+       \printFirstPageNotes
+       \ifnum\savetitlepagespan>1\relax%
+       \myfor{2}{\savetitlepagespan}{%
+       \global\setbox\els@boxb=\vsplit0 to \textheight%\@tempdima
+       \box\els@boxb}
+       \else%
+       \fi%
+       \box0%
+     \else
+       \elsarticleprelims%
+       \finalMaketitle\printFirstPageNotes
+      \fi
+    \gdef\thefootnote{\arabic{footnote}}}%
+   \fi
+  \fi
+ \fi
+\fi
+
+\let\@elsarticlemyfooter\@empty
+\let\@elsarticlemyfooteralign\@empty
+\def\@elsarticlemyfooteralignleft{L}
+\def\@elsarticlemyfooteralignright{R}
+\def\@elsarticlemyfooteraligncenter{C}
+
+\def\myfooter[#1]#2 %*%
+      {\gdef\@elsarticlemyfooteralign{#1}
+       \gdef\@elsarticlemyfooter{#2}}
+
+
+\def\myfooterfont#1{\gdef\@myfooterfont{#1}}
+\myfooterfont{\footnotesize\itshape}
+%    \end{macrocode}
+%    
+%\section{Headers/footers}
+%
+%    \begin{macrocode}
+\def\ps@pprintTitle{%
+     \let\@oddhead\@empty
+     \let\@evenhead\@empty
+     \def\@oddfoot
+       {\hbox to \textwidth%
+        {\ifnopreprintline\relax\else
+        \@myfooterfont%
+         \ifx\@elsarticlemyfooteralign\@elsarticlemyfooteraligncenter%
+           \hfil\@elsarticlemyfooter\hfil%
+         \else%
+         \ifx\@elsarticlemyfooteralign\@elsarticlemyfooteralignleft%
+           \@elsarticlemyfooter\hfill{}%
+         \else%
+         \ifx\@elsarticlemyfooteralign\@elsarticlemyfooteralignright%
+           {}\hfill\@elsarticlemyfooter%
+         \else%
+               Preprint submitted to \ifx\@journal\@empty%
+                 Elsevier%
+            \else\@journal\fi\hfill\@date\fi%
+         \fi%
+         \fi%
+         \fi%
+         }%
+       }%
+     \let\@evenfoot\@oddfoot}
+%    \end{macrocode}
+%
+% \section{Section headings}
+%
+%    \begin{macrocode}
+\def\@seccntDot{.}
+\def\@seccntformat#1{\csname the#1\endcsname\@seccntDot\hskip 0.5em}
+
+\renewcommand\section{\@startsection {section}{1}{\z@}%
+           {18\p@ \@plus 6\p@ \@minus 3\p@}%
+           {9\p@ \@plus 6\p@ \@minus 3\p@}%
+           {\normalsize\bfseries\boldmath}}
+\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
+           {12\p@ \@plus 6\p@ \@minus 3\p@}%
+           {3\p@ \@plus 6\p@ \@minus 3\p@}%
+           {\normalfont\normalsize\itshape}}
+\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
+           {12\p@ \@plus 6\p@ \@minus 3\p@}%
+           {\p@}%
+           {\normalfont\normalsize\itshape}}
+
+\def\paragraph{\secdef{\els@aparagraph}{\els@bparagraph}}
+\def\els@aparagraph[#1]#2{\elsparagraph[#1]{#2.}}
+\def\els@bparagraph#1{\elsparagraph*{#1.}}
+
+\newcommand\elsparagraph{\@startsection{paragraph}{4}{0\z@}%
+           {10\p@ \@plus 6\p@ \@minus 3\p@}%
+           {-6\p@}%
+           {\normalfont\itshape}}
+%    \end{macrocode}
+%
+%\section{List environment}
+%
+%    \begin{macrocode}
+\newdimen\leftMargin
+\leftMargin=2em
+\newtoks\@enLab  %\newtoks\@enfont
+\def\@enQmark{?}
+\def\@enLabel#1#2{%
+  \edef\@enThe{\noexpand#1{\@enumctr}}%
+  \@enLab\expandafter{\the\@enLab\csname the\@enumctr\endcsname}%
+  \@enloop}
+\def\@enSpace{\afterassignment\@enSp@ce\let\@tempa= }
+\def\@enSp@ce{\@enLab\expandafter{\the\@enLab\space}\@enloop}
+\def\@enGroup#1{\@enLab\expandafter{\the\@enLab{#1}}\@enloop}
+\def\@enOther#1{\@enLab\expandafter{\the\@enLab#1}\@enloop}
+\def\@enloop{\futurelet\@entemp\@enloop@}
+\def\@enloop@{%
+  \ifx A\@entemp         \def\@tempa{\@enLabel\Alph  }\else
+  \ifx a\@entemp         \def\@tempa{\@enLabel\alph  }\else
+  \ifx i\@entemp         \def\@tempa{\@enLabel\roman }\else
+  \ifx I\@entemp         \def\@tempa{\@enLabel\Roman }\else
+  \ifx 1\@entemp         \def\@tempa{\@enLabel\arabic}\else
+  \ifx \@sptoken\@entemp \let\@tempa\@enSpace         \else
+  \ifx \bgroup\@entemp   \let\@tempa\@enGroup         \else
+  \ifx \@enum@\@entemp   \let\@tempa\@gobble          \else
+                         \let\@tempa\@enOther
+             \fi\fi\fi\fi\fi\fi\fi\fi
+  \@tempa}
+\newlength{\@sep} \newlength{\@@sep}
+\setlength{\@sep}{.5\baselineskip plus.2\baselineskip
+            minus.2\baselineskip}
+\setlength{\@@sep}{.1\baselineskip plus.01\baselineskip
+            minus.05\baselineskip}
+\providecommand{\sfbc}{\rmfamily\upshape}
+\providecommand{\sfn}{\rmfamily\upshape}
+\def\@enfont{\ifnum \@enumdepth >1\let\@nxt\sfn \else\let\@nxt\sfbc \fi\@nxt}
+\def\enumerate{%
+   \ifnum \@enumdepth >3 \@toodeep\else
+      \advance\@enumdepth \@ne
+      \edef\@enumctr{enum\romannumeral\the\@enumdepth}\fi
+   \@ifnextchar[{\@@enum@}{\@enum@}}
+\def\@@enum@[#1]{%
+  \@enLab{}\let\@enThe\@enQmark
+  \@enloop#1\@enum@
+  \ifx\@enThe\@enQmark\@warning{The counter will not be printed.%
+   ^^J\space\@spaces\@spaces\@spaces The label is: \the\@enLab}\fi
+  \expandafter\edef\csname label\@enumctr\endcsname{\the\@enLab}%
+  \expandafter\let\csname the\@enumctr\endcsname\@enThe
+  \csname c@\@enumctr\endcsname7
+  \expandafter\settowidth
+            \csname leftmargin\romannumeral\@enumdepth\endcsname
+            {\the\@enLab\hskip\labelsep}%
+  \@enum@}
+\def\@enum@{\list{{\@enfont\csname label\@enumctr\endcsname}}%
+           {\usecounter{\@enumctr}\def\makelabel##1{\hss\llap{##1}}%
+     \ifnum \@enumdepth>1\setlength{\topsep}{\@@sep}\else
+           \setlength{\topsep}{\@sep}\fi
+     \ifnum \@enumdepth>1\setlength{\itemsep}{0pt plus1pt minus1pt}%
+      \else \setlength{\itemsep}{\@@sep}\fi
+     %\setlength\leftmargin{\leftMargin}%%%{1.8em}
+     \setlength{\parsep}{0pt plus1pt minus1pt}%
+     \setlength{\parskip}{0pt plus1pt minus1pt}
+                   }}
+
+\def\endenumerate{\par\ifnum \@enumdepth >1\addvspace{\@@sep}\else
+           \addvspace{\@sep}\fi \endlist}
+
+\def\sitem{\@noitemargtrue\@item[\@itemlabel *]}
+
+\def\itemize{\@ifnextchar[{\@Itemize}{\@Itemize[]}}
+
+\def\@Itemize[#1]{\def\next{#1}%
+  \ifnum \@itemdepth >\thr@@\@toodeep\else
+   \advance\@itemdepth\@ne
+  \ifx\next\@empty\else\expandafter\def\csname
+   labelitem\romannumeral\the\@itemdepth\endcsname{#1}\fi%
+  \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
+  \expandafter\list\csname\@itemitem\endcsname
+  {\def\makelabel##1{\hss\llap{##1}}}%
+ \fi}
+%    \end{macrocode}
+%
+%\section{Theorem environment}
+%
+%    \begin{macrocode}
+\def\newdefinition#1{%
+  \@ifnextchar[{\@odfn{#1}}{\@ndfn{#1}}}%]
+\def\@ndfn#1#2{%
+  \@ifnextchar[{\@xndfn{#1}{#2}}{\@yndfn{#1}{#2}}}
+\def\@xndfn#1#2[#3]{%
+  \expandafter\@ifdefinable\csname #1\endcsname
+    {\@definecounter{#1}\@newctr{#1}[#3]%
+     \expandafter\xdef\csname the#1\endcsname{%
+       \expandafter\noexpand\csname the#3\endcsname \@dfncountersep
+          \@dfncounter{#1}}%
+     \global\@namedef{#1}{\@dfn{#1}{#2}}%
+     \global\@namedef{end#1}{\@enddefinition}}}
+\def\@yndfn#1#2{%
+  \expandafter\@ifdefinable\csname #1\endcsname
+    {\@definecounter{#1}%
+     \expandafter\xdef\csname the#1\endcsname{\@dfncounter{#1}}%
+     \global\@namedef{#1}{\@dfn{#1}{#2}}%
+     \global\@namedef{end#1}{\@enddefinition}}}
+\def\@odfn#1[#2]#3{%
+  \@ifundefined{c@#2}{\@nocounterr{#2}}%
+    {\expandafter\@ifdefinable\csname #1\endcsname
+    {\global\@namedef{the#1}{\@nameuse{the#2}}
+  \global\@namedef{#1}{\@dfn{#2}{#3}}%
+  \global\@namedef{end#1}{\@enddefinition}}}}
+\def\@dfn#1#2{%
+  \refstepcounter{#1}%
+  \@ifnextchar[{\@ydfn{#1}{#2}}{\@xdfn{#1}{#2}}}
+\def\@xdfn#1#2{%
+  \@begindefinition{#2}{\csname the#1\endcsname}\ignorespaces}
+\def\@ydfn#1#2[#3]{%
+  \@opargbegindefinition{#2}{\csname the#1\endcsname}{#3}\ignorespaces}
+\def\@dfncounter#1{\noexpand\arabic{#1}}
+\def\@dfncountersep{.}
+\def\@begindefinition#1#2{\trivlist
+   \item[\hskip\labelsep{\bfseries #1\ #2.}]\upshape}
+\def\@opargbegindefinition#1#2#3{\trivlist
+      \item[\hskip\labelsep{\bfseries #1\ #2\ (#3).}]\upshape}
+\def\@enddefinition{\endtrivlist}
+
+\def\@begintheorem#1#2{\trivlist
+  \let\baselinestretch\@blstr
+   \item[\hskip \labelsep{\bfseries #1\ #2.}]\itshape}
+\def\@opargbegintheorem#1#2#3{\trivlist
+  \let\baselinestretch\@blstr
+      \item[\hskip \labelsep{\bfseries #1\ #2\ (#3).}]\itshape}
+
+\def\newproof#1{%
+  \@ifnextchar[{\@oprf{#1}}{\@nprf{#1}}}
+\def\@nprf#1#2{%
+  \@ifnextchar[{\@xnprf{#1}{#2}}{\@ynprf{#1}{#2}}}
+\def\@xnprf#1#2[#3]{%
+  \expandafter\@ifdefinable\csname #1\endcsname
+    {\@definecounter{#1}\@newctr{#1}[#3]%
+     \expandafter\xdef\csname the#1\endcsname{%
+       \expandafter\noexpand\csname the#3\endcsname \@prfcountersep
+          \@prfcounter{#1}}%
+     \global\@namedef{#1}{\@prf{#1}{#2}}%
+     \global\@namedef{end#1}{\@endproof}}}
+\def\@ynprf#1#2{%
+  \expandafter\@ifdefinable\csname #1\endcsname
+    {\@definecounter{#1}%
+     \expandafter\xdef\csname the#1\endcsname{\@prfcounter{#1}}%
+     \global\@namedef{#1}{\@prf{#1}{#2}}%
+     \global\@namedef{end#1}{\@endproof}}}
+\def\@oprf#1[#2]#3{%
+  \@ifundefined{c@#2}{\@nocounterr{#2}}%
+    {\expandafter\@ifdefinable\csname #1\endcsname
+    {\global\@namedef{the#1}{\@nameuse{the#2}}%
+  \global\@namedef{#1}{\@prf{#2}{#3}}%
+  \global\@namedef{end#1}{\@endproof}}}}
+\def\@prf#1#2{%
+  \refstepcounter{#1}%
+  \@ifnextchar[{\@yprf{#1}{#2}}{\@xprf{#1}{#2}}}
+\def\@xprf#1#2{%
+  \@beginproof{#2}{\csname the#1\endcsname}\ignorespaces}
+\def\@yprf#1#2[#3]{%
+  \@opargbeginproof{#2}{\csname the#1\endcsname}{#3}\ignorespaces}
+\def\@prfcounter#1{\noexpand\arabic{#1}}
+\def\@prfcountersep{.}
+\def\@beginproof#1#2{\trivlist\let\baselinestretch\@blstr
+   \item[\hskip \labelsep{\scshape #1.}]\rmfamily}
+\def\@opargbeginproof#1#2#3{\trivlist\let\baselinestretch\@blstr
+      \item[\hskip \labelsep{\scshape #1\ (#3).}]\rmfamily}
+\def\@endproof{\endtrivlist}
+\newcommand*{\qed}{\hbox{}\hfill$\Box$}
+
+\@ifundefined{@biboptions}{\xdef\@biboptions{numbers}}{}
+\InputIfFileExists{\jobname.spl}{}{}
+\ifnonatbib\relax\else
+  \RequirePackage[\@biboptions]{natbib}
+\fi
+\newwrite\splwrite
+\immediate\openout\splwrite=\jobname.spl
+\def\biboptions#1{\def\next{#1}\immediate\write\splwrite{%
+   \string\g@addto@macro\string\@biboptions{%
+    ,\expandafter\strip@prefix\meaning\next}}}
+
+\let\baselinestretch=\@blstr
+%    \end{macrocode}
+%
+%\section{Page dimensions and margins for final form}
+%
+%\subsection{Option 1p}
+%
+%    \begin{macrocode}
+\ifnum\jtype=1
+ \RequirePackage{geometry}
+ \geometry{twoside,
+  paperwidth=210mm,
+  paperheight=297mm,
+  textheight=562pt,
+  textwidth=384pt,
+  centering,
+  headheight=50pt,
+  headsep=12pt,
+  footskip=12pt,
+  footnotesep=24pt plus 2pt minus 12pt,
+ }
+ \global\let\bibfont=\footnotesize
+ \global\bibsep=0pt
+ \if@twocolumn\global\@twocolumnfalse\fi
+%
+%    \end{macrocode}
+%
+%\subsection{Option '3p'}
+%
+%    \begin{macrocode}
+\else\ifnum\jtype=3
+ \RequirePackage{geometry}
+ \geometry{twoside,
+  paperwidth=210mm,
+  paperheight=297mm,
+  textheight=622pt,
+  textwidth=468pt,
+  centering,
+  headheight=50pt,
+  headsep=12pt,
+  footskip=18pt,
+  footnotesep=24pt plus 2pt minus 12pt,
+  columnsep=2pc
+ }
+ \global\let\bibfont=\footnotesize
+ \global\bibsep=0pt
+ \if@twocolumn\input{fleqn.clo}\fi
+%    \end{macrocode}
+%
+%\subsection{Option '5p'}
+%
+%    \begin{macrocode}
+\else\ifnum\jtype=5
+ \RequirePackage{geometry}
+ \geometry{twoside,
+  paperwidth=210mm,
+  paperheight=297mm,
+  textheight=682pt,
+  textwidth=522pt,
+  centering,
+ headheight=50pt,
+  headsep=12pt,
+  footskip=18pt,
+  footnotesep=24pt plus 2pt minus 12pt,
+  columnsep=18pt
+ }%
+ \global\let\bibfont=\footnotesize
+ \global\bibsep=0pt
+ \input{fleqn.clo}
+ \global\@twocolumntrue
+%%
+%% End of option '5p'
+%%
+\fi\fi\fi
+%    \end{macrocode}
+%
+%\section{Other items}
+%
+%    \begin{macrocode}
+\def\journal#1{\gdef\@journal{#1}}
+ \let\@journal\@empty
+\newenvironment{frontmatter}{}{\maketitle}
+
+\long\def\@makecaption#1#2{%
+  \vskip\abovecaptionskip\footnotesize
+  \sbox\@tempboxa{#1: #2}%
+  \ifdim \wd\@tempboxa >\hsize
+    #1: #2\par
+  \else
+    \global \@minipagefalse
+    \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}%
+  \fi
+  \vskip\belowcaptionskip}
+
+\AtBeginDocument{\@ifpackageloaded{hyperref}
+  {\def\@linkcolor{blue}
+   \def\@anchorcolor{blue}
+   \def\@citecolor{blue}
+   \def\@filecolor{blue}
+   \def\@urlcolor{blue}
+   \def\@menucolor{blue}
+   \def\@pagecolor{blue}
+\begingroup
+  \@makeother\`%
+  \@makeother\=%
+  \edef\x{%
+    \edef\noexpand\x{%
+      \endgroup
+      \noexpand\toks@{%
+        \catcode 96=\noexpand\the\catcode`\noexpand\`\relax
+        \catcode 61=\noexpand\the\catcode`\noexpand\=\relax
+      }%
+    }%
+    \noexpand\x
+  }%
+\x
+\@makeother\`
+\@makeother\=
+}{}}
+%%
+\def\appendixname{Appendix}
+\renewcommand\appendix{\par
+  \setcounter{section}{0}%
+  \setcounter{subsection}{0}%
+  \setcounter{equation}{0}
+  \gdef\thefigure{\@Alph\c@section.\arabic{figure}}%
+  \gdef\thetable{\@Alph\c@section.\arabic{table}}%
+  \gdef\thesection{\appendixname~\@Alph\c@section}%
+  \@addtoreset{equation}{section}%
+  \gdef\theequation{\@Alph\c@section.\arabic{equation}}%
+  \addtocontents{toc}{\string\let\string\numberline\string\tmptocnumberline}{}{}
+}
+
+%%%% \numberline width calculation for appendix.
+\newdimen\appnamewidth
+\def\tmptocnumberline#1{%
+   \setbox0=\hbox{\appendixname}
+   \appnamewidth=\wd0
+   \addtolength\appnamewidth{2.5pc}
+   \hb@xt@\appnamewidth{#1\hfill}
+}
+
+%% Added for work with amsrefs.sty
+
+\@ifpackageloaded{amsrefs}%
+  {}
+  {%\let\bibsection\relax%
+  \AtBeginDocument{\def\cites@b#1#2,#3{%
+    \begingroup[%
+        \toks@{\InnerCite{#2}#1}%
+        \ifx\@empty#3\@xp\@gobble\fi
+        \cites@c#3%
+}}}
+%%
+%% Added for avoiding clash with cleveref.sty
+\@ifpackageloaded{cleveref}%
+ {}
+ {\def\tnotetext[#1]#2{\g@addto@macro\@tnotes{%
+    \refstepcounter{tnote}%
+    \immediate\write\@auxout{\string\Newlabel{#1}{\thetnote}}
+    \def\thefootnote{\ifcase\c@tnote\or$\star$\or$\star\star$\fi}%
+    \footnotetext{#2}}}
+%%%
+  \def\fntext[#1]#2{\g@addto@macro\@fnotes{%
+    \refstepcounter{fnote}%
+    \immediate\write\@auxout{\string\Newlabel{#1}{\thefnote}}
+    \def\thefootnote{\thefnote}%
+    \global\setcounter{footnote}{\c@fnote}%
+    \footnotetext{#2}}}
+%%%
+  \def\cortext[#1]#2{\g@addto@macro\@cornotes{%
+    \refstepcounter{cnote}%
+    \immediate\write\@auxout{\string\Newlabel{#1}{\thecnote}}
+    \def\thefootnote{\ifcase\c@cnote\or$\ast$\or
+    $\ast\ast$\fi}%
+    \footnotetext{#2}}}
+}
+
+\def\textmarker#1#2{\textcolor{#1}{#2}}%*%
+%</class>
+%
+%    \end{macrocode}
+% \Finale
+\endinput
+
+%%
+%% End of file 'elsarticle.dtx'
+%%
+
diff --git a/papers/variational_smoother/elsarticle.ins b/papers/variational_smoother/elsarticle.ins
new file mode 100644
index 0000000..3be91dd
--- /dev/null
+++ b/papers/variational_smoother/elsarticle.ins
@@ -0,0 +1,67 @@
+%%
+%% This file will generate fast loadable files and documentation
+%% driver files from the doc files in this package when run through
+%% LaTeX or TeX.
+%%
+%% Copyright 2007-2024 Elsevier Ltd
+%%
+%% This file is part of the 'Elsarticle Bundle'.
+%% ---------------------------------------------
+%%
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.3 of this license or (at your option) any
+%% later version.  The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%%
+%% The list of all files belonging to the 'Elsarticle Bundle' is
+%% given in the file 'manifest.txt'.
+%%
+%% $Id: elsarticle.ins 251 2024-04-06 10:53:35Z rishi $
+%%
+%%
+\input docstrip.tex
+%%\keepsilent
+
+\preamble
+
+Copyright 2007-2024 Elsevier Ltd
+
+This file is part of the 'Elsarticle Bundle'.
+-------------------------------------------
+
+It may be distributed under the conditions of the LaTeX Project Public
+License, either version 1.3 of this license or (at your option) any
+later version.  The latest version of this license is in
+   http://www.latex-project.org/lppl.txt
+and version 1.3 or later is part of all distributions of LaTeX
+version 1999/12/01 or later.
+
+The list of all files belonging to the 'Elsarticle Bundle' is
+given in the file `manifest.txt'.
+
+\endpreamble
+
+\askforoverwritefalse
+
+\generate{\file{elsarticle.cls}{\from{elsarticle.dtx}{class}}}
+\obeyspaces
+\Msg{*************************************************************}
+\Msg{*                                                           *}
+\Msg{* To finish the installation you have to move the following *}
+\Msg{* file into a directory searched by TeX:                    *}
+\Msg{*                                                           *}
+\Msg{*     elsarticle.cls                                        *}
+\Msg{*         and                                               *}
+\Msg{*     elsarticle-*.bst                                      *}
+\Msg{*                                                           *}
+\Msg{* To produce the documentation go to the ../contrib folder  *}
+\Msg{* and run the file elsdoc.tex through pdfLaTeX              *}
+\Msg{* or use the Makefile which is far more easier.             *}
+\Msg{*                                                           *}
+\Msg{* Happy TeXing!                                             *}
+\Msg{*                                                           *}
+\Msg{*************************************************************}
+
+\endbatchfile
diff --git a/papers/variational_smoother/jacobian_derivation.pdf b/papers/variational_smoother/jacobian_derivation.pdf
new file mode 100644
index 0000000..1617e30
Binary files /dev/null and b/papers/variational_smoother/jacobian_derivation.pdf differ
diff --git a/papers/variational_smoother/jacobian_derivation.tex b/papers/variational_smoother/jacobian_derivation.tex
new file mode 100644
index 0000000..e45c5f9
--- /dev/null
+++ b/papers/variational_smoother/jacobian_derivation.tex
@@ -0,0 +1,588 @@
+%% 
+%% Copyright 2007-2024 Elsevier Ltd
+%% 
+%% This file is part of the 'Elsarticle Bundle'.
+%% ---------------------------------------------
+%% 
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.3 of this license or (at your option) any
+%% later version.  The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%% 
+%% The list of all files belonging to the 'Elsarticle Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%% Template article for Elsevier's document class `elsarticle'
+%% with numbered style bibliographic references
+%% SP 2008/03/01
+%% $Id: elsarticle-template-num.tex 249 2024-04-06 10:51:24Z rishi $
+%%
+\documentclass[preprint,12pt]{elsarticle}
+
+%% Use the option review to obtain double line spacing
+%% \documentclass[authoryear,preprint,review,12pt]{elsarticle}
+
+%% Use the options 1p,twocolumn; 3p; 3p,twocolumn; 5p; or 5p,twocolumn
+%% for a journal layout:
+%% \documentclass[final,1p,times]{elsarticle}
+%% \documentclass[final,1p,times,twocolumn]{elsarticle}
+%% \documentclass[final,3p,times]{elsarticle}
+%% \documentclass[final,3p,times,twocolumn]{elsarticle}
+%% \documentclass[final,5p,times]{elsarticle}
+%% \documentclass[final,5p,times,twocolumn]{elsarticle}
+
+%% For including figures, graphicx.sty has been loaded in
+%% elsarticle.cls. If you prefer to use the old commands
+%% please give \usepackage{epsfig}
+
+%% The amssymb package provides various useful mathematical symbols
+\usepackage{amssymb}
+%% The amsmath package provides various useful equation environments.
+\usepackage{amsmath}
+\usepackage{bm}
+%% The amsthm package provides extended theorem environments
+%% \usepackage{amsthm}
+
+%% The lineno packages adds line numbers. Start line numbering with
+%% \begin{linenumbers}, end it with \end{linenumbers}. Or switch it on
+%% for the whole article with \linenumbers.
+\usepackage{lineno}
+
+%% Package for strikeout
+\usepackage[normalem]{ulem}
+
+% For creating tree diagrams
+\usepackage{tikz}
+\usetikzlibrary{shapes.geometric, arrows, positioning, trees}
+
+% For writing algorithms
+\usepackage[linesnumbered,ruled,vlined]{algorithm2e}
+
+% Make \paragraph have its own line
+\usepackage{indentfirst}
+\usepackage{titlesec}
+
+\titleformat{\paragraph}
+  {\normalfont\itshape}{\theparagraph}{1em}{}
+\titlespacing*{\paragraph}
+  {0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}
+
+% Define commands for contributors to comment
+\usepackage[svgnames]{xcolor}
+\newcommand{\pab}[1]{\textcolor{blue}{{\scriptsize PAB:} #1}}
+\newcommand{\rhs}[1]{\textcolor{violet}{{\scriptsize RHS:} #1}}
+
+\usepackage{empheq}
+\usepackage{xpatch}
+\makeatletter
+\newcommand{\colorboxed}[1]{\fcolorbox{blue}{white}{\m@th$\displaystyle#1$}}
+\xpatchcmd{\@Aboxed}{\boxed}{\colorboxed}{}{}
+\makeatother
+
+% other custom commands
+\newcommand{\Eq}[1]{Eq.~\eqref{#1}}
+\newcommand{\Fig}[1]{Fig.~\ref{#1}}
+\newcommand{\be}{\begin{equation}}
+\newcommand{\ee}{\end{equation}}
+
+\renewcommand{\vec}[1]{\bm{#1}}
+\DeclareMathOperator*{\argmax}{arg\,max}
+\DeclareMathOperator*{\argmin}{arg\,min}
+
+\journal{???}
+
+\begin{document}
+
+\begin{frontmatter}
+
+%% Title, authors and addresses
+
+%% use the tnoteref command within \title for footnotes;
+%% use the tnotetext command for theassociated footnote;
+%% use the fnref command within \author or \affiliation for footnotes;
+%% use the fntext command for theassociated footnote;
+%% use the corref command within \author for corresponding author footnotes;
+%% use the cortext command for theassociated footnote;
+%% use the ead command for the email address,
+%% and the form \ead[url] for the home page:
+%% \title{Title\tnoteref{label1}}
+%% \tnotetext[label1]{}
+%% \author{Name\corref{cor1}\fnref{label2}}
+%% \ead{email address}
+%% \ead[url]{home page}
+%% \fntext[label2]{}
+%% \cortext[cor1]{}
+%% \affiliation{organization={},
+%%             addressline={},
+%%             city={},
+%%             postcode={},
+%%             state={},
+%%             country={}}
+%% \fntext[label3]{}
+
+\title{Formulation of Gradient and Hessian Terms of the Distortion-Dilation Term}
+
+%% use optional labels to link authors explicitly to addresses:
+%% \author[label1,label2]{}
+%% \affiliation[label1]{organization={},
+%%             addressline={},
+%%             city={},
+%%             postcode={},
+%%             state={},
+%%             country={}}
+%%
+%% \affiliation[label2]{organization={},
+%%             addressline={},
+%%             city={},
+%%             postcode={},
+%%             state={},
+%%             country={}}
+
+\author[inl]{Patrick Behne} %% Author name
+
+%% Author affiliation
+\affiliation[inl]{organization={Idaho National Laboratory},%Department and Organization
+            addressline={1955 N. Fremont Ave}, 
+            city={Idaho Falls},
+            postcode={83415}, 
+            state={Idaho},
+            country={United States}}
+
+%% Abstract
+%\begin{abstract}
+%\end{abstract}
+
+%%Graphical abstract
+%\begin{graphicalabstract}
+%\includegraphics{grabs}
+%\end{graphicalabstract}
+
+%%Research highlights
+%\begin{highlights}
+%\item Research highlight 1
+%\item Research highlight 2
+%\end{highlights}
+
+%% Keywords
+%\begin{keyword}
+%\end{keyword}
+
+\end{frontmatter}
+
+%% Add \usepackage{lineno} before \begin{document} and uncomment 
+%% following line to enable line numbers
+\linenumbers
+
+%% main text
+%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%\nolinenumbers
+\section{Introduction}
+\label{sec:intro}
+
+The distortion-dilation functional of an $n$-dimensional (i.e., 2D or 3D) mesh to minimize is:
+\be
+\Aboxed{I_h(\vec{R}) = \sum_{c=1}^{N\text{cells}} \int_{\hat{\Omega}_c} E_\theta (S_c(\vec{R})) d \vec{\xi}} \,,
+\ee
+where:
+\begin{itemize}
+	\item $\vec{R} \in \mathcal{R}^{n \times N_\text{nodes}}$ is a vector containing the node locations of the mesh in the physical domain
+	\item $S(\vec{R})$ is the Jacobian of the mapping from the physical cell to the reference cell. The dependence of this mapping on the node locations $\vec{R}$ is made explicit.
+	\item $\vec{\xi}$ denotes the multidimensional reference coordinates.
+	\item $E_\theta (S(\vec{R}))$ is the distortion-dilation function.
+\end{itemize}
+
+The distortion-dilation function is given by
+\be
+\Aboxed{E_\theta(S(\vec{R})) = (1 - \theta) \beta(S(\vec{R})) + \theta \mu(S(\vec{R}))} \,,
+\ee
+where $\theta$ is a weight between zero and one, and $\beta$ and $\mu$ are measures of element distortion and dilation, given by:
+\be
+\Aboxed{\beta(S(\vec{R})) = \frac{\left(\frac{1}{n} \text{tr}(S^TS(\vec{R}))\right)^{\frac{n}{2}}}{\chi_\epsilon(|S(\vec{R})|)}}
+\ee
+and
+\be
+\Aboxed{\mu(S(\vec{R})) = \frac{v + \frac{|S(\vec{R})|^2}{v}}{2\chi_\epsilon(|S(\vec{R})|}} \,,
+\ee
+where $n$ is the dimension of the mesh, $|S|$ denotes the determinant of $S$, and $v$ is the arithmetic average value of the element-averaged $|S|$.
+The function $\chi_\epsilon(|S|)$ is used in place of $|S|$ such that the metrics are well-defined for degenerate and folded elements:
+\be
+\Aboxed{\chi_\epsilon(|S|) = \frac{1}{2} \left( |S| + \sqrt{\epsilon^2 + |S|^2} \right)} \,,
+\ee
+where $\epsilon$ is a small number that prevents $\chi_\epsilon$ from being zero.
+For brevity, $\chi_\epsilon(|S|$ and it's first ($\chi_\epsilon^\prime(|S|)$) and second ($\chi_\epsilon^{\prime \prime}(|S|)$) derivatives with respect to det$(S)$ will be abbreviated by $\chi_\epsilon$, $\chi_\epsilon^\prime$, and $\chi_\epsilon^{\prime \prime}$, respectively.
+These functions will never take parameters other than det$(S)$.
+
+\section{Minimization Proceedure}
+
+We utilize Newton's method to solve the following minimization problem:
+\be
+\vec{R}_\text{smooth} = \argmin_{\vec{R}} I_h(\vec{R}) \,.
+\ee
+At the minimum of $I_h$, the gradient of $I_h$ with respect to the components of $\vec{R}$ will be zero:
+\be
+\nabla_{\vec{R}} I_h(\vec{R}) \rvert_{\vec{R}_\text{smooth}} = \vec{0} \,.
+\ee
+Newton's method can be used to find $\vec{R}_\text{smooth}$.
+The update iteration $k$+1 is:
+\be
+\Aboxed{\vec{R}^{k+1} = \vec{R}^k - H^{-1}(I_h(\vec{R}^k)) \nabla_{\vec{R}} I_h(\vec{R}^k)} \,.
+\ee
+where $H(I_h)$ denotes the Jacobian of the gradient of $I_h$ (i.e., the Hessian):
+\be
+H(I_h) = \nabla_{\vec{R}} \nabla_{\vec{R}} I_h \,.
+\ee
+It is clear that in order to use Newton's method, we must first write down expressions for the gradient and Hessian of $I_h$.
+
+\section{Matrix Calculus Identities}
+\label{sec:matrix_calculus_identities}
+
+Some matrix calculus identities are important in this work.
+In this context, $S$ is a square matrix.
+The derivative of a scalar-valued function $f(S)$ with respect to $S$ is a matrix with the $k,l$ entry given by
+\be
+\left( \frac{\partial f(S)}{\partial S} \right)_{kl} = \frac{\partial f(S)}{\partial S_{kl}} \,.
+\ee
+The following identities hold for the matrix derivatives of $f(S) = |S|$ and $f(S) = \text{tr}(S^TS)$:
+\be
+\Aboxed{\frac{\partial |S|}{\partial S} = |S| S^{-T}} \,,
+\ee
+\be
+\Aboxed{\frac{\partial \text{tr}(S^TS)}{\partial S} = 2S} \,.
+\ee
+
+The derivative of a matrix-valued function $F(S)$ with respect to $S$ is a fourth-order tensor with the $i,j,k,\ell$ entry given by
+\be
+\left( \frac{\partial F(S)}{\partial S} \right)_{ijk\ell} = \frac{\partial F(S)_{ij}}{\partial S_{k\ell}} \,.
+\ee
+The following identity holds for the matrix derivative of $S^{-T}$ with respect to $S$:
+\be
+\Aboxed{\left( \frac{\partial S^{-T}}{\partial S} \right)_{ijk\ell} = - S^{-1}_{li} S^{-1}_{jk}}\,.
+\ee
+
+\section{Gradient of $I_h$}
+
+The gradient of $I_h$ is given by
+\be
+\begin{align*}
+\nabla_{\vec{R}} I_h(\vec{R}) &= \sum_{c=1}^{N\text{cells}} \int_{\hat{\Omega}_c}  \nabla_{\vec{R}} E_\theta (S_c(\vec{R})) d \vec{\xi} \\
+&= \sum_{c=1}^{N\text{cells}} \int_{\hat{\Omega}_c}  \left( (1 - \theta) \nabla_{\vec{R}} \beta (S_c(\vec{R})) + \theta \nabla_{\vec{R}} \mu (S_c(\vec{R})) \right) d \vec{\xi} \,.
+\end{align*}
+\ee
+It follows that we need to compute $\nabla_{\vec{R}} \beta$ and $\nabla_{\vec{R}} \mu$.
+
+\subsection{$\nabla_{\vec{R}} \beta$}
+\label{sec:grad_beta}
+
+By definition,
+\be
+\nabla_{\vec{R}} \beta(\vec{R}) = \nabla_{\vec{R}} \frac{\left(\frac{1}{n} \text{tr}(S^TS(\vec{R}))\right)^{\frac{n}{2}}}{\chi_\epsilon(|S(\vec{R})|)} \,.
+\ee
+Denoting the gradient with respect to $\vec{R}$ (i.e., $\nabla_{\vec{R}}$) by $\partial / \partial \vec{R}$, and employing chain rule,
+\be \label{eq:grad_beta}
+\begin{align*}
+\nabla_{\vec{R}} \beta(\vec{R}) &= \frac{\partial}{\partial \vec{R}} \beta(\vec{R}) \\
+&= \frac{\partial \beta(\vec{R})}{\partial S} \frac{\partial S}{\partial \vec{R}} \,,
+\end{align*}
+\ee
+or element-wise,
+\be \label{eq:grad_beta_element}
+\begin{align*}
+\nabla_{\vec{R}_\ell} \beta(\vec{R}) &= \frac{\partial}{\partial \vec{R}_\ell} \beta(\vec{R}) \\
+&= \sum_a \sum_b \frac{\partial \beta(\vec{R})}{\partial S_{ab}} \frac{\partial S_{ab}}{\partial \vec{R}_\ell} \,.
+\end{align*}
+\ee
+
+First, we will compute the term $\partial S / \partial \vec{R}$.
+In libMesh, the Jacobian matrix within cell $c$, $S(\vec{R}_c)$, has the following representation:
+\be
+S(\vec{R}_c) = \sum_{m=1}^{N_{\text{nodes}, c}} \vec{R}_{c,m} (\nabla_{\vec{\xi}} \phi_m(\vec{\xi}))^T \,,
+\ee
+where $\vec{R}_{c,m} \in \mathcal{R}^n$ are the physical coordinates of the $m$-th node in cell $c$ and $\phi_m$ is the spatial basis function for the $m$-th node.
+Note that this Jacobian matrix is of shape $(n, n)$.
+The expression for element $i,j$ is:
+\be
+S(\vec{R}_c)_{ij} = \sum_{m=1}^{N_{\text{nodes},c}} R_{c,m,i} \partial_{\xi_j} \phi_m(\vec{\xi}) \,,
+\ee
+where $R_{c,m,i}$ denotes the coordinate in the $i$-th dimension of node $\vec{R}_{c,m}$ and $\partial_{\xi_j}$ denotes the $j$-th component of the gradient operator $\nabla_\vec{\xi}$.
+Using this definition, we see that
+\be \label{eq:del_S_del_R}
+\Aboxed{\frac{\partial S(\vec{R}_c)_{i,j}}{\partial R_{c,m,k}} = \delta_{ik} \partial_{\xi_j} \phi_m(\vec{\xi})} \,.
+\ee
+Because \Eq{eq:del_S_del_R} holds for $i,j \in [0, n)$ and $k \in [0, n \times N_\text{nodes})$, $\partial S / \partial \vec{R}$ is a third-order tensor (i.e., the derivative of a matrix with respect to a vector).
+
+Next, we will compute the $\partial \beta / \partial S$ term.
+Note that in all derivations, we use product + chain rules as opposed to quotient rule because quotient rule sucks.
+Quotient rule is fake math invented by Big Mathematics so they had extra material to put in textbooks and sell them for more.
+On top of that, anyone who prefers to use quotient rule instead of writing $1 / \chi_\epsilon = \chi_\epsilon^{-1}$ is obviously delusional and should not be trusted.
+Also note that we utilized the identities from Section \ref{sec:matrix_calculus_identities} when using chain rule.
+\be \label{eq:del_beta_del_S}
+\begin{align*}
+\frac{\partial \beta}{\partial S} &= \frac{\partial}{\partial S} \frac{\left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}}}{\chi_\epsilon} \\
+&= \frac{\frac{n}{2} \left( \frac{1}{n} \text{tr}(S^TS) \right)^{\frac{n}{2}-1} \frac{1}{n} 2S}{\chi_\epsilon} - \frac{\left( \frac{1}{n} \text{tr}(S^TS) \right)^{\frac{n}{2}}}{\chi_\epsilon^2} \frac{\partial \chi_\epsilon (|S|)}{\partial S} \\
+&= \Aboxed{\left( \frac{\left( \frac{1}{n} \text{tr}(S^TS) \right)^{\frac{n}{2} - 1}}{\chi_\epsilon} \right) S - \left( \frac{\left( \frac{1}{n} \text{tr}(S^TS) \right)^\frac{n}{2}}{\chi_\epsilon^2} \chi_\epsilon^\prime |S| \right) S^{-T}} \,, \\
+\end{align*}
+\ee
+where we have used
+\be \label{eq:chi_prime}
+\Aboxed{\frac{\partial \chi_\epsilon}{\partial S} = \underbrace{\frac{1}{2} \left( 1 + \frac{|S|}{\sqrt{\epsilon^2 + |S|^2}} \right)}_{\chi_\epsilon^\prime} |S|S^{-T}} \,.
+\ee
+
+The results of Eqs.~\eqref{eq:del_S_del_R} and \eqref{eq:del_beta_del_S} can be substituted into \Eq{eq:grad_beta} and \Eq{eq:grad_beta_element} to obtain $\nabla_{\vec{R}} \beta(\vec{R})$ in terms of $S$ and $\phi_l$.
+Note that \Eq{eq:del_S_del_R} is a rank 3 tensor of dimension $(n, n, n \times N_\text{nodes})$ and \Eq{eq:del_beta_del_S} is a matrix of dimension $(n, n)$:
+\be
+\nabla_{\vec{R}} \beta(\vec{R}) = \underbrace{\frac{\partial \beta(\vec{R})}{\partial S}}_{(n, n)} \underbrace{\frac{\partial S}{\partial \vec{R}}}_{(n, n, n \times N_\text{nodes})}
+\ee
+The expected result for the gradient of a scalar function is a vector, which can be obtained by first multiplying common dimensions together and then summing over them to obtain a vector of length $n \times N_\text{nodes}$.
+Using Einstein notation, the $\ell$-th entry of this vector is given by
+\be
+\Aboxed{\left( \nabla_{\vec{R}} \beta \right)_\ell = \left( \frac{\partial \beta}{\partial S} \right)_{ab} \left( \frac{\partial S}{\partial \vec{R}} \right)_{ab \ell}} \,.
+\ee
+This result is in agreement with \Eq{eq:grad_beta_element}.
+
+\subsection{$\nabla_{\vec{R}} \mu$}
+\label{sec:grad_mu}
+
+By definition,
+\be
+\nabla_{\vec{R}} \mu(\vec{R}) = \nabla_{\vec{R}} \frac{v + \frac{|S(\vec{R})|^2}{v}}{2\chi_\epsilon(|S(\vec{R})|)} \,.
+\ee
+Using chain rule in the same manner as the previous section,
+\be \label{eq:grad_mu}
+\begin{align*}
+\nabla_{\vec{R}} \mu(\vec{R}) &= \frac{\partial}{\partial \vec{R}} \mu(\vec{R}) \\
+&= \frac{\partial \mu(\vec{R})}{\partial S} \frac{\partial S}{\partial \vec{R}} \,.
+\end{align*}
+\ee
+
+The $\partial S / \partial \vec{R}$ term is given by \Eq{eq:del_S_del_R}.
+Using product rule and the Section \ref{sec:matrix_calculus_identities} identities for chain rule,
+\be \label{eq:del_mu_del_S}
+\begin{align*}
+\frac{\partial \mu}{\partial S} &= \frac{\partial}{\partial S} \left( \frac{v + \frac{|S|^2}{v}}{2\chi_\epsilon} \right) \\
+				&= \left( \frac{|S|^2 }{v\chi_\epsilon} \right) S^{-T} - \left[ \frac{v + \frac{|S|^2}{v}}{2 \chi_\epsilon^2} \right] \frac{\partial \chi_\epsilon}{\partial S}  \\
+				&= \left( \frac{|S|^2 }{v\chi_\epsilon} \right) S^{-T} - \left( \left[ \frac{v + \frac{|S|^2}{v}}{2 \chi_\epsilon^2} \right] \chi_\epsilon^\prime |S| \right) S^{-T} \\
+				&= \frac{|S|}{\chi_\epsilon} \left( \frac{|S| }{v} - \left[ \frac{v + \frac{|S|^2}{v}}{2 \chi_\epsilon} \right] \chi_\epsilon^\prime \right) S^{-T} \\
+				&= \Aboxed{ \underbrace{\frac{1}{2v \chi_\epsilon} \left( -\chi_\epsilon^\prime |S|^3 + 2 \chi_\epsilon |S|^2 - v^2 \chi_\epsilon^\prime |S| \right)}_{:= \alpha(S)}  S^{-T} } \,,
+\end{align*}
+\ee
+where $\chi_\epsilon^\prime$ is given by \Eq{eq:chi_prime}.
+The results of Eqs.~\eqref{eq:del_S_del_R} and \eqref{eq:del_mu_del_S} can be substituted into \Eq{eq:grad_mu} to obtain $\nabla_{\vec{R}} \mu(\vec{R})$ in terms of $S$ and $\phi_l$.
+Note that \Eq{eq:del_S_del_R} is a rank 3 tensor of dimension $(n, n, n \times N_\text{nodes})$ and \Eq{eq:del_beta_del_S} is a matrix of dimension $(n, n)$:
+\be
+\nabla_{\vec{R}} \mu(\vec{R}) = \underbrace{\frac{\partial \mu(\vec{R})}{\partial S}}_{(n,n)} \underbrace{\frac{\partial S}{\partial \vec{R}}}_{(n,n,n \times N_\text{nodes})} \,.
+\ee
+The expected result for the gradient of a scalar function is a vector, which can be obtained by first multiplying common dimensions together and then summing over them to obtain a vector of length $n \times N_\text{nodes}$.
+Using Einstein notation, the $\ell$-th entry of this vector is given by
+\be
+\Aboxed{\left( \nabla_{\vec{R}} \mu \right)_\ell = \left( \frac{\partial \mu}{\partial S} \right)_{ab} \left( \frac{\partial S}{\partial \vec{R}} \right)_{ab \ell}} \,.
+\ee
+
+\section{Hessian of $I_h$}
+
+The Hessian of $I_h$ is given by
+\be
+\begin{align*}
+	H(I_h(\vec{R})) &= \sum_{c=1}^{N\text{cells}} \int_{\hat{\Omega}_c}  H(E_\theta (S_c(\vec{R}))) d \vec{\xi} \\
+	&= \sum_{c=1}^{N\text{cells}} \int_{\hat{\Omega}_c}  \left( (1 - \theta) H(\beta (S_c(\vec{R}))) + \theta H(\mu (S_c(\vec{R}))) \right) d \vec{\xi} \,.
+\end{align*}
+\ee
+Computing the Hessian of $I_h$ entails the computation of the Jacobian of the gradient of $I_h$, or loosely speaking,
+\be
+H(I_h) = \nabla_{\vec{R}} \nabla_{\vec{R}} I_h \,.
+\ee
+We computed the gradient of $I_h$ ($\nabla_{\vec{R}} I_h$) in the previous section.
+To compute the Hessian, we simply need to take the Jacobian of those results.
+
+\subsection{$\nabla_{\vec{R}} \nabla_{\vec{R}} \beta$}
+
+From Section~\ref{sec:grad_beta}, we have
+\be
+\begin{align*}
+\nabla_{\vec{R}} \beta(\vec{R}) &= \frac{\partial \beta(\vec{R})}{\partial S} \frac{\partial S}{\partial \vec{R}} \,, \\
+\frac{\partial S(\vec{R}_c)_{i,j}}{\partial R_{c,m,k}} &= \delta_{ik} \partial_{\xi_j} \phi_m(\vec{\xi}) \,, \\
+\frac{\partial \beta(\vec{R})}{\partial S_{k \ell}} &= \left( \frac{\left( \frac{1}{n} \text{tr}(S^TS) \right)^{\frac{n}{2} - 1}}{\chi_\epsilon} \right) S_{k \ell} - \left( \frac{\left( \frac{1}{n} \text{tr}(S^TS) \right)^\frac{n}{2}}{\chi_\epsilon^2} \chi_\epsilon^\prime |S| \right) S^{-T}_{k \ell} \,.
+\end{align*}
+\ee
+Applying another derivative with respect to $\vec{R}$, the Hessian of $\beta$ is expressed as:
+\be
+\label{eq:hessian_beta}
+\begin{align*}
+	H(\beta(\vec{R})) &= \frac{\partial}{\partial \vec{R}} \left( \frac{\partial \beta(\vec{R})}{\partial S} \frac{\partial S}{\partial \vec{R}} \right) \\
+	&= \frac{\partial}{\partial \vec{R}} \left( \frac{\partial \beta(\vec{R})}{\partial S} \right) \frac{\partial S}{\partial \vec{R}} + \frac{\partial \beta(\vec{R})}{\partial S} \frac{\partial}{\partial \vec{R}} \left( \frac{\partial S}{\partial \vec{R}} \right) \\
+	&= \frac{\partial}{\partial S} \left( \frac{\partial \beta(\vec{R})}{\partial S} \right) \frac{\partial S}{\partial \vec{R}} \frac{\partial S}{\partial \vec{R}} + \frac{\partial \beta(\vec{R})}{\partial S} \underbrace{\frac{\partial^2 S}{\partial \vec{R}^2}}_{= 0 \text{ by } \Eq{eq:del_S_del_R}} \\
+	&= \frac{\partial^2 \beta(\vec{R})}{\partial S^2} \frac{\partial S}{\partial \vec{R}} \frac{\partial S}{\partial \vec{R}} \,.
+\end{align*}
+\ee
+Entry-wise, this is
+\be
+\label{eq:hessian_beta_element}
+\begin{align*}
+	H(\beta(\vec{R}))_{\ell p}  &= \left( \frac{\partial}{\partial \vec{R}} \left( \frac{\partial}{\partial \vec{R}} \beta(\vec{R}) \right)_\ell \right)_p \\
+	&= \frac{\partial}{\partial R_p} \frac{\partial}{\partial R_\ell} \beta(\vec{R}) \\
+	&= \frac{\partial}{\partial R_p} \sum_a \sum_b \left( \frac{\partial \beta(\vec{R})}{\partial S_{ab}} \frac{\partial S_{ab}}{\partial R_\ell} \right) \\
+	&= \sum_a \sum_b \left[ \frac{\partial}{\partial R_p} \left( \frac{\partial \beta(\vec{R})}{\partial S_{ab}} \right) \frac{\partial S_{ab}}{\partial R_\ell} + \frac{\partial \beta(\vec{R})}{\partial S_{ab}} \frac{\partial}{\partial R_p} \left( \frac{\partial S_{ab}}{\partial R_\ell} \right) \right] \\
+	&= \sum_a \sum_b \left[ \sum_i \sum_j \frac{\partial}{\partial S_{ij}} \left( \frac{\partial \beta(\vec{R})}{\partial S_{ab}} \right) \frac{\partial S_{ab}}{\partial R_\ell} \frac{\partial S_{ij}}{\partial R_p} + \frac{\partial \beta(\vec{R})}{\partial S_{ab}} \underbrace{\frac{\partial^2 S_{ab}}{\partial R_p \partial R_\ell}}_{= 0 \text{ by } \Eq{eq:del_S_del_R}} \right] \\
+	&= \sum_a \sum_b \frac{\partial S_{ab}}{\partial R_\ell} \sum_i \sum_j \left( \frac{\partial^2 \beta(\vec{R})}{\partial S_{ij} \partial S_{ab}} \right) \left( \frac{\partial S_{ij}}{\partial R_p} \right) \,.
+\end{align*}
+\ee
+The term $\partial S / \partial \vec{R}$ is given by \Eq{eq:del_S_del_R}.
+The term $\partial^2 \beta / \partial S^2$ is given by differentiating \Eq{eq:del_beta_del_S} with respect to $S$.
+Using the identities from Section \ref{sec:matrix_calculus_identities},
+\be
+\begin{align*}
+	\frac{\partial^2 \beta(\vec{R})}{\partial S_{ab} \partial S_{ij}}
+&= \frac{\partial}{\partial S_{ab}} \left[ \left( \frac{\left( \frac{1}{n} \text{tr}(S^TS) \right)^{\frac{n}{2} - 1}}{\chi_\epsilon} \right) S_{ij} - \left( \frac{\left( \frac{1}{n} \text{tr}(S^TS) \right)^\frac{n}{2}}{\chi_\epsilon^2} \chi_\epsilon^\prime |S| \right) S^{-T}_{ij} \right] \\
+&= \frac{1}{\chi_\epsilon} \left[ \frac{n-2}{2} \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}-2} \frac{2S_{ab}}{n} S_{ij} + \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}-1} I_{ia} I_{jb} \right] \\
+&- \frac{1}{\chi_\epsilon^2} \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}-1} \chi_\epsilon^\prime |S| S^{-T}_{ab} S_{ij} \\
+&- \frac{1}{\chi_\epsilon^2} \left[ \frac{n}{2} \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}-1} \frac{2S_{ab}}{n}  \chi_\epsilon^\prime |S| S^{-T}_{ij} \right. \\
+&+ \left. \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}} \chi_\epsilon^{\prime \prime} |S|^2 S^{-T}_{ab} S^{-T}_{ij} \right. \\
+&+ \left. \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}} \chi_\epsilon^\prime |S| S^{-T}_{ab} S^{-T}_{ij} \right] \\
+&+ \frac{2}{\chi_\epsilon^3} \left[ \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}} \chi_\epsilon^\prime |S| S^{-T}_{ab} \chi_\epsilon^\prime |S| S^{-T}_{ij} \right] \\
+&+ \left( \frac{\left( \frac{1}{n} \text{tr}(S^TS) \right)^\frac{n}{2}}{\chi_\epsilon^2} \chi_\epsilon^\prime |S| \right) S^{-1}_{bi} S^{-1}_{ja} \\
+	\Aboxed{&= \left[ \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}-1} \frac{1}{\chi_\epsilon} \right] I_{ia} I_{jb} + \left[ \frac{n-2}{n \chi_\epsilon} \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}-2} \right] S_{ab} S_{ij}} \\
+\Aboxed{&- \left[ \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}-1}  \frac{\chi_\epsilon^\prime |S|}{\chi_\epsilon^2} \right] S^{-1}_{ba} S_{ij}
+- \left[ \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}-1} \frac{\chi_\epsilon^\prime |S|}{\chi_\epsilon^2} \right] S_{ab} S^{-1}_{ji}} \\
+\Aboxed{&+ \left(\frac{1}{n} \text{tr}(S^TS)\right)^{\frac{n}{2}} \left( \frac{|S|}{\chi_\epsilon^2} \right) \left[ \frac{2 \chi_\epsilon^\prime^2 |S|}{\chi_\epsilon} 
+- \chi_\epsilon^{\prime \prime} |S|
+- \chi_\epsilon^\prime \right] S^{-1}_{ba} S^{-1}_{ji}} \\
+\Aboxed{&- \left( \frac{\left( \frac{1}{n} \text{tr}(S^TS) \right)^\frac{n}{2}}{\chi_\epsilon^2} \chi_\epsilon^\prime |S| \right) S^{-1}_{bi} S^{-1}_{ja}} \,.
+\end{align*}
+\ee
+where
+\be
+\Aboxed{\chi_\epsilon^{\prime \prime} = \frac{1}{2} \left( \frac{1}{\sqrt{\epsilon^2 + |S|^2}} - \frac{|S|^2}{(\epsilon^2 + |S|^2)^{3/2}} \right)} \,.
+\ee
+
+\subsection{$\nabla_{\vec{R}} \nabla_{\vec{R}} \mu$}
+
+From Section~\ref{sec:grad_mu}, we have
+\be
+\begin{align*}
+\nabla_{\vec{R}} \mu(\vec{R}) &= \frac{\partial \mu(\vec{R})}{\partial S} \frac{\partial S}{\partial \vec{R}} \,, \\
+\frac{\partial S(\vec{R}_c)_{i,j}}{\partial R_{c,m,k}} &= \delta_{ik} \partial_{\xi_j} \phi_m(\vec{\xi}) \,, \\
+\frac{\partial \mu(\vec{R})}{\partial S} &= \alpha(S) S^{-T} \,, \\
+\alpha(S) &= \frac{1}{2v \chi_\epsilon} \left( -\chi_\epsilon^\prime |S|^3 + 2 \chi_\epsilon |S|^2 - v^2 \chi_\epsilon^\prime |S| \right) \,.
+\end{align*}
+\ee
+Applying another derivative with respect to $\vec{R}$, the Hessian of $\mu$ is expressed as:
+\be
+\label{eq:hessian_mu}
+\begin{align*}
+	H(\mu(\vec{R})) &= \frac{\partial}{\partial \vec{R}} \left( \frac{\partial \mu(\vec{R})}{\partial S} \frac{\partial S}{\partial \vec{R}} \right) \\
+	&= \frac{\partial}{\partial \vec{R}} \left( \frac{\partial \mu(\vec{R})}{\partial S} \right) \frac{\partial S}{\partial \vec{R}} + \frac{\partial \mu(\vec{R})}{\partial S} \frac{\partial}{\partial \vec{R}} \left( \frac{\partial S}{\partial \vec{R}} \right) \\
+	&= \frac{\partial}{\partial S} \left( \frac{\partial \mu(\vec{R})}{\partial S} \right) \frac{\partial S}{\partial \vec{R}} \frac{\partial S}{\partial \vec{R}} + \frac{\partial \mu(\vec{R})}{\partial S} \underbrace{\frac{\partial^2 S}{\partial \vec{R}^2}}_{= 0 \text{ by } \Eq{eq:del_S_del_R}} \\
+	&= \frac{\partial^2 \mu(\vec{R})}{\partial S^2} \frac{\partial S}{\partial \vec{R}} \frac{\partial S}{\partial \vec{R}} \,.
+\end{align*}
+\ee
+Entry-wise, this is
+\be
+\label{eq:hessian_mu_element}
+\begin{align*}
+	H(\mu(\vec{R}))_{\ell p}  &= \left( \frac{\partial}{\partial \vec{R}} \left( \frac{\partial}{\partial \vec{R}} \mu(\vec{R}) \right)_\ell \right)_p \\
+	&= \frac{\partial}{\partial R_p} \frac{\partial}{\partial R_\ell} \mu(\vec{R}) \\
+	&= \frac{\partial}{\partial R_p} \sum_a \sum_b \left( \frac{\partial \mu(\vec{R})}{\partial S_{ab}} \frac{\partial S_{ab}}{\partial R_\ell} \right) \\
+	&= \sum_a \sum_b \left[ \frac{\partial}{\partial R_p} \left( \frac{\partial \mu(\vec{R})}{\partial S_{ab}} \right) \frac{\partial S_{ab}}{\partial R_\ell} + \frac{\partial \mu(\vec{R})}{\partial S_{ab}} \frac{\partial}{\partial R_p} \left( \frac{\partial S_{ab}}{\partial R_\ell} \right) \right] \\
+	&= \sum_a \sum_b \left[ \sum_i \sum_j \frac{\partial}{\partial S_{ij}} \left( \frac{\partial \mu(\vec{R})}{\partial S_{ab}} \right) \frac{\partial S_{ab}}{\partial R_\ell} \frac{\partial S_{ij}}{\partial R_p} + \frac{\partial \mu(\vec{R})}{\partial S_{ab}} \underbrace{\frac{\partial^2 S_{ab}}{\partial R_p \partial R_\ell}}_{= 0 \text{ by } \Eq{eq:del_S_del_R}} \right] \\
+	&= \sum_a \sum_b \frac{\partial S_{ab}}{\partial R_\ell} \sum_i \sum_j \left( \frac{\partial^2 \mu(\vec{R})}{\partial S_{ij} \partial S_{ab}} \right) \left( \frac{\partial S_{ij}}{\partial R_p} \right) \,.
+\end{align*}
+\ee
+The term $\partial S / \partial \vec{R}$ is given by \Eq{eq:del_S_del_R}.
+The term $\partial^2 \mu / \partial S^2$ is given by differentiating \Eq{eq:del_mu_del_S} with respect to $S$.
+Using the identities from Section \ref{sec:matrix_calculus_identities},
+\be
+\begin{align*}
+\frac{\partial^2 \mu(\vec{R})}{\partial S_{ab} \partial S_{ij}}
+&= \frac{\partial}{\partial S_{ab}} \alpha(S) S^{-T}_{ij} \right) \\
+&= \left( \frac{\partial}{\partial S_{ab}} \alpha(S) \right) S^{-T}_{ij} + \alpha(S) \frac{\partial}{\partial S_{ab}} S^{-T}_{ij} \\
+&= \frac{\partial}{\partial S_{ab}} \left( \frac{1}{2v \chi_\epsilon} \left( -\chi_\epsilon^\prime |S|^3 + 2 \chi_\epsilon |S|^2 - v^2 \chi_\epsilon^\prime |S| \right) \right) S^{-T}_{ij} + \alpha(S) S^{-1}_{bi} S^{-1}_{ja} \\
+&= \left( -\frac{2 \alpha(S) \chi_\epsilon^\prime |S| S^{-T}_{ab}}{\chi_\epsilon} + \frac{1}{2v \chi_\epsilon^2} \big( -\chi_\epsilon^{\prime\prime} |S|^4 S^{-T}_{ab} - 3 \chi_\epsilon^\prime |S|^3 S^{-T}_{ab} + 2 \chi_\epsilon^\prime |S|^3 S^{-T}_{ab} \right. \\
+&+ \left. 4 \chi_\epsilon |S|^2 S^{-T}_{ab} - v^2 \chi_\epsilon^\prime |S| S^{-T}_{ab} - v^2 |S|^2 \chi_\epsilon^{\prime\prime} S^{-T}_{ab} \vphantom{\frac{1}{2v \chi_\epsilon}} \big) \right) S^{-T}_{ij} + \alpha(S) S^{-1}_{bi} S^{-1}_{ja} \\
+\Aboxed{&= \frac{|S|}{2v \chi_\epsilon^2} \Big( -4v \alpha(S) \chi_\epsilon \chi_\epsilon^\prime - \chi_\epsilon^{\prime\prime} |S|^3 - \chi_\epsilon^\prime |S|^2 + 4 \chi_\epsilon |S| - v^2 \left( \chi_\epsilon^\prime + |S| \chi_\epsilon^{\prime\prime} \right) \Big) S^{-1}_{ba} S^{-1}_{ji}} \\
+\Aboxed{&+ \alpha(S) S^{-1}_{bi} S^{-1}_{ja}} \,.
+\end{align*}
+\ee
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%% Use \section commands to start a section
+%\section{Example Section}
+%\label{sec1}
+%%% Labels are used to cross-reference an item using \ref command.
+%
+%Section text. See Subsection \ref{subsec1}.
+%
+%%% Use \subsection commands to start a subsection.
+%\subsection{Example Subsection}
+%\label{subsec1}
+%
+%Subsection text.
+
+%% Use \subsubsection, \paragraph, \subparagraph commands to 
+%% start 3rd, 4th and 5th level sections.
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Document_Structure#Sectioning_commands
+
+
+%% Refer following link for more details.
+%% https://en.wikibooks.org/wiki/LaTeX/Mathematics
+%% https://en.wikibooks.org/wiki/LaTeX/Advanced_Mathematics
+
+%%% Use a table environment to create tables.
+%%% Refer following link for more details.
+%%% https://en.wikibooks.org/wiki/LaTeX/Tables
+%\begin{table}[t]%% placement specifier
+%%% Use tabular environment to tag the tabular data.
+%%% https://en.wikibooks.org/wiki/LaTeX/Tables#The_tabular_environment
+%\centering%% For centre alignment of tabular.
+%\begin{tabular}{l c r}%% Table column specifiers
+%%% Tabular cells are separated by &
+%  1 & 2 & 3 \\ %% A tabular row ends with \\
+%  4 & 5 & 6 \\
+%  7 & 8 & 9 \\
+%\end{tabular}
+%%% Use \caption command for table caption and label.
+%\caption{Table Caption}\label{fig1}
+%\end{table}
+
+
+%%% Use figure environment to create figures
+%%% Refer following link for more details.
+%%% https://en.wikibooks.org/wiki/LaTeX/Floats,_Figures_and_Captions
+%\begin{figure}[t]%% placement specifier
+%%% Use \includegraphics command to insert graphic files. Place graphics files in 
+%%% working directory.
+%\centering%% For centre alignment of image.
+%\includegraphics{example-image-a}
+%%% Use \caption command for figure caption and label.
+%\caption{Figure Caption}\label{fig1}
+%%% https://en.wikibooks.org/wiki/LaTeX/Importing_Graphics#Importing_external_graphics
+%\end{figure}
+
+
+%%% The Appendices part is started with the command \appendix;
+%%% appendix sections are then done as normal sections
+%\appendix
+
+%%% For citations use: 
+%%%       \cite{<label>} ==> [1]
+%
+%%%
+%Example citation, See \cite{lamport94}.
+
+%% If you have bib database file and want bibtex to generate the
+%% bibitems, please use
+%%
+%\bibliographystyle{elsarticle-num} 
+%\bibliography{references}
+
+
+\end{document}
+
+\endinput
+%%
+%% End of file `elsarticle-template-num.tex'.