X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/95808e0cc34f861214ab26eb69af0dbfb485774f..refs/heads/master:/main.tex

diff --git a/main.tex b/main.tex
index 0460847..01df881 100644
--- a/main.tex
+++ b/main.tex
@@ -1,77 +1,22 @@
 
-%% 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}
-
-
+\documentclass{ws-ijbc}
 \usepackage{graphicx}
-\usepackage{caption}
-\usepackage{subcaption}
+%\usepackage{amsthm}
 
+%\usepackage{subcaption}
+\usepackage{subfigure}
 \usepackage{dsfont}
 \usepackage{stmaryrd}
 %\usepackage[font=footnotesize]{subfig}
 \usepackage{ifthen}
 \usepackage{color}
+%\usepackage{subfigure}
 \usepackage{algorithm2e}
 \usepackage{epstopdf}
 \usepackage[utf8]{inputenc}
 \usepackage[T1]{fontenc} 
 \usepackage[english]{babel}
-\usepackage{amsmath,amssymb,amsthm,latexsym,eufrak,euscript}
+%\usepackage{amsmath,amssymb,amsthm,latexsym,eufrak,euscript}
 \usepackage{pstricks,pst-node,pst-coil}
 
 
@@ -115,9 +60,10 @@
 \def \ts {\tau_{\rm stop}}
 
 
-\newtheorem*{xpl}{Running Example}
+%\newtheorem*{xpl}{Running Example}
+\newenvironment{xpl}[1][Running Example]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
 
-\newtheorem{definition}{Definition}
+%\newtheorem{definition}{Definition}
 \newtheorem{prpstn}{Proposition}
 \newtheorem{thrm}{Theorem}
 \newtheorem{crllr}{Corollary}
@@ -196,246 +142,6 @@
 
 
 
-% *** 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
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-% 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
@@ -458,9 +164,21 @@
 % 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-FranÃ§ois Couchot, Christophe Guyeux, Pierre-Cyrille Heam
-\thanks{LORIA, UniversitÃ© de Lorraine, Nancy, France}
-\thanks{FEMTO-ST Institute, University of Franche-ComtÃ©, Belfort, France}}
+\author{Sylvain Contassot-Vivier}
+\address{LORIA, UniversitÃ© de Lorraine, Nancy, France\\
+sylvain.contassotvivier@loria.fr}
+
+\author{Jean-FranÃ§ois Couchot}
+\address{FEMTO-ST Institute,  CNRS, Univ. Bourgogne Franche-ComtÃ© (UBFC), France\\
+jean-francois.couchot@univ-fcomte.fr}
+
+\author{Christophe Guyeux}
+\address{FEMTO-ST Institute,  CNRS, Univ. Bourgogne Franche-ComtÃ© (UBFC), France\\
+christophe.guyeux@univ-fcomte.fr}
+
+\author{Pierre-Cyrille Heam}
+\address{FEMTO-ST Institute,  CNRS, Univ. Bourgogne Franche-ComtÃ© (UBFC), France\\
+pierre-cyrille.heam@univ-fcomte.fr}
 
 
 
@@ -493,9 +211,6 @@
 
 
 
-% 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.
 % 
@@ -522,7 +237,7 @@
 
 
 % make the title area
-\maketitle
+%\maketitle
 
 % As a general rule, do not put math, special symbols or citations
 % in the abstract or keywords.
@@ -538,34 +253,6 @@
 % the classical statistical tests.
 % \end{abstract}
 
-\begin{abstract}
-
-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}
-
-
-
 
 % Note that keywords are not normally used for peerreview papers.
 % \begin{IEEEkeywords}
@@ -585,7 +272,35 @@ classical statistical tests.
 %
 % For peerreview papers, this IEEEtran command inserts a page break and
 % creates the second title. It will be ignored for other modes.
-\IEEEpeerreviewmaketitle
+\maketitle
+
+\begin{abstract}
+  Designing a pseudorandom number generator (PRNG) is a
+difficult  and complex  task.  Many  recent works  have considered  chaotic
+functions as the basis of built PRNGs: the quality of the output would
+indeed
+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,  
+embedding such kind of functions into a PRNG does not necessarily
+allow to get a  chaotic output,
+which could be required for simulating some chaotic behaviors.
+
+In a  previous work,  some of  the authors have  proposed the  idea of
+walking into  a $\mathsf{N}$-cube  where a balanced  Hamiltonian cycle
+has 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}
+
+
+\keywords{Pseudorandom Numbers Generator, Chaotic iterations, Random Walk}
 
 
 \section{Introduction}
@@ -594,7 +309,7 @@ classical statistical tests.
 \section{Preliminaries}\label{sec:preliminaries}
 \input{preliminaries}
 
-\section{Proof Of Chaos}\label{sec:proofOfChaos}
+\section{Proof of Chaos}\label{sec:proofOfChaos}
 \input{chaos}
 
 \section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}\label{sec:SCCfunc}
@@ -617,7 +332,15 @@ classical statistical tests.
 
 %\acknowledgements{...}
 
-\bibliographystyle{IEEEtran}
+\section*{Acknowledgements}
+This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01). 
+Computations presented in this article were realised on the supercomputing
+facilities provided by the M\'esocentre de calcul de Franche-Comt\'e.
+
+
+
+
+\bibliographystyle{ws-ijbc} 
 \bibliography{biblio}
 
 
@@ -796,9 +519,6 @@ classical statistical tests.
 
 % Can use something like this to put references on a page
 % by themselves when using endfloat and the captionsoff option.
-\ifCLASSOPTIONcaptionsoff
-  \newpage
-\fi
 
 
 
@@ -876,5 +596,3 @@ classical statistical tests.
 
 % that's all folks
 \end{document}
-
-
