%ADASS_PROCEEDINGS_FORM%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % SAMPLE2.TEX -- ADASS XII (2002) ASP Conference Proceedings sample % paper with complicated markup. Based on ADASS XI (01) version. % % This is a comprehensive example, meaning that we have made use of each % of the capabilities of the LaTeX + the ASPCONF macro package that we think % you may need to use. If you want to see a "base-bones" sample paper, % take a look at sample1.tex. % % Much of the input will be enclosed by braces (i.e., { }). The % percent sign, "%", denotes the start of a comment; text after it % will be ignored by LaTeX. You might also notice in some of the % examples below the use of "\ " after a period; this prevents LaTeX % from interpreting the period as the end of a sentence and putting % extra space after it. % % You should check your paper by processing it with LaTeX. For % details about how to run LaTeX as well as how to print out the User % Guide, consult the README file. % % If you do not have access to the LaTeX software or a laser printer % at your site, you can still prepare your paper following the % instructions in the User Guide. In such cases, the editors will % process the file and make any necessary editorial adjustments. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \documentclass[11pt,twoside]{article} % Leave intact \usepackage{adassconf} \usepackage{graphicx} % If you have the old LaTeX 2.09, and not the current LaTeX2e, comment % out the \documentclass and \usepackage lines above and uncomment % the following: %\documentstyle[11pt,twoside,adassconf]{article} \begin{document} % Leave intact %----------------------------------------------------------------------- % Paper ID Code %----------------------------------------------------------------------- % Enter the proper paper identification code. The ID code for your % paper is the session number associated with your presentation as % published in the official conference proceedings. You can % find this number locating your abstract in the printed proceedings % that you received at the meeting or on-line at the conference web % site; the ID code is the letter/number sequence proceeding the title % of your presentation. % % This will not appear in your paper; however, it allows different % papers in the proceedings to cross-reference each other. Note that % you should only have one \paperID, and it should not include a % trailing period. % \paperID{P7-8} %%%% ID=P7-8 %----------------------------------------------------------------------- % Paper Title %----------------------------------------------------------------------- % Enter the title of the paper. % % EXAMPLE: \title{A Breakthrough in Astronomical Software Development} % % If your title is so long as to fill the page header when you print it, % then please supply a short form as a \titlemark. % % EXAMPLE: % \title{Rapid Development for Distributed Computing, with Implications % for the Virtual Observatory} % \titlemark{Rapid Development for Distributed Computing} % \title{Determination of Initial Conditions of M81 Triplet Using Evolution Strategies} \titlemark{Evolution Strategies in Galaxy Interaction} %----------------------------------------------------------------------- % Authors of Paper %----------------------------------------------------------------------- % Enter the authors followed by their affiliations. The \author and % \affil commands may appear multiple times as necessary. List each % author by giving the first name or initials first followed by the % last name. Authors with the same affiliations should grouped % together. % % Try to limit the front matter to no more than three \author % commands. Group authors with the same affiliations. Too many % \author commands fills the first page of the paper with little % actual text. \author{Juan Carlos Gomez and Olac Fuentes} \affil{I.N.O.E., Luis Enrique Erro No. 1, Tonantzintla, Puebla, Mexico Email: jcgc@inaoep.mx} \author{Lia Athanassoula and Albert Bosma} \affil{Observatoire de Marseille, 2 Place le Verrier, 13248, Cedex 4, Marseille, France } % Notice that some of these authors have alternate affiliations, which % are identified by the \altaffilmark after each name. The actual alternate % affiliation information is typeset in footnotes at the bottom of the % first page, and the text itself is specified in \altaffiltext commands. % There is a separate \altaffiltext for each alternate affiliation % indicated above. %----------------------------------------------------------------------- % Contact Information %----------------------------------------------------------------------- % This information will not appear in the paper but will be used by % the editors in case you need to be contacted concerning your % submission. Enter your name as the contact along with your email % address. \contact{Juan Carlos Gomez} \email{jcgc@inaoep.mx} %----------------------------------------------------------------------- % Author Index Specification %----------------------------------------------------------------------- % Specify how each author name should appear in the author index. The % \paindex{ } should be used to indicate the primary author, and the % \aindex for all other co-authors. You MUST use the following % syntax: % % SYNTAX: \aindex{LASTNAME, F. M.} % % where F is the first initial and M is the second initial (if % used). This guarantees that authors that appear in multiple papers % will appear only once in the author index. \paindex{Gomez, J. C.} \aindex{Athanassoula, E.} \aindex{Fuentes, O.} \aindex{Bosma, A.} %----------------------------------------------------------------------- % Author list for page header %----------------------------------------------------------------------- % Please supply a list of author last names for the page header. in % one of these formats: % % EXAMPLES: % \authormark{LASTNAME} % \authormark{LASTNAME1 \& LASTNAME2} % \authormark{LASTNAME1, LASTNAME2, ... \& LASTNAMEn} % \authormark{LASTNAME et al.} % % Use the "et al." form in the case of seven or more authors, or if % the preferred form is too long to fit in the header. \authormark{Gomez, Athanassoula, Fuentes, \& Bosma} %----------------------------------------------------------------------- % Subject Index keywords %----------------------------------------------------------------------- % Enter up to 6 keywords describing your paper. These will NOT be % printed as part of your paper; however, they will be used to % generate the subject index for the proceedings. There is no % standard list; however, you can consult the indices for past ADASS % proceedings (http://iraf.noao.edu/ADASS/adass.html). \keywords{galaxies: interactions, kinematics, dynamics, methods: evolution strategies} %----------------------------------------------------------------------- % Abstract %----------------------------------------------------------------------- % Type abstract in the space below. Consult the User Guide and Latex % Information file for a list of supported macros (e.g. for typesetting % special symbols). Do not leave a blank line between \begin{abstract} % and the start of your text. \begin{abstract} % Leave intact In this work we present Evolution Strategies (ES) as an efficient method to approximate the initial conditions of the main interacting group of three galaxies in M81. The M81 group is one of the nearest groups of galaxies. Its biggest galaxy, M81, sits at the core of the group together with its two companions M82 and NGC3077. The interaction between these three galaxies is very well defined on an image taken in HI. In this first attempt we use non-self-gravitating simulations to approximate the initial conditions; even with that restriction our method reproduces the density distribution of the three galaxies with great precision. Results presented here show that ES is an ideally suited method to work in optimization problems in Astrophysics, where the solution is hard to find by common methods. In particular we argue that ES is a good method to find initial conditions of groups of interacting galaxies, where a large number of parameters need to be determined. \end{abstract} %----------------------------------------------------------------------- % Main Body %----------------------------------------------------------------------- % Place the text for the main body of the paper here. You should use % the \section command to label the various sections; use of % \subsection is optional. Significant words in section titles should % be capitalized. Sections and subsections will be numbered % automatically. \section{Introduction} It now established that galaxies are not "island universes", but rather interact with each other in pairs or in small or big groups. Interactions can form spirals, bars, warps, rings and bridges. Thus, observing the morphological and kinematics results of an interaction can give us crucial information about the interaction scenario. Yet very few detailed studies of individual interacting systems exist. The reason is that the number of free parameters in such simulations is very large and one needs an excessively large number of simulations to cover the corresponding parameter space. The problem of finding the right parameters for modelling the interaction of a given system of galaxies can be posed as an optimization problem. Indeed any simulation will give a projected surface density map and line-of-sight velocities. These can be compared to the corresponding observed quantities, and then the best model is the one that minimizes the difference. We will here use a method called Evolution Strategies (ES), which, while having much in common with Genetic Algorithms (GA) (Charbonneau 1995), is better suited for working with continuous spaces, i.e. real parameters. Since most of the parameters of interacting systems are continuous, this constitutes a clear incentive for trying out ES. We have chosen the M81 triplet as the interacting system to be studied. The M81 group is one of the nearest groups of galaxies. Its biggest galaxy, M81, sits in the core of the group together with its two nearby companion M82 (in the upper part of the image) and NGC3077 (in the lower part of the image). \section{Evolution Strategies} % We reset the footnote counter for the hyperlink since it does not % appear to recognize the previous 3 footnotes generated from the % altaffilmarks. The command \htmladdnormallinkfoot puts the link as a % footnote in the printed paper. The command \htmladdnormallink with % the same arguments will ignore the link in the printed copy. %\setcounter{footnote}{3} Evolution Strategies (ES) (Rechenberg 1975) is a technique for finding the minimum of a function with a large number of variables using ideas based on biological evolutionary process. We start by choosing $K$ individuals, each characterized by an object parameter vector $\bf O$ and a corresponding strategy parameter vector $\bf S$: \begin{equation} \mathbf{O}=o_{i}=\langle q_{1,i}, q_{2,i},\cdots,q_{L,i} \rangle i=1,\cdots,K \end{equation} \begin{equation} \mathbf{S}=s_{i}=\langle \sigma_{1,i},\sigma_{2,i},\cdots,\sigma_{L,i} \rangle i=1,\cdots,K \end{equation} The elements $q$ are the parameters we need to find, and $\bf S$ contains standard deviations of the $L$ variables $q_{l,i},l=1,\cdots,L$ In the initialization of the process, the first generation, the elements of the $\bf O$ and $\bf S$ vectors, can be chosen either totally at random, or with some help from previous knowledge about the system. Each of the $K$ individuals, i.e. each set of initial conditions, is used as input for the simulation program. The result of each simulation has to be evaluated with the help of a fitness function. The next sept is to produce a new population with the help of genetic operators: cross-over and mutation. For cross-over two individuals are chosen at random and in a such way that each individual is used once and only once. Mutation is applied to the individuals resulting from the cross-over operation. Each element of the new individual is calculated from the old individual using the simple equation: \begin{equation} q_{\mathrm{mut}}=q_{j}+N(0,\sigma_{j}) \end{equation} where $N(0,\sigma_{j})$ is a random number obtained from a normal distribution with a zero mean an a standard deviation $\sigma_{j}$, which is given from the strategy parameter vector. The process is repeated until the population converges. \section{Aplication to Interacting Systems of Galaxies} We use 30 individuals per iteration ($K=30$). In constituting the children population we apply first cross-over and then mutation to the parent population, then we merge both populations, select the $K$ best individuals from this merged population, and use the result as input for the next iteration. In order to obtain the fitness fuction we used mainly the HI density information, summarized in a $48\times48$ grid. We also grided the simulation results on a similar grid and then obtained the fitness as the Kullback-Leibler distance (Kullback \& Leibler 1951). For the simulation we use the test particle approach. In this approximation the mass of each galaxy is assumed to be concentrated in a single point in its center, while the disc, which responds most to the interaction, is represented by test particles, initially on co-planar circular orbits around the center of the galaxy. This approach is very fast and thus allows us to run the very large number of simulations necessary for tackling this problem. Furthermore, in our case the galaxies are not inter-penetrating and thus they are perturbed only in their outer parts, making the test particle approach fairly adequate. \section{Results} We obtained the density matrix of the original image simply by scanning the HI density map given in (Yun 1997). By using only this information we obtained a good fit to the density matrix after 100 generations, i.e. a total of $100\times30$ simulations. The images in Figure 1 show the best simulation reached and the original HI image. Table 1 shows the corresponding parameters for the best simulation. \begin{figure}[t] \epsscale{.8} \plotone{P7-8_f1.eps} \centering \caption{Simulated and HI images for M81 group} \end{figure} Although the density was fairly well reproduced in this way, the velocities were innacurate. So, in future work we are planning to introduce some velocity information to improve the velocity distribution. \section{Conclusions} In this work we presented an efficient method, based on ES, to approximate the initial conditions of the M81 triplet. Even with the several simplifying assumptions done in simulations, searching with ES has demonstrated to be an excellent method for optimization problems where an exploration of continuous parameters spaces is needed; ES could find a good simulation that match very well the HI density distribution in this problem. We are planning to extend the application of ES to the study of other interacting systems. \subsection{Future Work} In order to improve the method, the possibility of implementing a parallelization of the ES could be considered with the purpose of reducing the computing time required. Also, methods based on self-gravitating N-body simulations can be used to improve the match between simulations and the HI density distribution. \begin{table}[t] \resizebox{\linewidth}{!}{% \centering \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline $z_{2}$ &$z_{3}$ &$V_{x1}$ &$V_{y1}$ &$V_{x2}$ &$V_{y2}$ &$V_{x3}$ & $V_{y3}$ &$i_{1}$ &$PA_{1}$ &$i_{2}$ &$PA_{2}$ &$i_{3}$ & $PA_{3}$ &$m_{1}$ &$m_{2}$ &$m_{3}$ &$t$ \\ \hline 62.05 &11.14 &3.17 &1.59 &-61.91 &41.78 &-168.75 &-0.90 &44.90 &113.37 &38.62 &32.58 &53.83 &232.87 &19.47 &1.04 &1.06 &812\\ \hline \end{tabular}% }\caption{Parameters to produce the simulation in Figure 1} \tablenotetext{}{Index 1 is for M81, 2 for M82 and 3 for NGC3077} \end{table} %\begin{deluxetable}{crrrrrrrrrrr} %\scriptsize %\tablecaption{Terribly relevant tabular information. \label{P7-8:T1.10-tbl-1}} %\tablehead{ %\colhead{Star} & \colhead{Height} & \colhead{$d_{x}$} & \colhead{$d_{y}$} & %\colhead{$n$} & \colhead{$\chi^2$} & \colhead{$R_{min}$} & %\multicolumn{1}{c}{$P$\tablenotemark{a}} & \colhead{$P R_{maj}$} & %\colhead{$P R_{min}$} & \multicolumn{1}{c}{$\Theta$\tablenotemark{b}}} %\startdata %1 &33472.5 &$-$0.1 &0.4 &53 &27.4 &1.940 &3.900 &68.3 &116.2 &$-$27.639 \nl %2 &27802.4 &$-$0.3 &$-$0.2 &60 &3.7 &1.510 &2.156 &6.8 &7.5 &$-$26.764 \nl %3 &29210.6 &0.9 &0.3 &60 &3.4 &1.551 &2.159 &6.7 &7.3 &$-$40.272 \nl %4 &32733.8 &$-$1.2 &$-$0.5 &41 &54.8 &2.156 &4.313 &117.4 &78.2 &$-$35.847 \nl %5 & 9607.4 &$-$0.4 &$-$0.4 &60 &1.4 &1.574 &2.343 &8.0 &8.9 &$-$33.417 \nl %6 &31638.6 &1.6 &0.1 &39 &315.2 &3.075 &7.488 &92.1 &25.3 &$-$12.052 \nl %\enddata % Text for table footnotes must follow the tabular environment but must % be inside the table environment. Note that it is OK to put \ref's % in \tablenotetext's. %\tablenotetext{a}{Sample footnote for Table~\ref{P7-8:T1.10-tbl-1}} %\tablenotetext{b}{Another sample footnote for %Table~\ref{P7-8:T1.10-tbl-1}} \tablenotetext{c}{Footnote with no call %out} \tablenotetext{d}{Another footnote with no call out} %\tablenotetext{e}{A further additional footnote with no call out} %\end{deluxetable} % In the figure environment the \caption command should contain only the % caption text. The "Figure N." identification is generated by the % \caption command on its own. % % In this example we insert the \epscale command before the \plotone % command to override the default scaling of the figure. % % You cannot use footnotes within figures. %\begin{figure} %\epsscale{.80} %\plotone{figure.eps} %\caption{A particularly ghostly figure.} \label{P7-8:T1.10-fig-1} %\end{figure} % The same tabular data presented above in the deluxetable environment is % aligned below within the "tabular" environment. Observe % that our tabular environment is embedded within a "center" environment, % which is in turn inside a "table" environment. % % We need the table environment for autonumbering and caption generation, % which is why it is not enough to have a centered tabular. % % Within the tabular environment, please note that we use no vertical % rules, and the horizontal rules are inserted with \tableline (*not* \hline). % Note that a couple of the column headings require special annotation, i.e., % footnotes for tables. They are marked and tagged with \tablenotemark. % \tablenotemarks could be placed on individual data entries as well, % but try not to go berserk doing this. % % It is necessary to \label tables and figures *after* the \caption has been % specified because the table/figure number is generated by \caption, not % by \begin{whatever}. % Text for table footnotes must follow the tabular environment but must % be inside the table environment. Note that it is OK to put \ref's % in \tablenotetext's. % Finally, we have a little acknowledgments section. \acknowledgments We are grateful to CONACYT for partially supports this work. % That's the end of the main body of the paper. Now we will have some % back matter. % %----------------------------------------------------------------------- % References %----------------------------------------------------------------------- % Now comes the reference list. Since we typed out the citations ourselves, % the reference list is enclosed in a "references" environment. Each % new reference begins with a \reference command which sets up the proper % indentation. Typography that may be required in the reference list by % the editorial staff must be included by the author. % % Observe the "standard" order for bibliographic material: author name(s), % publication year, journal name, volume, and page number for articles. % Some journal names are available as macros; see the package % instructions for a listing of which ones have been "macro-ized". % % There is no need to engage in any other typographic manipulation. % % List your references below within the reference environment % (i.e. between the \begin{references} and \end{references} tags). % Each new reference should begin with a \reference command which sets % up the proper indentation. Observe the following order when listing % bibliographical information for each reference: author name(s), % publication year, journal name, volume, and page number for % articles. Note that many journal names are available as macros; see % the User Guide for a listing "macro-ized" journals. % % Note the following are some of the tricks that can be used: % % o \& is used to format an ampersand symbol (&). % o \'e and \`e puts an accent agu and accent grave, respectively, % over the letter e. See the User Guide for details on % formatting special characters. % o "\ " after a period prevents LaTeX from interpreting the period % as an end of a sentence. % o \aj is a macro that expands to "Astron. J." See the User Guide % for a full list of journal macros % o \adassviii is a macro that expands to the full title, editor, % and publishing information for the ADASS VIII conference % proceedings. Such macros are defined for ADASS conferences I % through X. % o When referencing a paper in the current volume, use the % \adassviii and \paperref macros. The argument to \paperref is % the paper ID code for the paper you are referencing. See the % note in the "Paper ID Code" section above for details on how to % determine the paper ID code for the paper you reference. % \begin{references} \reference Charbonneau, P.\ 1995, \apjs, 101, 309 \reference Kullback, S., \& Leibler, R.\ A.\ 1951, Ann. of Math. St., 22, 76 \reference Rechenberg, I.\ 1973, Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution, Stuttgart: Fromman-Holzboog \reference Wahde, M., \& Donner, K.\ J.\ 2001, \aap, 115 \reference Wahde, M.\ 1998, \aaps, 132, 417 \\ \reference Yun, M.\ S.\ 1997, IAU Symposium, 186 \end{references} % Do not place any material after the references section \end{document} % Leave intact