X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/3fc31015143d2bab7226a54390f3e1c5eba8f4d5..23dcb45dd9df2aff12c4ca42d4d96ff2c039358e:/main.tex

diff --git a/main.tex b/main.tex
index d8445bf..01df881 100644
--- a/main.tex
+++ b/main.tex
@@ -1,21 +1,22 @@
 
-\documentclass[preprint,review,12pt]{elsarticle}
-
+\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}
 
 
@@ -59,9 +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}
@@ -162,12 +164,21 @@
 % a separate \thanks must be used for each paragraph as LaTeX2e's \thanks
 % was not built to handle multiple paragraphs
 %
-\author[label1]{Sylvain Contassot-Vivier}
-\author[label2]{Jean-FranÃ§ois Couchot}
-\author[label2]{Christophe Guyeux}
-\author[label2]{Pierre-Cyrille Heam}
-\address[label1]{LORIA, UniversitÃ© de Lorraine, Nancy, France}
-\address[label2]{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}
 
 
 
@@ -242,31 +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 considered 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 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}
-
-
-
 
 % Note that keywords are not normally used for peerreview papers.
 % \begin{IEEEkeywords}
@@ -288,6 +274,34 @@ classical statistical tests.
 % creates the second title. It will be ignored for other modes.
 \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}
 \input{intro}
@@ -295,7 +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}
@@ -326,7 +340,7 @@ facilities provided by the M\'esocentre de calcul de Franche-Comt\'e.
 
 
 
-\bibliographystyle{elsarticle-num} 
+\bibliographystyle{ws-ijbc} 
 \bibliography{biblio}
 
 
