diff --git a/manuscript.md b/manuscript.md index 711c493..bb06142 100644 --- a/manuscript.md +++ b/manuscript.md @@ -6,10 +6,12 @@ author: correspond: true affiliation: "My City University" address: "Orenomachi, Orenoshi, Orenoken, Japan" + email: "one@myuni.ac.jp" - number: 2 name: "Author Two" affiliation: "My Other City University" address: "Hokanomachi, Orenoshi, Orenoken, Japan" + email: "two@myuni.ac.jp" email: "xxx@myuni.ac.jp" titleshort: "Paperlighter Example" authorshort: "Author One et.al." @@ -19,302 +21,321 @@ linkDir: appendix: - appendix/1 - appendix/2 -abstract: - Using \LaTeX{} to write papers is concise and convenient. However, for - writing in life, complicated \LaTeX{} style-files (e.g., elegantpaper) - are difficult to access, or submission style-files (e.g., journal or - conference) are not free indeed. To tackle these problems and satisfy an - elegant and straightforward scientific writing, - \textbf{paperlighter.sty}, a one-column style-file, is designed. This - document is edited from icml2022.sty and provides a basic paper - template. Compared to icml2022.sty, paperlighter.sty contain fewer - operations, reducing adjustment while keep graceful. - \textbf{\textit{Notably, the paper's main content only describes the format of icml2022.sty. We place the content to show the actual effect of paperlighter.sty.}} +abstractTex: + \abstract{To investigate the physical nature of the `nuc\-leated instability' of + proto giant planets, the stability of layers + in static, radiative gas spheres is analysed on the basis of Baker's + standard one-zone model.} + {To investigate the physical nature of the `nuc\-leated instability' of + proto giant planets, the stability of layers + in static, radiative gas spheres is analysed on the basis of Baker's + standard one-zone model.} + {It is shown that stability depends only upon the equations of state, the opacities and the local + thermodynamic state in the layer. Stability and instability can + therefore be expressed in the form of stability equations of state + which are universal for a given composition.} + {The stability equations of state are + calculated for solar composition and are displayed in the domain + $-14 \leq \lg \rho / \mathrm{[g\, cm^{-3}]} \leq 0 $, + $ 8.8 \leq \lg e / \mathrm{[erg\, g^{-1}]} \leq 17.7$. These displays + may be + used to determine the one-zone stability of layers in stellar + or planetary structure models by directly reading off the value of + the stability equations for the thermodynamic state of these layers, + specified + by state quantities as density $\rho$, temperature $T$ or + specific internal energy $e$. + Regions of instability in the $(\rho,e)$-plane are described + and related to the underlying microphysical processes.} + {Vibrational instability is found to be a common phenomenon + at temperatures lower than the second He ionisation + zone. The $\kappa$-mechanism is widespread under `cool' + conditions.} + {} +keywords: giant planet formation -- $\kappa$-mechanism -- stability of gas spheres +acknowledgements: + Part of this work was supported by the German + \emph{Deut\-sche For\-schungs\-ge\-mein\-schaft, DFG\/} project + number Ts~17/2--1. --- +# Introduction + + In the \emph{nucleated instability\/} (also called core + instability) hypothesis of giant planet + formation, a critical mass for static core envelope + protoplanets has been found. \citet{langley00} determined + the critical mass of the core to be about $12 \,M_\oplus$ + ($M_\oplus=5.975 \times 10^{27}\,\mathrm{g}$ is the Earth mass), which + is independent of the outer boundary + conditions and therefore independent of the location in the + solar nebula. This critical value for the core mass corresponds + closely to the cores of today's giant planets. + + Although no hydrodynamical study has been available many workers + conjectured that a collapse or rapid contraction will ensue + after accumulating the critical mass. The main motivation for + this article + is to investigate the stability of the static envelope at the + critical mass. With this aim the local, linear stability of static + radiative gas spheres is investigated on the basis of Baker's + (\citeyear{mitchell80}) standard one-zone model. + + Phenomena similar to the ones described above for giant planet + formation have been found in hydrodynamical models concerning + star formation where protostellar cores explode + (Tscharnuter \citeyear{kearns89}, Balluch \citeyear{MachineLearningI}), + whereas earlier studies found quasi-steady collapse flows. The + similarities in the (micro)physics, i.e., constitutive relations of + protostellar cores and protogiant planets serve as a further + motivation for this study. + + +# Baker's standard one-zone model + + \begin{figure*} + \centering + \caption{Adiabatic exponent $\Gamma_1$. + $\Gamma_1$ is plotted as a function of + $\lg$ internal energy $\mathrm{[erg\,g^{-1}]}$ and $\lg$ + density $\mathrm{[g\,cm^{-3}]}$.} + \label{FigGam}% + \end{figure*} + + In this section the one-zone model of \citet{DudaHart2nd}, + originally used to study the Cephe{\"{\i}}d pulsation mechanism, will + be briefly reviewed. The resulting stability criteria will be + rewritten in terms of local state variables, local timescales and + constitutive relations. + + \citet{DudaHart2nd} investigates the stability of thin layers in + self-gravitating, + spherical gas clouds with the following properties: + \begin{itemize} + \item hydrostatic equilibrium, + \item thermal equilibrium, + \item energy transport by grey radiation diffusion. + \end{itemize} + For the one-zone-model Baker obtains necessary conditions + for dynamical, secular and vibrational (or pulsational) + stability (Eqs.\ (34a,\,b,\,c) in Baker \citeyear{DudaHart2nd}). Using Baker's + notation: + +\noindent + and with the definitions of the \emph{local cooling time\/} + (see Fig.~\ref{FigGam}) + \begin{equation} + \tau_{\mathrm{co}} = \frac{E_{\mathrm{th}}}{L_{r0}} \,, + \end{equation} + and the \emph{local free-fall time} + \begin{equation} + \tau_{\mathrm{ff}} = + \sqrt{ \frac{3 \pi}{32 G} \frac{4\pi r_0^3}{3 M_{\mathrm{r}}} +}\,, + \end{equation} + Baker's $K$ and $\sigma_0$ have the following form: + \begin{eqnarray} + \sigma_0 & = & \frac{\pi}{\sqrt{8}} + \frac{1}{ \tau_{\mathrm{ff}}} \\ + K & = & \frac{\sqrt{32}}{\pi} \frac{1}{\delta} + \frac{ \tau_{\mathrm{ff}} } + { \tau_{\mathrm{co}} }\,; + \end{eqnarray} + where $E_{\mathrm{th}} \approx m (P_0/{\rho_0})$ has been used and + \begin{equation} + \begin{array}{l} + \delta = - \left( + \frac{ \partial \ln \rho }{ \partial \ln T } + \right)_P \\ + e=mc^2 + \end{array} + \end{equation} + is a thermodynamical quantity which is of order $1$ and equal to $1$ + for nonreacting mixtures of classical perfect gases. The physical + meaning of $\sigma_0$ and $K$ is clearly visible in the equations + above. $\sigma_0$ represents a frequency of the order one per + free-fall time. $K$ is proportional to the ratio of the free-fall + time and the cooling time. Substituting into Baker's criteria, using + thermodynamic identities and definitions of thermodynamic quantities, + \begin{displaymath} + \Gamma_1 = \left( \frac{ \partial \ln P}{ \partial\ln \rho} + \right)_{S} \, , \; + \chi^{}_\rho = \left( \frac{ \partial \ln P}{ \partial\ln \rho} + \right)_{T} \, , \; + \kappa^{}_{P} = \left( \frac{ \partial \ln \kappa}{ \partial\ln P} + \right)_{T} + \end{displaymath} + \begin{displaymath} + \nabla_{\mathrm{ad}} = \left( \frac{ \partial \ln T} + { \partial\ln P} \right)_{S} \, , \; + \chi^{}_T = \left( \frac{ \partial \ln P} + { \partial\ln T} \right)_{\rho} \, , \; + \kappa^{}_{T} = \left( \frac{ \partial \ln \kappa} + { \partial\ln T} \right)_{T} + \end{displaymath} + one obtains, after some pages of algebra, the conditions for + \emph{stability\/} given + below: + \begin{eqnarray} + \frac{\pi^2}{8} \frac{1}{\tau_{\mathrm{ff}}^2} + ( 3 \Gamma_1 - 4 ) + & > & 0 \label{ZSDynSta} \\ + \frac{\pi^2}{\tau_{\mathrm{co}} + \tau_{\mathrm{ff}}^2} + \Gamma_1 \nabla_{\mathrm{ad}} + \left[ \frac{ 1- 3/4 \chi^{}_\rho }{ \chi^{}_T } + ( \kappa^{}_T - 4 ) + + \kappa^{}_P + 1 + \right] + & > & 0 \label{ZSSecSta} \\ + \frac{\pi^2}{4} \frac{3}{\tau_{ \mathrm{co} } + \tau_{ \mathrm{ff} }^2 + } + \Gamma_1^2 \, \nabla_{\mathrm{ad}} \left[ + 4 \nabla_{\mathrm{ad}} + - ( \nabla_{\mathrm{ad}} \kappa^{}_T + + \kappa^{}_P + ) + - \frac{4}{3 \Gamma_1} + \right] + & > & 0 \label{ZSVibSta} + \end{eqnarray} + + For a physical discussion of the stability criteria see \citet{DudaHart2nd} or \citet{anonymous}. + + We observe that these criteria for dynamical, secular and + vibrational stability, respectively, can be factorized into + \begin{enumerate} + \item a factor containing local timescales only, + \item a factor containing only constitutive relations and + their derivatives. + \end{enumerate} + The first factors, depending on only timescales, are positive + by definition. The signs of the left hand sides of the + inequalities~(\ref{ZSDynSta}), (\ref{ZSSecSta}) and (\ref{ZSVibSta}) + therefore depend exclusively on the second factors containing + the constitutive relations. Since they depend only + on state variables, the stability criteria themselves are \emph{ + functions of the thermodynamic state in the local zone}. The + one-zone stability can therefore be determined + from a simple equation of state, given for example, as a function + of density and + temperature. Once the microphysics, i.e.\ the thermodynamics + and opacities (see Table~\ref{KapSou}), are specified (in practice + by specifying a chemical composition) the one-zone stability can + be inferred if the thermodynamic state is specified. + The zone -- or in + other words the layer -- will be stable or unstable in + whatever object it is imbedded as long as it satisfies the + one-zone-model assumptions. Only the specific growth rates + (depending upon the time scales) will be different for layers + in different objects. + + \begin{table} + \caption[]{Opacity sources.} + \label{KapSou} + $$ + \begin{array}{p{0.5\linewidth}l} + \hline + \noalign{\smallskip} + Source & T / {[\mathrm{K}]} \\ + \noalign{\smallskip} + \hline + \noalign{\smallskip} + Yorke 1979, Yorke 1980a & \leq 1700^{\mathrm{a}} \\ + + Kr\"ugel 1971 & 1700 \leq T \leq 5000 \\ + Cox \& Stewart 1969 & 5000 \leq \\ + \noalign{\smallskip} + \hline + \end{array} + $$ + \end{table} + + We will now write down the sign (and therefore stability) + determining parts of the left-hand sides of the inequalities + (\ref{ZSDynSta}), (\ref{ZSSecSta}) and (\ref{ZSVibSta}) and thereby + obtain \emph{stability equations of state}. + + The sign determining part of inequality~(\ref{ZSDynSta}) is + $3\Gamma_1 - 4$ and it reduces to the + criterion for dynamical stability + \begin{equation} + \Gamma_1 > \frac{4}{3}\,\cdot + \end{equation} + Stability of the thermodynamical equilibrium demands + \begin{equation} + \chi^{}_\rho > 0, \;\; c_v > 0\, , + \end{equation} + and + \begin{equation} + \chi^{}_T > 0 + \end{equation} + holds for a wide range of physical situations. + With + \begin{eqnarray} + \Gamma_3 - 1 = \frac{P}{\rho T} \frac{\chi^{}_T}{c_v}&>&0\\ + \Gamma_1 = \chi_\rho^{} + \chi_T^{} (\Gamma_3 -1)&>&0\\ + \nabla_{\mathrm{ad}} = \frac{\Gamma_3 - 1}{\Gamma_1} &>&0 + \end{eqnarray} + we find the sign determining terms in inequalities~(\ref{ZSSecSta}) + and (\ref{ZSVibSta}) respectively and obtain the following form + of the criteria for dynamical, secular and vibrational + \emph{stability}, respectively: + \begin{eqnarray} + 3 \Gamma_1 - 4 =: S_{\mathrm{dyn}} > & 0 & \label{DynSta} \\ + \frac{ 1- 3/4 \chi^{}_\rho }{ \chi^{}_T } ( \kappa^{}_T - 4 ) + + \kappa^{}_P + 1 =: S_{\mathrm{sec}} > & 0 & \label{SecSta} \\ + 4 \nabla_{\mathrm{ad}} - (\nabla_{\mathrm{ad}} \kappa^{}_T + + \kappa^{}_P) + - \frac{4}{3 \Gamma_1} =: S_{\mathrm{vib}} + > & 0\,.& \label{VibSta} + \end{eqnarray} + The constitutive relations are to be evaluated for the + unperturbed thermodynamic state (say $(\rho_0, T_0)$) of the zone. + We see that the one-zone stability of the layer depends only on + the constitutive relations $\Gamma_1$, + $\nabla_{\mathrm{ad}}$, $\chi_T^{},\,\chi_\rho^{}$, + $\kappa_P^{},\,\kappa_T^{}$. + These depend only on the unperturbed + thermodynamical state of the layer. Therefore the above relations + define the one-zone-stability equations of state + $S_{\mathrm{dyn}},\,S_{\mathrm{sec}}$ + and $S_{\mathrm{vib}}$. See Fig.~\ref{FigVibStab} for a picture of + $S_{\mathrm{vib}}$. Regions of secular instability are + listed in Table~1. + + \begin{figure} + \centering + \caption{Vibrational stability equation of state + $S_{\mathrm{vib}}(\lg e, \lg \rho)$. + $>0$ means vibrational stability. + } + \label{FigVibStab} + \end{figure} + +# Conclusions + + \begin{enumerate} + \item The conditions for the stability of static, radiative + layers in gas spheres, as described by Baker's (\citeyear{DudaHart2nd}) + standard one-zone model, can be expressed as stability + equations of state. These stability equations of state depend + only on the local thermodynamic state of the layer. + \item If the constitutive relations -- equations of state and + Rosseland mean opacities -- are specified, the stability + equations of state can be evaluated without specifying + properties of the layer. + \item For solar composition gas the $\kappa$-mechanism is + working in the regions of the ice and dust features + in the opacities, the $\mathrm{H}_2$ dissociation and the + combined H, first He ionization zone, as + indicated by vibrational instability. These regions + of instability are much larger in extent and degree of + instability than the second He ionization zone + that drives the Cephe{\"\i}d pulsations. + \end{enumerate} -# Format of the Paperlighter -Format of paperlighter is defined in this section. - -## Dimensions - -The text of the paper has an overall width of -6.75\textasciitilde{}inches, and height of 9.0\textasciitilde{}inches. -The left margin should be 0.75\textasciitilde{}inches and the top margin -1.0\textasciitilde{}inch (2.54\textasciitilde{}cm). The right and bottom -margins will depend on whether you print on US letter or A4 paper, but -all final versions must be produced for US letter size. - -The paper body should be set in 10\textasciitilde{}point type with a -vertical spacing of 11\textasciitilde{}points. Please use Times typeface -throughout the text. - -## Title - -The paper title should be set in 14\textasciitilde{}point bold type and -centered between two horizontal rules that are 1\textasciitilde{}point -thick, with 1.0\textasciitilde{}inch between the top rule and the top -edge of the page. Capitalize the first letter of content words and put -the rest of the title in lower case. - -## Author Information for Submission - -Use \verb+\lighterauthor{...}+ to specify authors and -\verb+\lighteraddress{...}+ to specify affiliations. (Read the TeX code -used to produce this document for an example usage.) The author -information will not be printed unless \texttt{accepted} is passed as an -argument to the style file. - -## Abstract - -The paper abstract should begin in the left column, -0.4\textasciitilde{}inches below the final address. The heading -`Abstract’ should be centered, bold, and in 11\textasciitilde{}point -type. The abstract body should use 10\textasciitilde{}point type, with a -vertical spacing of 11\textasciitilde{}points, and should be indented -0.25\textasciitilde{}inches more than normal on left-hand and right-hand -margins. Insert 0.4\textasciitilde{}inches of blank space after the -body. Keep your abstract brief and self-contained, limiting it to one -paragraph and roughly 4–6 sentences. Gross violations will require -correction at the camera-ready phase. - -## Partitioning the Text - -You should organize your paper into sections and paragraphs to help -readers place a structure on the material and understand its -contributions. - -### Sections and Subsections - -Section headings should be numbered, flush left, and set in -11\textasciitilde{}pt bold type with the content words capitalized. -Leave 0.25\textasciitilde{}inches of space before the heading and -0.15\textasciitilde{}inches after the heading. - -Similarly, subsection headings should be numbered, flush left, and set -in 10\textasciitilde{}pt bold type with the content words capitalized. -Leave 0.2\textasciitilde{}inches of space before the heading and -0.13\textasciitilde{}inches afterward. - -Finally, subsubsection headings should be numbered, flush left, and set -in 10\textasciitilde{}pt small caps with the content words capitalized. -Leave 0.18\textasciitilde{}inches of space before the heading and -0.1\textasciitilde{}inches after the heading. - -Please use no more than three levels of headings. - -### Paragraphs and Footnotes - -Within each section or subsection, you should further partition the -paper into paragraphs. Do not indent the first line of a given -paragraph, but insert a blank line between succeeding ones. - -You can use footnotes\footnote{Footnotes -should be complete sentences.} to provide readers with additional -information about a topic without interrupting the flow of the paper. -Indicate footnotes with a number in the text where the point is most -relevant. Place the footnote in 9\textasciitilde{}point type at the -bottom of the column in which it appears. Precede the first footnote in -a column with a horizontal rule of -0.8\textasciitilde{}inches.\footnote{Multiple footnotes can -appear in each column, in the same order as they appear in the text, -but spread them across columns and pages if possible.} - -\begin{figure}[ht] -\vskip 0.2in -\begin{center} -\centerline{\includegraphics[width=\columnwidth]{Figure/icml_numpapers.eps}} -\caption{Historical locations and number of accepted papers for International -Machine Learning Conferences (ICML 1993 -- ICML 2008) and International -Workshops on Machine Learning (ML 1988 -- ML 1992). At the time this figure was -produced, the number of accepted papers for ICML 2008 was unknown and instead -estimated.} -\label{icml-historical} -\end{center} -\vskip -0.2in -\end{figure} - -## Figures - -You may want to include figures in the paper to illustrate your approach -and results. Such artwork should be centered, legible, and separated -from the text. Lines should be dark and at least -0.5\textasciitilde{}points thick for purposes of reproduction, and text -should not appear on a gray background. - -Label all distinct components of each figure. If the figure takes the -form of a graph, then give a name for each axis and include a legend -that briefly describes each curve. Do not include a title inside the -figure; instead, the caption should serve this function. - -Number figures sequentially, placing the figure number and caption -\emph{after} the graphics, with at least 0.1\textasciitilde{}inches of -space before the caption and 0.1\textasciitilde{}inches after it, as in -\cref{icml-historical}. The figure caption should be set in -9\textasciitilde{}point type and centered unless it runs two or more -lines, in which case it should be flush left. You may float figures to -the top or bottom of a column, and you may set wide figures across both -columns (use the environment \texttt{figure*} in \LaTeX). Always place -two-column figures at the top or bottom of the page. - -## Algorithms - -If you are using \LaTeX, please use the -\texttt{algorithm\textquotesingle{}\textquotesingle{}\ and}algorithmic’’ -environments to format pseudocode. These require the corresponding -stylefiles, algorithm.sty and algorithmic.sty, which are supplied with -this package. \cref{alg:example} shows an example. - -\begin{algorithm}[tb] - \caption{Bubble Sort} - \label{alg:example} -\begin{algorithmic} - \STATE {\bfseries Input:} data $x_i$, size $m$ - \REPEAT - \STATE Initialize $noChange = true$. - \FOR{$i=1$ {\bfseries to} $m-1$} - \IF{$x_i > x_{i+1}$} - \STATE Swap $x_i$ and $x_{i+1}$ - \STATE $noChange = false$ - \ENDIF - \ENDFOR - \UNTIL{$noChange$ is $true$} -\end{algorithmic} -\end{algorithm} - -## Tables - -You may also want to include tables that summarize material. Like -figures, these should be centered, legible, and numbered consecutively. -However, place the title \emph{above} the table with at least -0.1\textasciitilde{}inches of space before the title and the same after -it, as in \cref{sample-table}. The table title should be set in -9\textasciitilde{}point type and centered unless it runs two or more -lines, in which case it should be flush left. - -\begin{table}[t] -\caption{Classification accuracies for naive Bayes and flexible -Bayes on various data sets.} -\label{sample-table} -\vskip 0.15in -\begin{center} -\begin{small} -\begin{sc} -\begin{tabular}{lcccr} -\toprule -Data set & Naive & Flexible & Better? \\ -\midrule -Breast & 95.9$\pm$ 0.2& 96.7$\pm$ 0.2& $\surd$ \\ -Cleveland & 83.3$\pm$ 0.6& 80.0$\pm$ 0.6& $\times$\\ -Glass2 & 61.9$\pm$ 1.4& 83.8$\pm$ 0.7& $\surd$ \\ -Credit & 74.8$\pm$ 0.5& 78.3$\pm$ 0.6& \\ -Horse & 73.3$\pm$ 0.9& 69.7$\pm$ 1.0& $\times$\\ -Meta & 67.1$\pm$ 0.6& 76.5$\pm$ 0.5& $\surd$ \\ -Pima & 75.1$\pm$ 0.6& 73.9$\pm$ 0.5& \\ -Vehicle & 44.9$\pm$ 0.6& 61.5$\pm$ 0.4& $\surd$ \\ -\bottomrule -\end{tabular} -\end{sc} -\end{small} -\end{center} -\vskip -0.1in -\end{table} - -Tables contain textual material, whereas figures contain graphical -material. Specify the contents of each row and column in the table’s -topmost row. Again, you may float tables to a column’s top or bottom, -and set wide tables across both columns. Place two-column tables at the -top or bottom of the page. - -## Theorems and such - -The preferred way is to number definitions, propositions, lemmas, etc. -consecutively, within sections, as shown below. - -\begin{definition} -\label{def:inj} -A function $f:X \to Y$ is injective if for any $x,y\in X$ different, $f(x)\ne f(y)$. -\end{definition} - -Using \cref{def:inj} we immediate get the following result: - -\begin{proposition} -If $f$ is injective mapping a set $X$ to another set $Y$, -the cardinality of $Y$ is at least as large as that of $X$ -\end{proposition} -\begin{proof} -Left as an exercise to the reader. -\end{proof} - -\cref{lem:usefullemma} stated next will prove to be useful. - -\begin{lemma} -\label{lem:usefullemma} -For any $f:X \to Y$ and $g:Y\to Z$ injective functions, $f \circ g$ is injective. -\end{lemma} -\begin{theorem} -\label{thm:bigtheorem} -If $f:X\to Y$ is bijective, the cardinality of $X$ and $Y$ are the same. -\end{theorem} - -An easy corollary of \cref{thm:bigtheorem} is the following: - -\begin{corollary} -If $f:X\to Y$ is bijective, -the cardinality of $X$ is at least as large as that of $Y$. -\end{corollary} -\begin{assumption} -The set $X$ is finite. -\label{ass:xfinite} -\end{assumption} -\begin{remark} -According to some, it is only the finite case (cf. \cref{ass:xfinite}) that is interesting. -\end{remark} - -## Citations and References - -If you rely on the \LaTeX\{\} bibliographic facility, use -\texttt{natbib.sty} included in the style-file package to obtain -reference. - -Citations within the text should include the authors’ last names and -year. If the authors’ names are included in the sentence, place only the -year in parentheses, for example when referencing Arthur Samuel’s -pioneering work \yrcite{Samuel59}. Otherwise place the entire reference -in parentheses with the authors and year separated by a comma -\cite{Samuel59}. List multiple references separated by semicolons -\cite{kearns89,Samuel59,mitchell80}. Use the `et\textasciitilde{}al.’ -construct only for citations with three or more authors or after listing -all authors to a publication in an earlier reference -\cite{MachineLearningI}. - -Use an unnumbered first-level section heading for the references, and -use a hanging indent style, with the first line of the reference flush -against the left margin and subsequent lines indented by 10 points. The -references at the end of this document give examples for journal -articles \cite{Samuel59}, conference publications \cite{langley00}, book -chapters \cite{Newell81}, books \cite{DudaHart2nd}, edited volumes -\cite{MachineLearningI}, technical reports \cite{mitchell80}, and -dissertations \cite{kearns89}. - -Alphabetize references by the surnames of the first authors, with single -author entries preceding multiple author entries. Order references for -the same authors by year of publication, with the earliest first. Make -sure that each reference includes all relevant information (e.g., page -numbers). - -Please put some effort into making references complete, presentable, and -consistent, e.g.~use the actual current name of authors. If using -bibtex, please protect capital letters of names and abbreviations in -titles, for example, use \{B\}ayesian or \{L\}ipschitz in your .bib -file. - -# Acknowledgements - -Acknowledgements is an unnumbered section at the end of the paper. -Typically, this will include thanks to colleagues who contributed to the -ideas, and to funding agencies and corporate sponsors that provided -financial support.