new

[hayette_paper1.git] / paper.tex

%% bare_adv.tex
%% V1.3
%% 2007/01/11
%% by Michael Shell
%% See:
%% http://www.michaelshell.org/
%% for current contact information. 
%%
%% This is a skeleton file demonstrating the advanced use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.7 or later) with an IEEE Computer
%% Society journal paper.
%%
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
%% and
%% http://www.ieee.org/

%%*************************************************************************
%% Legal Notice:
%% This code is offered as-is without any warranty either expressed or
%% implied; without even the implied warranty of MERCHANTABILITY or
%% FITNESS FOR A PARTICULAR PURPOSE!
%% User assumes all risk.
%% In no event shall IEEE or any contributor to this code be liable for
%% any damages or losses, including, but not limited to, incidental,
%% consequential, or any other damages, resulting from the use or misuse
%% of any information contained here.
%%
%% All comments are the opinions of their respective authors and are not
%% necessarily endorsed by the IEEE.
%%
%% This work is distributed under the LaTeX Project Public License (LPPL)
%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
%% distributed and modified. A copy of the LPPL, version 1.3, is included
%% in the base LaTeX documentation of all distributions of LaTeX released
%% 2003/12/01 or later.
%% Retain all contribution notices and credits.
%% ** Modified files should be clearly indicated as such, including  **
%% ** renaming them and changing author support contact information. **
%%
%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%%                    bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex
%%*************************************************************************

% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices can trigger bugs that do  ***
% *** not appear when using other class files.                            ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/



% IEEEtran V1.7 and later provides for these CLASSINPUT macros to allow the
% user to reprogram some IEEEtran.cls defaults if needed. These settings
% override the internal defaults of IEEEtran.cls regardless of which class
% options are used. Do not use these unless you have good reason to do so as
% they can result in nonIEEE compliant documents. User beware. ;)
%
%\newcommand{\CLASSINPUTbaselinestretch}{1.0} % baselinestretch
%\newcommand{\CLASSINPUTinnersidemargin}{1in} % inner side margin
%\newcommand{\CLASSINPUToutersidemargin}{1in} % outer side margin
%\newcommand{\CLASSINPUTtoptextmargin}{1in}   % top text margin
%\newcommand{\CLASSINPUTbottomtextmargin}{1in}% bottom text margin



% Note that the a4paper option is mainly intended so that authors in
% countries using A4 can easily print to A4 and see how their papers will
% look in print - the typesetting of the document will not typically be
% affected with changes in paper size (but the bottom and side margins will).
% Use the testflow package mentioned above to verify correct handling of
% both paper sizes by the user's LaTeX system.
%
% Also note that the "draftcls" or "draftclsnofoot", not "draft", option
% should be used if it is desired that the figures are to be displayed in
% draft mode.
%
\documentclass[12pt,journal,compsoc]{IEEEtran}
% The Computer Society requires 12pt.
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
% \documentclass[10pt,journal,compsoc]{../sty/IEEEtran}


% For Computer Society journals, IEEEtran defaults to the use of
% Palatino/Palladio as is done in IEEE Computer Society journals.
% To go back to Times Roman, you can use this code:
%\renewcommand{\rmdefault}{ptm}\selectfont





% Some very useful LaTeX packages include:
% (uncomment the ones you want to load)



% *** MISC UTILITY PACKAGES ***
%
%\usepackage{ifpdf}
% Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
% compilation based on whether the output is pdf or dvi.
% usage:
% \ifpdf
%   % pdf code
% \else
%   % dvi code
% \fi
% The latest version of ifpdf.sty can be obtained from:
% http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
% Also, note that IEEEtran.cls V1.7 and later provides a builtin
% \ifCLASSINFOpdf conditional that works the same way.
% When switching from latex to pdflatex and vice-versa, the compiler may
% have to be run twice to clear warning/error messages.






% *** CITATION PACKAGES ***
%
\ifCLASSOPTIONcompsoc
  % IEEE Computer Society needs nocompress option
  % requires cite.sty v4.0 or later (November 2003)
  % \usepackage[nocompress]{cite}
\else
  % normal IEEE
  % \usepackage{cite}
\fi
% cite.sty was written by Donald Arseneau
% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
% \cite{} output to follow that of IEEE. Loading the cite package will
% result in citation numbers being automatically sorted and properly
% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
% \cite will automatically add leading space, if needed. Use cite.sty's
% noadjust option (cite.sty V3.8 and later) if you want to turn this off.
% cite.sty is already installed on most LaTeX systems. Be sure and use
% version 4.0 (2003-05-27) and later if using hyperref.sty. cite.sty does
% not currently provide for hyperlinked citations.
% The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
% The documentation is contained in the cite.sty file itself.
%
% Note that some packages require special options to format as the Computer
% Society requires. In particular, Computer Society  papers do not use
% compressed citation ranges as is done in typical IEEE papers
% (e.g., [1]-[4]). Instead, they list every citation separately in order
% (e.g., [1], [2], [3], [4]). To get the latter we need to load the cite
% package with the nocompress option which is supported by cite.sty v4.0
% and later. Note also the use of a CLASSOPTION conditional provided by
% IEEEtran.cls V1.7 and later.





% *** GRAPHICS RELATED PACKAGES ***
%
\ifCLASSINFOpdf
  % \usepackage[pdftex]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../pdf/}{../jpeg/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
\else
  % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
  % will default to the driver specified in the system graphics.cfg if no
  % driver is specified.
  % \usepackage[dvips]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../eps/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.eps}
\fi
% graphicx was written by David Carlisle and Sebastian Rahtz. It is
% required if you want graphics, photos, etc. graphicx.sty is already
% installed on most LaTeX systems. The latest version and documentation can
% be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/graphics/
% Another good source of documentation is "Using Imported Graphics in
% LaTeX2e" by Keith Reckdahl which can be found as epslatex.ps or
% epslatex.pdf at: http://www.ctan.org/tex-archive/info/
%
% latex, and pdflatex in dvi mode, support graphics in encapsulated
% postscript (.eps) format. pdflatex in pdf mode supports graphics
% in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
% that all non-photo figures use a vector format (.eps, .pdf, .mps) and
% not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
% which can result in "jaggedy"/blurry rendering of lines and letters as
% well as large increases in file sizes.
%
% You can find documentation about the pdfTeX application at:
% http://www.tug.org/applications/pdftex



%\usepackage{ps4pdf}
% dvi->ps workflow is required to use such packages as psfrag.sty and
% pstricks.sty. However, Rolf Niepraschk's ps4pdf.sty provides a way to
% apply psfrag/pstricks effects to .eps figures and then get the resultant
% figures in .pdf form. Thus, providing an easier way for migrating from
% .eps to .pdf figures. After ps4pdf.sty loads, if:
% 1. producing .dvi output: the output file will consist ONLY of the
%    figures (or other constructs encased within \PSforPDF commands)
% 2. producing .pdf output: pdflatex will look in the filename-pics.pdf
%    file, where filename is the basename of the tex document, for the
%    graphics (or other constructs encased within \PSforPDF commands).
%    NOTE: If you ever change your figures, you must remember to remake
%    the filename-pics.pdf file.
%
% This way you can do a:
%
% latex filename
% dvips -Ppdf -o filename-pics.ps filename.dvi
% ps2pdf filename-pics.ps filename-pics.pdf
%
% to produce a filename-pics.pdf graphics container that contains
% .pdf versions of the graphics with psfrag, pstricks, etc. features.
% Note that you will not typically be able to view the figures in
% filename-pics.ps because of an offset. However, you will be able to
% view them in filename-pics.pdf. Also, note that when ps4pdf is in effect
% with .dvi output, you may get harmless over/under full box warnings -
% ignore them.
% Then, run pdflatex:
%
% pdflatex filename
%
% to use pdflatex to make PDF output, automatically using the figures in
% filename-pics.pdf. Alternatively, you could use dvips -i option to
% obtain separate .pdf files for each figure:
%
% dvips -Ppdf -i -E -o fig filename
%
% then convert each figure to pdf via a command such as epstopdf and then
% use pdflatex with these pdf figures and then to dispense with ps4pdf.
%
% Remember to rerun through latex/dvips/ps2pdf if you ever change your
% figures so that filename-pics.pdf gets updated.
% ps4pdf requires David Kastrup's preview-latex and a recent LaTeX system
% (circa 2001 or later). The ps4pdf package and documentation can be
% obtained at: http://www.ctan.org/tex-archive/macros/latex/contrib/ps4pdf/
% The preview-latex package and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/preview/
%
% provide a bogus \PSforPDF, even when not loading pd4pdf. This way we can
% stop loading ps4pdf.sty if we choose to make separate .pdf versions of
% each of our figures.
\providecommand{\PSforPDF}[1]{#1}
% Note that in order for ps4pdf to work, all commands related to psfrag,
% pstricks, etc. must be called within the PSforPDF command. This applies
% even when *loading* via \usepackage psfrag.sty, etc.


%\PSforPDF{\usepackage{psfrag}}
% psfrag.sty was written by Craig Barratt, Michael C. Grant, and
% David Carlisle. It allows you to substitute LaTeX commands for text in
% imported EPS graphic files. In this way, LaTeX symbols can be placed into
% graphics that have been generated by other applications. You must use
% latex->dvips->ps2pdf workflow (not direct pdf output from pdflatex) if
% you wish to use this capability because it works via some PostScript
% tricks. Alternatively, the graphics could be processed as separate files
% via psfrag and dvips, then converted to PDF for inclusion in the main file
% which uses pdflatex. ps4pdf.sty (above) provides a way of doing this all
% at once within the main file.
% Docs are in "The PSfrag System" by Michael C. Grant and David Carlisle.
% There is also some information about using psfrag in "Using Imported
% Graphics in LaTeX2e" by Keith Reckdahl which documents the graphicx
% package (see above). The psfrag package and documentation can be obtained
% at: http://www.ctan.org/tex-archive/macros/latex/contrib/psfrag/
%
% Note that the current version of psfrag does not "turn itself off" when
% running under pdf output. This will result in a harmless warning
% about a non-PDF \special. However, to silence this, a bogus psfrag
% command can be provided instead of loading psfrag.sty when PDF output
% is being used. Thus, a more complex alternative conditional loading scheme
% can be employed instead of the straightforword way above:
%
%\ifCLASSINFOpdf
% if outputting PDF, do not use or load psfrag.sty as current versions
% output a non-PDF special that generates a harmless, but annoying warning.
% Instead, we provide a bogus \psfrag command that does nothing with
% its arguments. This is a tad tricky because \psfrag can have up to six
% arguments four of which are optional: \psfrag{}[][][][]{}
% Code based on that in psfrag.sty
%\makeatletter
%\def\psfrag{\@ifstar{\@BOGUSpsfraga}{\@BOGUSpsfraga}}
%\def\@BOGUSpsfraga{\begingroup
%   \@makeother\"\@makeother\*\@makeother\!\@makeother\~%
%   \@makeother\:\@makeother\\\@makeother\%\@makeother\#%
%   \@makeother\ \@BOGUSpsfragb}
%\def\@BOGUSpsfragb#1{\endgroup
%                \@ifnextchar [{\@BOGUSpsfragc}%
%                              {\@BOGUSpsfrag}}
%\def\@BOGUSpsfragc[#1]{\@ifnextchar [{\@BOGUSpsfragd}%
%                                     {\@BOGUSpsfrag}}
%\def\@BOGUSpsfragd[#1]{\@ifnextchar [{\@BOGUSpsfrage}%
%                                     {\@BOGUSpsfrag}}
%\def\@BOGUSpsfrage[#1]{\@ifnextchar [{\@BOGUSpsfragf}%
%                                     {\@BOGUSpsfrag}}
%\def\@BOGUSpsfragf[#1]{\@BOGUSpsfrag}
%\def\@BOGUSpsfrag#1{\ignorespaces}
%\makeatother
%\else
% using dvi output, load psfrag, but funnel it through PSforPDF
% as required by ps4pdf.sty
%\PSforPDF{\usepackage{psfrag}}
%\fi





% *** MATH PACKAGES ***
%
%\usepackage[cmex10]{amsmath}
% A popular package from the American Mathematical Society that provides
% many useful and powerful commands for dealing with mathematics. If using
% it, be sure to load this package with the cmex10 option to ensure that
% only type 1 fonts will utilized at all point sizes. Without this option,
% it is possible that some math symbols, particularly those within
% footnotes, will be rendered in bitmap form which will result in a
% document that can not be IEEE Xplore compliant!
%
% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
% thus preventing page breaks from occurring within multiline equations. Use:
%\interdisplaylinepenalty=2500
% after loading amsmath to restore such page breaks as IEEEtran.cls normally
% does. amsmath.sty is already installed on most LaTeX systems. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/





% *** SPECIALIZED LIST PACKAGES ***
%\usepackage{acronym}
% acronym.sty was written by Tobias Oetiker. This package provides tools for
% managing documents with large numbers of acronyms. (You don't *have* to
% use this package - unless you have a lot of acronyms, you may feel that
% such package management of them is bit of an overkill.)
% Do note that the acronym environment (which lists acronyms) will have a
% problem when used under IEEEtran.cls because acronym.sty relies on the
% description list environment - which IEEEtran.cls has customized for
% producing IEEE style lists. A workaround is to declared the longest
% label width via the IEEEtran.cls \IEEEiedlistdecl global control:
%
% \renewcommand{\IEEEiedlistdecl}{\IEEEsetlabelwidth{SONET}}
% \begin{acronym}
%
% \end{acronym}
% \renewcommand{\IEEEiedlistdecl}{\relax}% remember to reset \IEEEiedlistdecl
%
% instead of using the acronym environment's optional argument.
% The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/acronym/


%\usepackage{algorithmic}
% algorithmic.sty was written by Peter Williams and Rogerio Brito.
% This package provides an algorithmic environment fo describing algorithms.
% You can use the algorithmic environment in-text or within a figure
% environment to provide for a floating algorithm. Do NOT use the algorithm
% floating environment provided by algorithm.sty (by the same authors) or
% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
% algorithm float types and packages that provide these will not provide
% correct IEEE style captions. The latest version and documentation of
% algorithmic.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
% There is also a support site at:
% http://algorithms.berlios.de/index.html
% Also of interest may be the (relatively newer and more customizable)
% algorithmicx.sty package by Szasz Janos:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/




% *** ALIGNMENT PACKAGES ***
%
%\usepackage{array}
% Frank Mittelbach's and David Carlisle's array.sty patches and improves
% the standard LaTeX2e array and tabular environments to provide better
% appearance and additional user controls. As the default LaTeX2e table
% generation code is lacking to the point of almost being broken with
% respect to the quality of the end results, all users are strongly
% advised to use an enhanced (at the very least that provided by array.sty)
% set of table tools. array.sty is already installed on most systems. The
% latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/tools/


%\usepackage{mdwmath}
%\usepackage{mdwtab}
% Also highly recommended is Mark Wooding's extremely powerful MDW tools,
% especially mdwmath.sty and mdwtab.sty which are used to format equations
% and tables, respectively. The MDWtools set is already installed on most
% LaTeX systems. The lastest version and documentation is available at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/mdwtools/


% IEEEtran contains the IEEEeqnarray family of commands that can be used to
% generate multiline equations as well as matrices, tables, etc., of high
% quality.


%\usepackage{eqparbox}
% Also of notable interest is Scott Pakin's eqparbox package for creating
% (automatically sized) equal width boxes - aka "natural width parboxes".
% Available at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/eqparbox/





% *** SUBFIGURE PACKAGES ***
%\ifCLASSOPTIONcompsoc
%\usepackage[tight,normalsize,sf,SF]{subfigure}
%\else
%\usepackage[tight,footnotesize]{subfigure}
%\fi
% subfigure.sty was written by Steven Douglas Cochran. This package makes it
% easy to put subfigures in your figures. e.g., "Figure 1a and 1b". For IEEE
% work, it is a good idea to load it with the tight package option to reduce
% the amount of white space around the subfigures. Computer Society papers
% use a larger font and \sffamily font for their captions, hence the
% additional options needed under compsoc mode. subfigure.sty is already
% installed on most LaTeX systems. The latest version and documentation can
% be obtained at:
% http://www.ctan.org/tex-archive/obsolete/macros/latex/contrib/subfigure/
% subfigure.sty has been superceeded by subfig.sty.


%\ifCLASSOPTIONcompsoc
%  \usepackage[caption=false]{caption}
%  \usepackage[font=normalsize,labelfont=sf,textfont=sf]{subfig}
%\else
%  \usepackage[caption=false]{caption}
%  \usepackage[font=footnotesize]{subfig}
%\fi
% subfig.sty, also written by Steven Douglas Cochran, is the modern
% replacement for subfigure.sty. However, subfig.sty requires and
% automatically loads Axel Sommerfeldt's caption.sty which will override
% IEEEtran.cls handling of captions and this will result in nonIEEE style
% figure/table captions. To prevent this problem, be sure and preload
% caption.sty with its "caption=false" package option. This is will preserve
% IEEEtran.cls handing of captions. Version 1.3 (2005/06/28) and later
% (recommended due to many improvements over 1.2) of subfig.sty supports
% the caption=false option directly:
%\ifCLASSOPTIONcompsoc
%  \usepackage[caption=false,font=normalsize,labelfont=sf,textfont=sf]{subfig}
%\else
%  \usepackage[caption=false,font=footnotesize]{subfig}
%\fi
%
% The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/
% The latest version and documentation of caption.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/caption/




% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/


%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
% which rewrites many portions of the LaTeX2e float routines. It may not work
% with other packages that modify the LaTeX2e float routines. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
% Documentation is contained in the stfloats.sty comments as well as in the
% presfull.pdf file. Do not use the stfloats baselinefloat ability as IEEE
% does not allow \baselineskip to stretch. Authors submitting work to the
% IEEE should note that IEEE rarely uses double column equations and
% that authors should try to avoid such use. Do not be tempted to use the
% cuted.sty or midfloat.sty packages (also by Sigitas Tolusis) as IEEE does
% not format its papers in such ways.


%\ifCLASSOPTIONcaptionsoff
%  \usepackage[nomarkers]{endfloat}
% \let\MYoriglatexcaption\caption
% \renewcommand{\caption}[2][\relax]{\MYoriglatexcaption[#2]{#2}}
%\fi
% endfloat.sty was written by James Darrell McCauley and Jeff Goldberg.
% This package may be useful when used in conjunction with IEEEtran.cls'
% captionsoff option. Some IEEE journals/societies require that submissions
% have lists of figures/tables at the end of the paper and that
% figures/tables without any captions are placed on a page by themselves at
% the end of the document. If needed, the draftcls IEEEtran class option or
% \CLASSINPUTbaselinestretch interface can be used to increase the line
% spacing as well. Be sure and use the nomarkers option of endfloat to
% prevent endfloat from "marking" where the figures would have been placed
% in the text. The two hack lines of code above are a slight modification of
% that suggested by in the endfloat docs (section 8.3.1) to ensure that
% the full captions always appear in the list of figures/tables - even if
% the user used the short optional argument of \caption[]{}.
% IEEE papers do not typically make use of \caption[]'s optional argument,
% so this should not be an issue. A similar trick can be used to disable
% captions of packages such as subfig.sty that lack options to turn off
% the subcaptions:
% For subfig.sty:
% \let\MYorigsubfloat\subfloat
% \renewcommand{\subfloat}[2][\relax]{\MYorigsubfloat[]{#2}}
% For subfigure.sty:
% \let\MYorigsubfigure\subfigure
% \renewcommand{\subfigure}[2][\relax]{\MYorigsubfigure[]{#2}}
% However, the above trick will not work if both optional arguments of
% the \subfloat/subfig command are used. Furthermore, there needs to be a
% description of each subfigure *somewhere* and endfloat does not add
% subfigure captions to its list of figures. Thus, the best approach is to
% avoid the use of subfigure captions (many IEEE journals avoid them anyway)
% and instead reference/explain all the subfigures within the main caption.
% The latest version of endfloat.sty and its documentation can obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/endfloat/
%
% The IEEEtran \ifCLASSOPTIONcaptionsoff conditional can also be used
% later in the document, say, to conditionally put the References on a
% page by themselves.





% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/misc/
% Read the url.sty source comments for usage information. Basically,
% \url{my_url_here}.


% NOTE: PDF thumbnail features are not required in IEEE papers
%       and their use requires extra complexity and work.
%\ifCLASSINFOpdf
%  \usepackage[pdftex]{thumbpdf}
%\else
%  \usepackage[dvips]{thumbpdf}
%\fi
% thumbpdf.sty and its companion Perl utility were written by Heiko Oberdiek.
% It allows the user a way to produce PDF documents that contain fancy
% thumbnail images of each of the pages (which tools like acrobat reader can
% utilize). This is possible even when using dvi->ps->pdf workflow if the
% correct thumbpdf driver options are used. thumbpdf.sty incorporates the
% file containing the PDF thumbnail information (filename.tpm is used with
% dvips, filename.tpt is used with pdftex, where filename is the base name of
% your tex document) into the final ps or pdf output document. An external
% utility, the thumbpdf *Perl script* is needed to make these .tpm or .tpt
% thumbnail files from a .ps or .pdf version of the document (which obviously
% does not yet contain pdf thumbnails). Thus, one does a:
%
% thumbpdf filename.pdf
%
% to make a filename.tpt, and:
%
% thumbpdf --mode dvips filename.ps
%
% to make a filename.tpm which will then be loaded into the document by
% thumbpdf.sty the NEXT time the document is compiled (by pdflatex or
% latex->dvips->ps2pdf). Users must be careful to regenerate the .tpt and/or
% .tpm files if the main document changes and then to recompile the
% document to incorporate the revised thumbnails to ensure that thumbnails
% match the actual pages. It is easy to forget to do this!
%
% Unix systems come with a Perl interpreter. However, MS Windows users
% will usually have to install a Perl interpreter so that the thumbpdf
% script can be run. The Ghostscript PS/PDF interpreter is also required.
% See the thumbpdf docs for details. The latest version and documentation
% can be obtained at.
% http://www.ctan.org/tex-archive/support/thumbpdf/
% Be sure and use only version 3.8 (2005/07/06) or later of thumbpdf as
% earlier versions will not work properly with recent versions of pdfTeX
% (1.20a and later).


% NOTE: PDF hyperlink and bookmark features are not required in IEEE
%       papers and their use requires extra complexity and work.
% *** IF USING HYPERREF BE SURE AND CHANGE THE EXAMPLE PDF ***
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\newcommand\MYhyperrefoptions{bookmarks=true,bookmarksnumbered=true,
pdfpagemode={UseOutlines},plainpages=false,pdfpagelabels=true,
colorlinks=true,linkcolor={black},citecolor={black},pagecolor={black},
urlcolor={black},
pdftitle={Bare Demo of IEEEtran.cls for Computer Society Journals},%<!CHANGE!
pdfsubject={Typesetting},%<!CHANGE!
pdfauthor={Michael D. Shell},%<!CHANGE!
pdfkeywords={Computer Society, IEEEtran, journal, LaTeX, paper,
             template}}%<^!CHANGE!
%\ifCLASSINFOpdf
%\usepackage[\MYhyperrefoptions,pdftex]{hyperref}
%\else
%\usepackage[\MYhyperrefoptions,breaklinks=true,dvips]{hyperref}
%\usepackage{breakurl}
%\fi
% One significant drawback of using hyperref under DVI output is that the
% LaTeX compiler cannot break URLs across lines or pages as can be done
% under pdfLaTeX's PDF output via the hyperref pdftex driver. This is
% probably the single most important capability distinction between the
% DVI and PDF output. Perhaps surprisingly, all the other PDF features
% (PDF bookmarks, thumbnails, etc.) can be preserved in
% .tex->.dvi->.ps->.pdf workflow if the respective packages/scripts are
% loaded/invoked with the correct driver options (dvips, etc.).
% As most IEEE papers use URLs sparingly (mainly in the references), this
% may not be as big an issue as with other publications.
%
% That said, recently Vilar Camara Neto introduced his breakurl.sty
% package which permits hyperref to easily break URLs even in dvi
% mode. Note that breakurl, unlike most other packages, must be loaded
% AFTER hyperref. The latest version of breakurl and its documentation can
% be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/breakurl/
% breakurl.sty is not for use under pdflatex pdf mode. Versions 1.10
% (September 23, 2005) and later are recommened to avoid bugs in earlier
% releases.
%
% The advanced features offer by hyperref.sty are not required for IEEE
% submission, so users should weigh these features against the added
% complexity of use. Users who wish to use hyperref *must* ensure that
% their hyperref version is 6.72u or later *and* IEEEtran.cls is version
% 1.6b or later.
% The package options above demonstrate how to enable PDF bookmarks
% (a type of table of contents viewable in Acrobat Reader) as well as
% PDF document information (title, subject, author and keywords) that is
% viewable in Acrobat reader's Document_Properties menu. PDF document
% information is also used extensively to automate the cataloging of PDF
% documents. The above set of options ensures that hyperlinks will not be
% colored in the text and thus will not be visible in the printed page,
% but will be active on "mouse over". USING COLORS OR OTHER HIGHLIGHTING
% OF HYPERLINKS CAN RESULT IN DOCUMENT REJECTION BY THE IEEE, especially if
% these appear on the "printed" page. IF IN DOUBT, ASK THE RELEVANT
% SUBMISSION EDITOR. You may need to add the option hypertexnames=false if
% you used duplicate equation numbers, etc., but this should not be needed
% in normal IEEE work.
% The latest version of hyperref and its documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/hyperref/





% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )


% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}

\usepackage{graphicx, subfigure}
\usepackage{caption}
\usepackage[utf8]{inputenc}
\usepackage{url}
\usepackage{hyperref}
\usepackage{float}
%%%%\usepackage[latin1]{inputenc}
\usepackage[textsize=footnotesize]{todonotes}
\begin{document}
%
% paper title
% can use linebreaks \\ within to get better formatting as desired
\title{Contribution of Statistical Implicative Analysis (SIA) combined with the Item Response Theory (IRT)}
%
%
% author names and IEEE memberships
% note positions of commas and nonbreaking spaces ( ~ ) LaTeX will not break
% a structure at a ~ so this keeps an author's name from being broken across
% two lines.
% use \thanks{} to gain access to the first footnote area
% a separate \thanks must be used for each paragraph as LaTeX2e's \thanks
% was not built to handle multiple paragraphs
%
%
%\IEEEcompsocitemizethanks is a special \thanks that produces the bulleted
% lists the Computer Society journals use for "first footnote" author
% affiliations. Use \IEEEcompsocthanksitem which works much like \item
% for each affiliation group. When not in compsoc mode,
% \IEEEcompsocitemizethanks becomes like \thanks and
% \IEEEcompsocthanksitem becomes a line break with idention. This
% facilitates dual compilation, although admittedly the differences in the
% desired content of \author between the different types of papers makes a
% one-size-fits-all approach a daunting prospect. For instance, compsoc
% journal papers have the author affiliations above the "Manuscript
% received ..."  text while in non-compsoc journals this is reversed. Sigh.

\author{Hayette~Khaled,~\IEEEmembership{University of Bejaia, ~Algeria,}
        and~Raphaël ~Couturier,~\IEEEmembership{University of Franche-Comte, ~France}% <-this % stops a space
\IEEEcompsocitemizethanks{\IEEEcompsocthanksitem H. Khaled is from the University of Bejaia.\protect\\
% note need leading \protect in front of \\ to get a newline within \thanks as
% \\ is fragile and will error, could use \hfil\break instead.
E-mail: hayette.khaled$@$univ\-bejaia.dz, aya\_info6$@$yahoo.fr
\IEEEcompsocthanksitem R.Couturier is from the University of Franche-Comte.\protect\\
E-mail: raphael.couturier$@$univ-fcomte.fr}% <-this % stops a space

%%%%%%%%%%%%%%%%%%%%%%%%%\thanks{Manuscript received April 19, 2005; revised January 11, 2007.}

} %aya???

% note the % following the last \IEEEmembership and also \thanks -
% these prevent an unwanted space from occurring between the last author name
% and the end of the author line. i.e., if you had this:
%
% \author{....lastname \thanks{...} \thanks{...} }
%                     ^------------^------------^----Do not want these spaces!
%
% a space would be appended to the last name and could cause every name on that
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% instance, "\textbf{A} \textbf{B}" will typeset as "A B" not "AB". To get
% "AB" then you have to do: "\textbf{A}\textbf{B}"
% \thanks is no different in this regard, so shield the last } of each \thanks
% that ends a line with a % and do not let a space in before the next \thanks.
% Spaces after \IEEEmembership other than the last one are OK (and needed) as
% you are supposed to have spaces between the names. For what it is worth,
% this is a minor point as most people would not even notice if the said evil
% space somehow managed to creep in.



% The paper headers
%%%%%%%%%%%%%%%%%%%%\markboth{Journal of \LaTeX\ Class Files,~Vol.~6, No.~1, January~2007}%  %aya???
%%%%%%%%%%%%%%%%%%%%{Shell \MakeLowercase{\textit{et al.}}: Bare Advanced Demo of IEEEtran.cls for Journals} %aya???
% The only time the second header will appear is for the odd numbered pages
% after the title page when using the twoside option.
%
% *** Note that you probably will NOT want to include the author's ***
% *** name in the headers of peer review papers.                   ***
% You can use \ifCLASSOPTIONpeerreview for conditional compilation here if
% you desire.



% The publisher's ID mark at the bottom of the page is less important with
% Computer Society journal papers as those publications place the marks
% outside of the main text columns and, therefore, unlike regular IEEE
% journals, the available text space is not reduced by their presence.
% If you want to put a publisher's ID mark on the page you can do it like
% this:
%\IEEEpubid{0000--0000/00\$00.00~\copyright~2007 IEEE}
% or like this to get the Computer Society new two part style.
%\IEEEpubid{\makebox[\columnwidth]{\hfill 0000--0000/00/\$00.00~\copyright~2007 IEEE}%

%%%%%%%%%%\IEEEoverridecommandlockouts

\IEEEpubid{\makebox[\columnwidth]{978-1-4799-7508-2/14/\$31.00~\copyright~2014 IEEE \hfill} \hspace{\columnsep}\makebox[\columnwidth]{ }}


%\hspace{\columnsep}\makebox[\columnwidth]{Published by the IEEE Computer Society\hfill}}
% Remember, if you use this you must call \IEEEpubidadjcol in the second
% column for its text to clear the IEEEpubid mark (Computer Society jorunal
% papers don't need this extra clearance.)



% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}



% for Computer Society papers, we must declare the abstract and index terms
% PRIOR to the title within the \IEEEcompsoctitleabstractindextext IEEEtran
% command as these need to go into the title area created by \maketitle.
\IEEEcompsoctitleabstractindextext{%


\begin{abstract}
%\boldmath
In this paper we illustrate the benefits of combining Statistical
Implicative Analysis (SIA) method with the Items Response Theory (IRT)
throw a study of the computer science students' marks of Bejaia
University. SIA is used to discover and analyze the most relevant
implications between different studied modules. The IRT, in
opposition, allows us to analyze the items quality and their calibration (difficulty) by providing the construction of  independent scales from the test data (students and modules). An analysis of the results is proposed with a comparison with the results that we have obtained in the paper \cite{Khaled14} in which we applied the SIA on students' marks.

\end{abstract}
% IEEEtran.cls defaults to using nonbold math in the Abstract.
% This preserves the distinction between vectors and scalars. However,
% if the journal you are submitting to favors bold math in the abstract,
% then you can use LaTeX's standard command \boldmath at the very start
% of the abstract to achieve this. Many IEEE journals frown on math
% in the abstract anyway. In particular, the Computer Society does
% not want either math or citations to appear in the abstract.

% Note that keywords are not normally used for peerreview papers.
\begin{IEEEkeywords}
SIA, IRT, Students' Marks.
\end{IEEEkeywords}}

\newcommand{\rc}[1]{\color{blue}{[RC: #1]}\color{black}}
% make the title area
\maketitle


% To allow for easy dual compilation without having to reenter the
% abstract/keywords data, the \IEEEcompsoctitleabstractindextext text will
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% here as \IEEEdisplaynotcompsoctitleabstractindextext when compsoc mode
% is not selected <OR> if conference mode is selected - because compsoc
% conference papers position the abstract like regular (non-compsoc)
% papers do!
\IEEEdisplaynotcompsoctitleabstractindextext
% \IEEEdisplaynotcompsoctitleabstractindextext has no effect when using
% compsoc under a non-conference mode.


% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle



\section{INTRODUCTION}
% Computer Society journal papers do something a tad strange with the very
% first section heading (almost always called "Introduction"). They place it
% ABOVE the main text! IEEEtran.cls currently does not do this for you.
% However, You can achieve this effect by making LaTeX jump through some
% hoops via something like:
%
%\ifCLASSOPTIONcompsoc
%  \noindent\raisebox{2\baselineskip}[0pt][0pt]%
%  {\parbox{\columnwidth}{\section{Introduction}\label{sec:introduction}%
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%  \vspace{-1\baselineskip}\vspace{-\parskip}\par
%\else
%  \section{Introduction}\label{sec:introduction}\par
%\fi
%
% Admittedly, this is a hack and may well be fragile, but seems to do the
% trick for me. Note the need to keep any \label that may be used right
% after \section in the above as the hack puts \section within a raised box.



% The very first letter is a 2 line initial drop letter followed
% by the rest of the first word in caps (small caps for compsoc).
%
% form to use if the first word consists of a single letter:
% \IEEEPARstart{A}{demo} file is ....
%
% form to use if you need the single drop letter followed by
% normal text (unknown if ever used by IEEE):
% \IEEEPARstart{A}{}demo file is ....
%
% Some journals put the first two words in caps:
% \IEEEPARstart{T}{his demo} file is ....
%
% Here we have the typical use of a "T" for an initial drop letter
% and "HIS" in caps to complete the first word.
\IEEEPARstart{T}{he} Item Response Theory (IRT) is a statistical model
of measure, relatively recent, \cite{Pini12}. It allows to deal with the problems for which classical psychometrics do not always provide satisfactory responses and solutions. It attempts to estimate the item's independence property of a particular group of individuals. In other words, IRT seeks to elaborate measurement instruments whose characteristics are not excessively influenced by a reference group.

IRT is based on probabilistic models. These models are based on the principle that the response of an individual to the item (including the probability of providing a correct response) is determined by two kinds of factors:  on the first hand, the competence of the subject (called latent traits); on the second hand, the item properties: its degree of difficulty, its discrimination power and the "chance" that may play a role in some cases.

IRT was proposed for the first time in the psychometrics field to assess the ability \cite{Xinming}. After that, it was used in various fields such as medicine \cite{Michael13}, smoking among adolescents \cite{Hedeker06}, etc.  \rc{pas
  cohérent de dire que ca a été utilisé en 2014 puis après et parlé de
  2013 }  Furthermore, it is widely used in education to calibrate and evaluate the items in the tests as well as the subject's ability. In recent decades, the educational evaluation had used more and more techniques based on IRT in order to develop tests.

For example, in \cite{Johns06} the authors have designed several experiments to test IRT models which were used as a tool for students modeling in intelligent tutoring system. The models were tested using real data of high school students using the Wayang Outpost tutoring system. A cross-validation model was developed and three metrics of prediction accuracy measuring were compared. The results show that the trained models predict with an accuracy of 72\% if a student response is a multiple choice problem correctly, so we can say that these models have a good predictive power.

In \cite{Hamdare14} the authors proposed an adaptive assessment system based on the IRT. This system allows to personalize, dynamically, questions for students based on their response  to the previous question, it also adjusts the difficulty of the evaluation questions depending on the student's ability; so this will help teachers to acquire a valid and reliable measurement of student skills.

In \cite{Rowan01}, researchers from the Michigan University worked on the elaboration of measures based on surveys on the educational content knowledge of teachers, identifying three dimensions to measure, namely: knowledge content, knowledge of student thinking and knowledge of teaching strategies; in order to analyze their effects on student success. Researchers establish questionnaires for teachers concerning the three dimensions previously mentioned. Then they apply the computer commercial program BILOG to analyze and score the questionnaires that are based on the IRT to exclude questions that decrease the reliability of adjustment.

The Aix-Marseille IREM's research team developed an assessing adaptive method in
\cite{Bodin10} that they  test on  the socle  commun in  terms of  knowledge and
skills. It aims  to response the following questions: what  knowledge and skills
are required to individuals, regardless of  training courses that each one could
have followed or not? How is it  possible to position individuals in relation to
the socle requests?

The adaptive method consists to form a referential R that contains knowledge and skills to evaluate. A set of questions Q is associated to the referential; and the cohesive implicative tree of CHIC \cite{Couturier05} or \cite{couturier08:bc} is used to determine the questions that correspond to the same unit of competence.

%%RAPH: ici on parle de SIA mais il n'y a pas eu de description du SIA ??? la je pense que la discription on la trouve dans les deux références précédente \cite{Couturier05} or \cite{couturier08:bc} 
\rc{Il manque toujours une présentation de SIA plus ou moins ici}


The test principle is to take randomly the first question (q1, p) to ask to the person p then the next question will be chosen according to the implicative graph built with the SIA questions. The test is stopped when the amplitude of the confidence interval for the estimated score falls below a chosen confidence interval.
The adaptive test on R consists in estimating the score of a person on the set of questions Q from his answer $s$ to a subset Q' using the probabilistic estimation function of IRT. The authors show that the combination of the SIA and the IRT allows to envisage very reliable tests.

In the literature, all works that use the IRT show that there are interesting contributions coming from the  educational field. These works focus in general on questionnaires refinement of a tutoring system or test web system or the study of teachers' knowledge and their impact on students' success.

There are few studies that address students' marks. In our work \cite{Khaled14}, we used the statistical implicative analysis (SIA) \cite{Gras08} and \cite{Gras13} to identify relevant implications between modules.

Our goal in this paper is to show the benefits and contributions of both SIA and IRT methods through an example on Bejaia University student's marks. We have cited previously a work that also combines these two methods on test questions for which responses $s$ are represented with binary data. In our case we deal with polytomous data, i.e., with several modalities, obtained by partitioning student's marks into three groups with the ``dynamic clouds'' algorithm. Hence there are 3 groups of student: students with weak results, with average results and with good results. So even if student's marks are generally high or in contrast very low, we have the 3 groups previously stated.

In the following of this paper we introduce the Item Response Theory (IRT) then, we show our analysis and results. Finally, we present a comparison between the results obtained with IRT and those obtained with SIA initially presented in \cite{Khaled14} and updated.

% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)
%%%%%%%%%%%%%%%%%I wish you the best of success.  %aya???

%%%%%%%%%%%%%%%%%%%%%\hfill mds   %aya???

%%%%%%%%%%%%%%%%%%\hfill January 11, 2007   %aya???


\section{Item Response Theory(IRT), \cite{Pini12}, \cite{Hamdare14}, \cite{DaiTrang13},\cite{Rizopoulos06}}
IRT models are  mathematical functions called item characteristic
functions. These functions specify the probability to anwser  correctly an item, in terms of item and individual parameters. They are represented graphically by a continuous curve called item's characteristic curve (ICC) (see Figure~\ref{fig:01}), it describes the relationship between the individual latent trait (represented by $\theta$) and the probability that this individual succeed the item i.

% figure1
\begin{figure}[ht]
\centering
\includegraphics[width=0.3\textwidth]{Rplot_ICC}
\caption{Item Characteristic Curve (ICC).}
\label{fig:01}

\end{figure}

There are three IRT models: the one parameter model (or Rasch model), the two-parameter model and the three-parameter model. All the three models have an item difficulty parameter represented by $b_{i}$.

\begin{itemize}
  \item The one-parameter model equation is given as follows:
$$P_{i}(\theta)= \frac{\exp^{(\theta-b_{i})}}{1+\exp^{(\theta-b_{i})}}$$

  \item The two-parameter model equation is given as follows:
$$P_{i}(\theta)= \frac{\exp^{\alpha_{i}(\theta-b_{i})}}{1+\exp^{\alpha_{i}(\theta-b_{i})}}$$

  \item The three-parameter model equation is given as follows:
$$P_{i}(\theta)= C_{i}+(1-C_{i})\frac{\exp^{\alpha_{i}(\theta-b_{i})}}{1+\exp^{\alpha_{i}(\theta-b_{i})}}$$

\end{itemize}

In addition, the two-parameter and the three-parameter models have a discrimination parameter denoted by $\alpha$; related to the speed of probability change when the trait latent changes. The three-parameter model contains a third parameter, called pseudo-guessing parameter denoted by $C$ which represents the probability that a subject, with low ability, response $s$ correctly an item i by randomly choosing one of the proposed options.

There are two main branches of IRT: the unidimensional (UIRT) and multidimensional (MIRT). The first branch operates on the assumption that there is an idea or message through the content of all the items and the test instruments are developed to measure this single idea. The second branch in turn assumes that the items are grouped into different domain and the test instruments are used to measure these multiple domain construction \cite{DaiTrang13}.

The most common models of IRT are dichotomous ones with two response categories for items and polytomous models with multiple ordinal response categories for items. In our case we will treat the marks of students which are between zero and twenty that will be divided into three groups, so they represent polytomous data.

Polytomous data include multiple choice items data, open mathematical questions, Likert scales, ordinal items, the scales assessment responses and graded test responses or survey questions. The type of IRT model used to describe the interaction between subjects and test items depends on the nature of the data collected. Several models were used to polytomous data, such as partial credit model (PCM), the generalized partial credit model (GPCM), nominal response model (NRM) and the graded response model (GRM). This last model is proposed by Samejima (1969), it is the best suitable for the treatment of student marks, its logistics form is expressed as follow:\\

% formule 4
\begin{eqnarray}
  P(Y_{ijk} = k|\theta_{j},b_{ik},a_{i})=&  \nonumber\\
  \frac{1}{1 + \exp ^{\alpha_{i}(\theta_{i}-b_{i,k})}} - \frac{1}{1 + \exp ^{\alpha_{i}(\theta_{i}-b_{i,k+1})}}&
\end{eqnarray}

\section{Analysis and Results}
\subsection{Data description}
The population considered is the $2^{nd}$ year students of Computer Science Department of the University A / Mira Bejaia during the years 2010, 2011 and 2012. The $2^{nd}$ year students are assessed on linear programming module (LP), languages theory (LTH), mathematical logic (MatLog), numerical analysis (NumA), operating system (OS), probability and statistics (PS), signal processing (SP), software engineering (SWE), algorithm and data structure (ALDSTR2 ), architecture (ARCH), database (DB) and data structure (DSTR1).

Students' marks are represented by a ".csv" file (an example is shown in Figure~\ref{tab:01}). It contains students' identifiers in the lines and modules studied in the columns followed by the variable "p" to specify that the variables (modules marks) need to be partitioned into a fixed number of intervals, we use the dynamic clustering algorithm (nu\'{e}es dynamiques) \cite{Diday71} which automatically forms the intervals that have distinct boundaries.\\
\rc{je ne crois pas que tu as expliqué que PS1 ca veut dire faible en
  PS... C'est indispensable}

%tableau 1
\begin{figure}[htbp]
\begin{tabular}{|c|c|c|c|c|c|}
\hline
\texttt    & ARCH p & DSTR1 p & IS p   \\ \hline
\texttt  09MI0025 & 11,25 & 9,88 & 11,5 \\ \hline
\texttt  09MI0034 & 9,38 & 11,38 & 7,33  \\ \hline
\texttt  09MI0590 & 10,63 & 9,38 & 8,67  \\ \hline
\texttt  09MI0061 & 11,38 & 14,69 & 10,5  \\ \hline
\texttt   ... & ... & ... & ...\\
\hline

\end{tabular}
\caption{Data example type .csv}
\label{tab:01}
\end{figure}

To process these data with the IRT we chose the graded response model (GRM) with two parameters that gives the difficulty and the discrimination of modules. The choice of this model is due to the fact that the student' marks are partitioned into three categories (weak, average and good results) thus they represent polytomous data which can be processed by the GRM model.
Analysis of results was performed by plotting the characteristic curves of the modules as shown in the following figure:

%figure 2

\begin{figure}[ht]
\centering
\includegraphics[width=0.4\textwidth]{Rplot02}
\caption{Item Characteristic Curve obtained by the GRM model.}
\label{fig:03}
\end{figure}

In Figure~\ref{fig:03}, the curve 1 (black) represents the probability to fail the module depending on the student's ability, curve 2 (red) represents the probability of having an average result in the module depending on the student's ability and the curve 3 (green) represents the probability of success in the module according to the student's ability. This figure shows that students with weak results (capacity between - 4 and - 2) have a high probability of failing the module and almost null of succeeding it, unlike students with good results (capacity between 2 and 4) that have a high probability of succeeding module and almost null of failing it.

\subsection{Results of IRT model and analysis}
In the following we present some items' characteristic curves (ICC) (Item represents a module) in $2^{nd}$ years for the promotions 2010-2011 (Figure~\ref{fig:04}), 2011-2012 (Figure~\ref{fig:05}) and 2012-2013 (Figure~\ref{fig:06}).

% -------------- figure 4 -------------------%
%%
\begin{figure}[ht!]
     \begin{center}
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_01}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_08}
        }%
     \end{center}
     \caption{$2^{nd}$ year ICC of 2010-2011.}%
     \label{fig:04}
\end{figure}
%%
% -------------- End of figure 4 ----------------------%


% -------------- figure 5 -------------------%
%%
\begin{figure}[ht!]
     \begin{center}
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_01}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_09}
        }%
     \end{center}
     \caption{$2^{nd}$ year ICC of 2011-2012.}%
     \label{fig:05}
\end{figure}
%%
% -------------- End of figure 5 ----------------------%

% -------------- figure 6 -------------------%
%%
\begin{figure}[ht!]
     \begin{center}
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_01}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_08}
        }%
     \end{center}
     \caption{$2^{nd}$ year ICC of 2012-2013.}%
          \label{fig:06}
\end{figure}
%%
% -------------- End of figure 6 ----------------------%

According to Figures~\ref{fig:04}, \ref{fig:05} and~\ref{fig:06} presented above

and Figures~\ref{fig:08}, \ref{fig:09}, and \ref{fig:10} in appendix; we note that we have substantially the same
results for  different years. We see  that the specialty modules  ARCH and STRD1
(Figures~\ref{fig:03}, \ref{fig:04} and  \ref{fig:05}), NumA, PS, MatLog, TSIG, ALDSTR2, DB, OS,  LTH, LP and SWE
(Figures~\ref{fig:08}, \ref{fig:09} and \ref{fig:10}) are the most  discriminating (we observe steeper curves), i.e. these
modules make  the difference between students  with weak results and  those with
good results unlike English4 and English3 (Figures~\ref{fig:03}, \ref{fig:04} and \ref{fig:05}), and IS, English3
and French4 (Figures~\ref{fig:08}, \ref{fig:09} and \ref{fig:10}) which are not.

We know  that in general,  students with good  results in computer  science work
well in all the specialty modules and students with low results in computer have
similar  results in  all specialty  modules. This  is confirmed  by the  results
presented above.

Students with  good results, i.e. with  an ability greater than  $2$, for example;
have a  probability close to $1$  to success speciality modules  and a probability
close to $0$  to fail them. In  contrast students with low results,  those with an
ability  less than  $-2$,  for example,  have a  probability close  to $1$  to fail
specialty modules and a null probability of succeeding them.

Being good in computer science does not mean being good in language modules (French and
English) and, in the same way, being weak in computer science does not mean being
weak in language modules. In Figures~\ref{fig:03},
\ref{fig:04} and \ref{fig:05} it can be observed that  these modules
are not discriminative. \rc{On pourrait pas donner les valeurs de discriminant
  ou extremum (je ne me rappelle plus)}

The information  system module (IS)  (Figures~\ref{fig:08}, \ref{fig:09} and \ref{fig:10} in the  Appendix), is
also not  discriminative and  this is  explained by the  fact that  it is  not a
computer  science   speciality  module.    It  concerns   business  organization,
management,  etc. For  students  who  have average  results  (whose capacity  is
between -2 and 2), curves 2 (red)  show that they have a medium probability (0.5
to 0.7) to succeed specialty modules.

\subsection{SIA method results and analysis}
%%aya %% In  the  following  we  present  some  implicative  graphs  resulting  from  the application of the statistical implicative  analysis (SIA) on the students marks presented above,  this work  has been the  subject of the  paper \cite{Khaled14} published in ISKO-Maghreb (2014). However, we have used a different model compared to our previous work. This new  model is more suited to situations when there are many students.

In the following we present some implicative graphs resulting from the
application of the statistical implicative analysis (SIA) on the
students marks presented above. This work was the subject of the
paper \cite{Khaled14} published in ISKO-Maghreb (2014).  The
implicative graph is used in the context of the assessment of skills,
it identifies the implications in the modules. For example, we can see
 implications like: if students have good results in this module,
generally they also have good results in this module. For the
ccomputation of the implicative graph, we have used a different model
compared to our previous work. This new model is more suited to
situations when there are many students. The new implication intensity
is call implifiance and it is defined in  \cite{Gras15}. This index 
mixes the confidence and implication. In practice, we keep only
implications greater than a given threshold. These implication are
represented by arrows.


%%RAPH ici, je pense qu'il faudrait rappeler un peu comment le SIA fonctionne, expliquer un peu plus le partitionnement et aussi expliquer qu'on va utiliser la mesure d'implifiance qui mixe la confiance et l'implication ???
The intervals of students' marks here are also divided into three sub intervals identifying students with week, average and good results. For
example, the module DSTR1 was partitioned into the following sub intervals:

DSTR11 from 5.94 to 10.38, DSTR12 from 10.5 to 13.38, DSTR13 from 13.5 to 18.38. DSTR11 reflects students who are weak at DSTR1, DSTR12 students who are average and DSTR13 students who are good at DSTR1.

\rc{Je pense qu'il faut grossir les 2 figures. J'ai fait en sorte
  qu'elle soit plus grosse mais tu les as bcp réduite, donc il faut
  que tu refasses la capture d'écran. Attention, j'ai renuméroté les
  figures, car il y avait un numéro en double, il faut vérifier si les
numéro sont correctes.}
%figure 6
\begin{figure*}[htbp]
\centering
\includegraphics{fig6As}
\caption{Implicative Graph $2^{nd}$ year 2010-2011.}
\label{fig:07}
\end{figure*}

%figure 7
\begin{figure*}[htbp]
\centering
\includegraphics{fig7As}
\caption{Implicative Graph $2^{nd}$ year 2011-2012.}
\label{fig:08}
\end{figure*}

The criterion used to look for the implications of implicative graphs is the implifiance shown in \cite{Gras15}; it presents a combination between the confidence criteria and intensity of implication.

We see in these figures that the arcs are weighted. The weights
represent the confidence, if we take the example of confidence 71.05
between the modules ALDSTR2.1 and DSTR1.1 in Figure~\ref{fig:07} this
means that if a student is weak in ALDSTR2 has a 71.05\% chance to be
weak in DSTR1. All implications we have got are interesting because
they almost all have confidence above 60.

We observe on both Figures~\ref{fig:07} and \ref{fig:08} implications that are repeated over two consecutive years. We see clearly that a module mastered by good students causes other modules mastred by good students (eg DSTR1.3 $\rightarrow$ ALDSTR2.3, DSTR1.3 $\rightarrow$ LTH3, ALDSTR2.3 $\rightarrow$ DB3). It is the same for modules failed by weak students that involve other modules failed by weak students (eg PS1 $\rightarrow$ DSTR1.1). We do not see in the figures the average students we explain this by the fact that a student who is average in a module may be weak or good in other modules and he is not necessarily average in all modules.

\subsection{Comparison of SIA and IRT results}
In the paper \cite{Khaled14} we presented the results of statistical
implicative analysis (SIA) application on student marks; we postponed
some (Figures~\ref{fig:07} and \ref{fig:08}) in this paper
\rc{vérifier les numéros, je suis perdu. Sinon s'il faut voir quelque
  chose sur les figures, je ne vois rien, tellement c'est petit}. The results show that the
implications between modules are generally repeated on three
promotions (2010-2011, 2011-2012 and 2012-2013). These implications
are interesting because they correspond to the successes or failures
of students (successful modules involve other successful modules and
modules failed by students involve other failed modules). We also
noted the implications between modules which are linked by their
content or the teacher who gives the lectures.

We note that the SIA gives us very interesting implications between
modules, it allows us to say if a student success the module X then he
will tend to success another module Y.

Items Response Theory (IRT) for its part, shows us what modules are discriminating (depending on the ability of students), besides it indicates the difficulty of the modules.

According to the results obtained in \cite{Khaled14} and those of this
paper, we think that the Statistical Implicative Analysis and Items
Response Theory give us different information. The first one gives us
the implications between modules. The second provides information on
the probability of a student to succeed or not a module depending on
his ability and the module difficulty. So SIA and IRT are
complementary and provide valuable insights to analyze the results of
the students of the concerned department. We encourage teachers to
analyze the results of their pupils or students with SIA and IRT to
have information enabling them to better understand the results of the
pupils or students.


\section{Conclusion}
We applied the Statistical Implicative Analysis method and the Items Response Theory on the Bejaia university students' marks through the three promotions 2010-2011, 2011-2012 and 2012-2013.

The marks are partitioned into three intervals using the dynamic clustering algorithm to have students with good results, with average results and students with weak results. Then we used both methods SIA and IRT in order to compare their results.

For SIA we used the RCHIC software to plot implicative graphs that
gives us relevant implications between the different modules. For IRT
we used the GRM two-parameters model to estimate and plot the items
characteristic curves.

The results of both methods show that they are complementary. So the
SIA gives us the most relevant implications between modules; while the
IRT gives us the difficulty of the modules and shows that students
with good ability have a high probability to have good result in all
the specialty modules. Similarly, students with weak ability have a
high probability to have weak results in all the speciality modules.

We advise teachers to use these methods to analyze the grades of their
students to determine the difficulty of the modules, to improve
courses or examination subjects for example. Furthermore, these two
methods can be used to refine the modules of a specialty; they are
used to determine the modules that have a relationship with the
specialty. Thus, it is possible to make choice for the training
modules.

In the near future, we plan to test both methods on larger data such
as the International Program for Student Assessment (PISA). These data
are collected as part of the international PISA survey which is
conducted every three years since 2000 with young people of 15 years
old in most OCDE countries and in many partner countries. This survey
evaluates the acquisition of essential knowledge and skills to
everyday life after compulsory schooling. This work will also be an
opportunity to assess the performance of other machine learning
methods through statistical environment R.

\rc{Sinon quand on compile la biblio, il y a des tas de warning, ca
  serait bien de les corriger}


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\else
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% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
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\bibliography{biblio}
\bibliographystyle{plain}
%%\begin{thebibliography}{1}

%% \bibitem{IEEEhowto:Bodin}

%% A.~Bodin and al (2010), \emph{Vers un test adaptatif - criteri\'{e}, combinant l'utilisation de l'IRT et de l'ASI, pour l'\'{e}valuation du socle commun de connaissances et de comp\'{e}tences},\hskip 1em plus
%%   0.5em minus 0.4em\relax Quaderni di Ricerca in Didattica (Mathematics),n 020, 383-409.

%% \bibitem{IEEEhowto:Couturier}

%% R.~Couturier (2008), \emph{Statistical Implicative Analysis. In CHIC: CohesiveHierarchical Implicative Classification}, \hskip 1em plus
%%   0.5em minus 0.4em\relax volume 127 of Studies in Computational Intelligence, Springer ; 41-52.

%% \bibitem{IEEEhowto:Couturier}
%% R.~Couturier and R.~Gras (2005), \emph{CHIC: Traitement de donn\'{e}es avec l'analyse implicative, Revue des nouvelles technologies de l'information}, \hskip 1em plus
%%   0.5em minus 0.4em\relax n 03, 679-684.

%% \bibitem{IEEEhowto:Dai-Trang}
%% L.~Dai-Trang (2013), \emph{Applying item responsetheorymodeling in educationalresearch}, \hskip 1em plus
%%   0.5em minus 0.4em\relax These: Philosophie, Ames Iowa aux \'{E}tats-Unis : Universit\'{e} d'\'{E}tat de sciences et technologie de l'Iowa, 187 p.

%% \bibitem{IEEEhowto:Diday}
%% E.~Diday (1971), \emph{La m\'{e}thode des nu\'{e}es dynamiques, Journal revue de statistique appliqu\'{e}}, \hskip 1em plus
%%   0.5em minus 0.4em\relax n 0 19 (2), 19-34.

%% \bibitem{IEEEhowto:Gras}
%% R.~Gras and al (2008), \emph{Statistical Implicative Analysis, Theory and Applications}, \hskip 1em plus
%%   0.5em minus 0.4em\relax eds, Springer.

%% \bibitem{IEEEhowto:Gras}
%% R.~Gras and al (2013), \emph{L'analyse statistique implicative, M\'{e}thode exploratoire et confirmatoire \`{a} la recherche de causalit\'{e}s, sous la direction de Gras R.}, \hskip 1em plus
%%   0.5em minus 0.4em\relax eds, C\'{e}padu\`{e}s Editions, 522 pages, ISBN 978.2.36493.056.8.

%% \bibitem{IEEEhowto:Gras}
%% R.~Gras, R.~Couturier, P.~Gregori (2015), \emph{Un mariage arrang\'{e} entre l'implication et la confiance ?}, \hskip 1em plus
%%   0.5em minus 0.4em\relax A.S.I.8.

%% \bibitem{IEEEhowto:Hamdare}
%% S.~Hamdare (2014), \emph{An Adaptive Evaluation System to Test Student Caliber using Item Response Theory}, \hskip 1em plus
%%   0.5em minus 0.4em\relax IJMTER, 329-333.

%% \bibitem{IEEEhowto:Hedeker} ??? aya
%% D.~Hedeker and al (2006), \emph{Application of Item Response Theory Models for Intensive Longitudinal Data},\hskip 1em plus
%%   0.5em minus 0.4em\relax in T.A. Walls \& J.L. Schafer (Eds.), Models for Intensive Longitudinal Data,Oxford University Press, New York, 84-108.

%% \bibitem{IEEEhowto:Johns}
%% J.~Johns, S.~Mahadevan, B.~Woolf (2006), \emph{Estimating Student Proficiency Using an Item Response Theory Model}, \hskip 1em plus
%%   0.5em minus 0.4em\relax In : Mitsuru Ikeda, Kevin D. Ashley, Tak-Wai Chan. Intelligent Tutoring Systems. Taiwan: Springer, 473-480.

%% \bibitem{IEEEhowto:Khaled}
%% H.~Khaled, S.~Ghanem, R.~Couturier (2014), \emph{Analysis of Bejaia University Computer Science students' marks through the CHIC software and Statistical Implicative Analysis}, \hskip 1em plus
%%   0.5em minus 0.4em\relax ISKO-Maghreb, (n 0 94).

%% \bibitem{IEEEhowto:Michael} ??? aya
%% L.~Michael (2013), \emph{An application of item response theory to fMRI data: Prospects and pitfalls}, \hskip 1em plus
%%   0.5em minus 0.4em\relax Psychiatry Research: Neuroimaging, n 0 du volume212(n 0 3), 167 6174.

%% \bibitem{IEEEhowto:Bodin}
%%A.~Bodin (2010), \emph{Vers un test adaptatif - criteri\'{e}, combinant l'utilisation de l'IRT et de l'ASI, pour l'\'{e}valuation du socle
%%commun de connaissances et de comp\'{e}tences}, \hskip 1em plus
%%  0.5em minus 0.4em\relax Quaderni di Ricerca in Didattica (Mathematics),n°20, 383-409.


%% \bibitem{IEEEhowto:Rowan} ??? aya
%% B.~Rowan and al (2001), \emph{Measuring Teachers' Pedagogical Content Knowledge in Surveys: An Exploratory Study}, \hskip 1em plus
%%   0.5em minus 0.4em\relax Philadelphia, PA: Consortium for Policy Research in Education, Ministry of Education, Youth and Sports.

%% \bibitem{IEEEhowto:Rizopoulo}
%% D.~Rizopoulo (2006), \emph{ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses}, \hskip 1em plus
%%   0.5em minus 0.4em\relax Journal of Statistical Software, n 0 du volume 17 (n 05), 1-25.

%% \bibitem{IEEEhowto:Xinming}
%% A.~Xinming, Y.~Yiu-Fai (2014), \emph{Item Response Theory: What It Is and How You Can Use the IRT Procedure to Apply It}, \hskip 1em plus
%%   0.5em minus 0.4em\relax SAS Institute Inc.



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% annexe 
\newpage
Appendix

In this appendix we present the items characteristic curves of all the modules studied in the $2^{nd}$ year through three promotions namely 2010-2011, 2011-2012 and 2012-2013.

In the Figures~\ref{fig:08}, \ref{fig:09} and \ref{fig:10} we see the items characteristic curves (ICC) of all the modules assured in the second year for the three promotions 2010-2011, 2011-2012 and 2012-2013, each  contains three curves, the black one (number 1) presents the students who are weak in the module, the red one (number 2) presents the ones who are average and the green curve (number 3) presents the students who are good in the module.

We note on the three figures that the items characteristic curves are almost the same for the three promotions. We also affirm that the modules are divided in two groups; those that are discriminants (ARCH, DSTR1, NumA, P.S, MatLog, SP, ALDSTR2, DB, OS, LTH, LP and SWE); they present the specialty modules and the ones that are not (English4, French3, IS, English3 and French4).



% -------------- figure 9 -------------------%
%%
\begin{figure}[ht!]
     \begin{center}
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_01}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_02}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_03}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_04}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_05}
        }%
     \end{center}
   % \caption{$2^{nd}$ year ICC of 2010-2011.}%
\end{figure}

\begin{figure}[ht!]
     \begin{center}
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_06}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_07}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_08}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2010_2011_09}
        }%
     \end{center}
    \caption{$2^{nd}$ year ICC of 2010-2011.}%
    \label{fig:09}
\end{figure}
%%
% -------------- End of figure 9 ----------------------%

% -------------- figure 10 -------------------%
%%


\begin{figure}[ht!]
     \begin{center}
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_01}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_02}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_03}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_04}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_05}
        }%
     \end{center}
   % \caption{$2^{nd}$ year ICC of 2011-2012.}%
\end{figure}

\begin{figure}[ht!]
     \begin{center}
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_06}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_07}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_08}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_09}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2011_2012_10}
        }%
     \end{center}
    \caption{$2^{nd}$ year ICC of 2011-2012.}%
    \label{fig:10}
\end{figure}
%%
% -------------- End of figure 10 ----------------------%

% -------------- figure 11 -------------------%
%%

\begin{figure}[t!]
     \begin{center}
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_01}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_02}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_03}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_04}
        }%
     \end{center}
    %\caption{$2^{nd}$ year ICC of 2012-2013.}%
\end{figure}

\begin{figure}[ht!]
     \begin{center}
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_05}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_06}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_07}
        }\\ %  ------- End of the first row ----------------------%
        \subfigure{%
            \includegraphics[width=0.5\textwidth]{Rplot_L2_2012_2013_08}
        }%
     \end{center}
    \caption{$2^{nd}$ year ICC of 2012-2013.}%
    \label{fig:11}
\end{figure}
%%
% -------------- End of figure 11 ----------------------%








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