X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/d68de43fbfbc44e3363780b39401bf1d2683f9d8..a57f211cb3b73d523ff516e65f2559b296775c11:/main.tex?ds=inline diff --git a/main.tex b/main.tex index 773caee..6225751 100644 --- a/main.tex +++ b/main.tex @@ -1,4 +1,62 @@ -\documentclass{ita} + +%% bare_jrnl.tex +%% V1.4b +%% 2015/08/26 +%% by Michael Shell +%% see http://www.michaelshell.org/ +%% for current contact information. +%% +%% This is a skeleton file demonstrating the use of IEEEtran.cls +%% (requires IEEEtran.cls version 1.8b or later) with an IEEE +%% journal paper. +%% +%% Support sites: +%% http://www.michaelshell.org/tex/ieeetran/ +%% http://www.ctan.org/pkg/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 the 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. ** +%%************************************************************************* + + +% *** Authors should verify (and, if needed, correct) their LaTeX system *** +% *** with the testflow diagnostic prior to trusting their LaTeX platform *** +% *** with production work. The IEEE's font choices and paper sizes can *** +% *** trigger bugs that do not appear when using other class files. *** *** +% The testflow support page is at: +% http://www.michaelshell.org/tex/testflow/ + + + +\documentclass[journal]{IEEEtran} +% +% If IEEEtran.cls has not been installed into the LaTeX system files, +% manually specify the path to it like: +% \documentclass[journal]{../sty/IEEEtran} + + \usepackage{graphicx} \usepackage{caption} \usepackage{subcaption} @@ -10,12 +68,10 @@ \usepackage{color} \usepackage{algorithm2e} \usepackage{epstopdf} -%\usepackage{ntheorem} - \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[english]{babel} -\usepackage{amsmath,amssymb,latexsym,eufrak,euscript} +\usepackage{amsmath,amssymb,amsthm,latexsym,eufrak,euscript} \usepackage{pstricks,pst-node,pst-coil} @@ -35,16 +91,17 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \definecolor{bleuclair}{rgb}{0.75,0.75,1.0} +\newcommand{\danger}{!!} \newcommand{\ANNOT}[1]{ ~\linebreak \centerline{ - {\Huge{\danger}} + {\Huge{$\Rightarrow$}} \large\fcolorbox{black}{bleuclair}{ \begin{minipage}[h]{.8\linewidth} #1 \end{minipage} } - {\Huge{\danger}} + {\Huge{$\Leftarrow$}} } } @@ -60,6 +117,14 @@ \newtheorem*{xpl}{Running Example} +\newtheorem{definition}{Definition} +\newtheorem{prpstn}{Proposition} +\newtheorem{thrm}{Theorem} +\newtheorem{crllr}{Corollary} +\newtheorem{lmm}{Lemma} + + + \newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}} %\newcommand{\ie}{\textit{i.e.}} \newcommand{\Nats}[0]{\ensuremath{\mathbb{N}}} @@ -80,30 +145,448 @@ + +% 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/pkg/ifpdf +% 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 *** +% +%\usepackage{cite} +% 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 the 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 +% such as if a citation ever needs to be enclosed in parenthesis. +% cite.sty is already installed on most LaTeX systems. Be sure and use +% version 5.0 (2009-03-20) and later if using hyperref.sty. +% The latest version can be obtained at: +% http://www.ctan.org/pkg/cite +% The documentation is contained in the cite.sty file itself. + + + + + + +% *** 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/pkg/graphicx +% Another good source of documentation is "Using Imported Graphics in +% LaTeX2e" by Keith Reckdahl which can be found at: +% http://www.ctan.org/pkg/epslatex +% +% 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). The 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 + + + + + +% *** MATH PACKAGES *** +% +%\usepackage{amsmath} +% A popular package from the American Mathematical Society that provides +% many useful and powerful commands for dealing with mathematics. +% +% 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/pkg/amsmath + + + + + +% *** SPECIALIZED LIST PACKAGES *** +% +%\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 the 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/pkg/algorithms +% Also of interest may be the (relatively newer and more customizable) +% algorithmicx.sty package by Szasz Janos: +% http://www.ctan.org/pkg/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/pkg/array + + +% IEEEtran contains the IEEEeqnarray family of commands that can be used to +% generate multiline equations as well as matrices, tables, etc., of high +% quality. + + + + +% *** SUBFIGURE PACKAGES *** +%\ifCLASSOPTIONcompsoc +% \usepackage[caption=false,font=normalsize,labelfont=sf,textfont=sf]{subfig} +%\else +% \usepackage[caption=false,font=footnotesize]{subfig} +%\fi +% subfig.sty, written by Steven Douglas Cochran, is the modern replacement +% for subfigure.sty, the latter of which is no longer maintained and is +% incompatible with some LaTeX packages including fixltx2e. 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 non-IEEE style figure/table captions. To prevent this problem, be sure +% and invoke subfig.sty's "caption=false" package option (available since +% subfig.sty version 1.3, 2005/06/28) as this is will preserve IEEEtran.cls +% handling of captions. +% Note that the Computer Society format requires a larger sans serif font +% than the serif footnote size font used in traditional IEEE formatting +% and thus the need to invoke different subfig.sty package options depending +% on whether compsoc mode has been enabled. +% +% The latest version and documentation of subfig.sty can be obtained at: +% http://www.ctan.org/pkg/subfig + + + + +% *** 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. +% Be aware that LaTeX2e kernels dated 2015 and later have fixltx2e.sty's +% corrections already built into the system in which case a warning will +% be issued if an attempt is made to load fixltx2e.sty as it is no longer +% needed. +% The latest version and documentation can be found at: +% http://www.ctan.org/pkg/fixltx2e + + +%\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/pkg/stfloats +% Do not use the stfloats baselinefloat ability as the IEEE does not allow +% \baselineskip to stretch. Authors submitting work to the IEEE should note +% that the 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 the IEEE does not format its papers in +% such ways. +% Do not attempt to use stfloats with fixltx2e as they are incompatible. +% Instead, use Morten Hogholm'a dblfloatfix which combines the features +% of both fixltx2e and stfloats: +% +% \usepackage{dblfloatfix} +% The latest version can be found at: +% http://www.ctan.org/pkg/dblfloatfix + + + + +%\ifCLASSOPTIONcaptionsoff +% \usepackage[nomarkers]{endfloat} +% \let\MYoriglatexcaption\caption +% \renewcommand{\caption}[2][\relax]{\MYoriglatexcaption[#2]{#2}} +%\fi +% endfloat.sty was written by James Darrell McCauley, Jeff Goldberg and +% Axel Sommerfeldt. 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 8.4.1) 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}} +% However, the above trick will not work if both optional arguments of +% the \subfloat 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/pkg/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 and documentation can be obtained at: +% http://www.ctan.org/pkg/url +% Basically, \url{my_url_here}. + + + + +% *** 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} + + +\begin{document} +% +% paper title +% Titles are generally capitalized except for words such as a, an, and, as, +% at, but, by, for, in, nor, of, on, or, the, to and up, which are usually +% not capitalized unless they are the first or last word of the title. +% Linebreaks \\ can be used within to get better formatting as desired. +% Do not put math or special symbols in the title. \title{Random Walk in a N-cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations} -\begin{document} +% +% +% 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 +% +\author{Sylvain Contassot-Vivier, Jean-François Couchot, Christophe Guyeux, Pierre-Cyrille Heam +\thanks{LORIA, Université de Lorraine, Nancy, France} +\thanks{FEMTO-ST Institute, University of Franche-Comté, Belfort, France}} + + + +% \author{Michael~Shell,~\IEEEmembership{Member,~IEEE,} +% John~Doe,~\IEEEmembership{Fellow,~OSA,} +% and~Jane~Doe,~\IEEEmembership{Life~Fellow,~IEEE}% <-this % stops a space +% \thanks{M. Shell was with the Department +% of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, +% GA, 30332 USA e-mail: (see http://www.michaelshell.org/contact.html).}% <-this % stops a space +% \thanks{J. Doe and J. Doe are with Anonymous University.}% <-this % stops a space +% \thanks{Manuscript received April 19, 2005; revised August 26, 2015.}} + +% 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 +% line to be shifted left slightly. This is one of those "LaTeX things". For +% 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. -\author{Jean-François Couchot, Christophe Guyeux, Pierre-Cyrille Heam} -\address{FEMTO-ST Institute, University of Franche-Comté, Belfort, France} -\keywords{Pseudorandom Number Generator, Theory of Chaos, Markov Matrice, Hamiltonian Path, Mixing Time, Stopping Time, Statistical Test} -\subjclass{34C28, 37A25,11K45} +% The paper headers +\markboth{Journal of \LaTeX\ Class Files,~Vol.~14, No.~8, August~2015}% +{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for IEEE Journals} +% 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. + + + + +% 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~2015 IEEE} +% Remember, if you use this you must call \IEEEpubidadjcol in the second +% column for its text to clear the IEEEpubid mark. + + + +% use for special paper notices +%\IEEEspecialpapernotice{(Invited Paper)} + + + + +% make the title area +\maketitle + +% As a general rule, do not put math, special symbols or citations +% in the abstract or keywords. + + +% \begin{abstract} +% This paper is dedicated to the design of chaotic random generators +% and extends previous works proposed by some of the authors. +% We propose a theoretical framework proving both the chaotic properties and +% that the limit distribution is uniform. +% A theoretical bound on the stationary time is given and +% practical experiments show that the generators successfully pass +% the classical statistical tests. +% \end{abstract} \begin{abstract} -This paper is dedicated to the design of chaotic random generators -and extends previous works proposed by some of the authors. -We propose a theoretical framework proving both the chaotic properties and -that the limit distribution is uniform. -A theoretical bound on the stationary time is given and -practical experiments show that the generators successfully pass -the classical statistical tests. + +Designing a pseudorandom number generator (PRNG) is a hard and complex task. +Many recent works have consider chaotic functions as the basis of built +PRNGs: +the quality of the output would be an obvious consequence of some chaos +properties. +However, there is no direct reasoning that goes from chaotic functions to +uniform distribution of the output. +Moreover, it is not clear that embedding such kind of functions into a PRNG +allows to get a chaotic output, which could be required for simulating +some chaotic behaviours. + +In a previous work, some of the authors have proposed the idea of walking +into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle have been +removed as the basis of a chaotic PRNG. In this article, all the difficult +issues observed in the previous work have been tackled. The chaotic behavior +of the whole PRNG is proven. The construction of the balanced Hamiltonian +cycle is theoretically and practically solved. An upper bound of the +expected length of the walk to obtain a uniform distribution is calculated. +Finally practical experiments show that the generators successfully pass the +classical statistical tests. + + \end{abstract} -\maketitle + + + +% Note that keywords are not normally used for peerreview papers. +% \begin{IEEEkeywords} +% IEEE, IEEEtran, journal, \LaTeX, paper, template. +% \end{IEEEkeywords} + + + + + + +% 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} \input{intro} @@ -117,11 +600,11 @@ the classical statistical tests. \section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}\label{sec:SCCfunc} \input{generating} -\section{(Locally) Balanced Hamiltonian Cycle}\label{sec:hamilton} +\section{Balanced Hamiltonian Cycle}\label{sec:hamilton} \input{hamilton} -\section{Stopping Time}\label{sec:hypercube} +\section{Mixing Time}\label{sec:hypercube} \input{stopping} \section{Experiments}\label{sec:prng} @@ -134,7 +617,264 @@ the classical statistical tests. %\acknowledgements{...} -\bibliographystyle{alpha} +\bibliographystyle{IEEEtran} \bibliography{biblio} + +%\section{Introduction} +% The very first letter is a 2 line initial drop letter followed +% by the rest of the first word in caps. +% +% 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 the 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}{his} demo file is intended to serve as a ``starter file'' +% for IEEE journal papers produced under \LaTeX\ using +% IEEEtran.cls version 1.8b and later. +% % 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. + +% \hfill mds + +% \hfill August 26, 2015 + +% \subsection{Subsection Heading Here} +% Subsection text here. + +% % needed in second column of first page if using \IEEEpubid +% %\IEEEpubidadjcol + +% \subsubsection{Subsubsection Heading Here} +% Subsubsection text here. + + +% % An example of a floating figure using the graphicx package. +% % Note that \label must occur AFTER (or within) \caption. +% % For figures, \caption should occur after the \includegraphics. +% % Note that IEEEtran v1.7 and later has special internal code that +% % is designed to preserve the operation of \label within \caption +% % even when the captionsoff option is in effect. However, because +% % of issues like this, it may be the safest practice to put all your +% % \label just after \caption rather than within \caption{}. +% % +% % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class +% % option should be used if it is desired that the figures are to be +% % displayed while in draft mode. +% % +% %\begin{figure}[!t] +% %\centering +% %\includegraphics[width=2.5in]{myfigure} +% % where an .eps filename suffix will be assumed under latex, +% % and a .pdf suffix will be assumed for pdflatex; or what has been declared +% % via \DeclareGraphicsExtensions. +% %\caption{Simulation results for the network.} +% %\label{fig_sim} +% %\end{figure} + +% % Note that the IEEE typically puts floats only at the top, even when this +% % results in a large percentage of a column being occupied by floats. + + +% % An example of a double column floating figure using two subfigures. +% % (The subfig.sty package must be loaded for this to work.) +% % The subfigure \label commands are set within each subfloat command, +% % and the \label for the overall figure must come after \caption. +% % \hfil is used as a separator to get equal spacing. +% % Watch out that the combined width of all the subfigures on a +% % line do not exceed the text width or a line break will occur. +% % +% %\begin{figure*}[!t] +% %\centering +% %\subfloat[Case I]{\includegraphics[width=2.5in]{box}% +% %\label{fig_first_case}} +% %\hfil +% %\subfloat[Case II]{\includegraphics[width=2.5in]{box}% +% %\label{fig_second_case}} +% %\caption{Simulation results for the network.} +% %\label{fig_sim} +% %\end{figure*} +% % +% % Note that often IEEE papers with subfigures do not employ subfigure +% % captions (using the optional argument to \subfloat[]), but instead will +% % reference/describe all of them (a), (b), etc., within the main caption. +% % Be aware that for subfig.sty to generate the (a), (b), etc., subfigure +% % labels, the optional argument to \subfloat must be present. If a +% % subcaption is not desired, just leave its contents blank, +% % e.g., \subfloat[]. + + +% % An example of a floating table. Note that, for IEEE style tables, the +% % \caption command should come BEFORE the table and, given that table +% % captions serve much like titles, are usually capitalized except for words +% % such as a, an, and, as, at, but, by, for, in, nor, of, on, or, the, to +% % and up, which are usually not capitalized unless they are the first or +% % last word of the caption. Table text will default to \footnotesize as +% % the IEEE normally uses this smaller font for tables. +% % The \label must come after \caption as always. +% % +% %\begin{table}[!t] +% %% increase table row spacing, adjust to taste +% %\renewcommand{\arraystretch}{1.3} +% % if using array.sty, it might be a good idea to tweak the value of +% % \extrarowheight as needed to properly center the text within the cells +% %\caption{An Example of a Table} +% %\label{table_example} +% %\centering +% %% Some packages, such as MDW tools, offer better commands for making tables +% %% than the plain LaTeX2e tabular which is used here. +% %\begin{tabular}{|c||c|} +% %\hline +% %One & Two\\ +% %\hline +% %Three & Four\\ +% %\hline +% %\end{tabular} +% %\end{table} + + +% % Note that the IEEE does not put floats in the very first column +% % - or typically anywhere on the first page for that matter. Also, +% % in-text middle ("here") positioning is typically not used, but it +% % is allowed and encouraged for Computer Society conferences (but +% % not Computer Society journals). Most IEEE journals/conferences use +% % top floats exclusively. +% % Note that, LaTeX2e, unlike IEEE journals/conferences, places +% % footnotes above bottom floats. This can be corrected via the +% % \fnbelowfloat command of the stfloats package. + + + + +% \section{Conclusion} +% The conclusion goes here. + + + + + +% % if have a single appendix: +% %\appendix[Proof of the Zonklar Equations] +% % or +% %\appendix % for no appendix heading +% % do not use \section anymore after \appendix, only \section* +% % is possibly needed + +% % use appendices with more than one appendix +% % then use \section to start each appendix +% % you must declare a \section before using any +% % \subsection or using \label (\appendices by itself +% % starts a section numbered zero.) +% % + + +% \appendices +% \section{Proof of the First Zonklar Equation} +% Appendix one text goes here. + +% % you can choose not to have a title for an appendix +% % if you want by leaving the argument blank +% \section{} +% Appendix two text goes here. + + +% % use section* for acknowledgment +% \section*{Acknowledgment} + + +% The authors would like to thank... + + +% Can use something like this to put references on a page +% by themselves when using endfloat and the captionsoff option. +\ifCLASSOPTIONcaptionsoff + \newpage +\fi + + + +% trigger a \newpage just before the given reference +% number - used to balance the columns on the last page +% adjust value as needed - may need to be readjusted if +% the document is modified later +%\IEEEtriggeratref{8} +% The "triggered" command can be changed if desired: +%\IEEEtriggercmd{\enlargethispage{-5in}} + +% references section + +% can use a bibliography generated by BibTeX as a .bbl file +% BibTeX documentation can be easily obtained at: +% http://mirror.ctan.org/biblio/bibtex/contrib/doc/ +% The IEEEtran BibTeX style support page is at: +% http://www.michaelshell.org/tex/ieeetran/bibtex/ +%\bibliographystyle{IEEEtran} +% argument is your BibTeX string definitions and bibliography database(s) +%\bibliography{IEEEabrv,../bib/paper} +% +% manually copy in the resultant .bbl file +% set second argument of \begin to the number of references +% (used to reserve space for the reference number labels box) +% \begin{thebibliography}{1} + +% \bibitem{IEEEhowto:kopka} +% H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus +% 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999. + +% \end{thebibliography} + +% biography section +% +% If you have an EPS/PDF photo (graphicx package needed) extra braces are +% needed around the contents of the optional argument to biography to prevent +% the LaTeX parser from getting confused when it sees the complicated +% \includegraphics command within an optional argument. (You could create +% your own custom macro containing the \includegraphics command to make things +% simpler here.) +%\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell} +% or if you just want to reserve a space for a photo: + +% \begin{IEEEbiography}{Michael Shell} +% Biography text here. +% \end{IEEEbiography} + +% % if you will not have a photo at all: +% \begin{IEEEbiographynophoto}{John Doe} +% Biography text here. +% \end{IEEEbiographynophoto} + +% % insert where needed to balance the two columns on the last page with +% % biographies +% %\newpage + +% \begin{IEEEbiographynophoto}{Jane Doe} +% Biography text here. +% \end{IEEEbiographynophoto} + +% You can push biographies down or up by placing +% a \vfill before or after them. The appropriate +% use of \vfill depends on what kind of text is +% on the last page and whether or not the columns +% are being equalized. + +%\vfill + +% Can be used to pull up biographies so that the bottom of the last one +% is flush with the other column. +%\enlargethispage{-5in} + + + +% that's all folks \end{document} + +