\maketitle
\begin{abstract}
-This is the abstract
+
\end{abstract}
\section{Introduction}
+Random numbers are used in many scientific applications and simulations. On
+finite state machines, like computers, it is not possible to generate random
+numbers but only pseudo-random numbers. In practice, a good pseudo-random number
+generator (PRNG) needs to verify some features to be used by scientists. It is
+important to be able to generate pseudo-random numbers efficiently, the
+generation needs to be reproducible and a PRNG needs to satisfy many usual
+statistical properties. Finally, from our point a view, it is essential to prove
+that a PRNG is chaotic. Devaney~\cite{Devaney} proposed a common mathematical
+formulation of chaotic dynamical systems.
+
+In a previous work~\cite{bgw09:ip} we have proposed a new familly of chaotic
+PRNG based on chaotic iterations (IC). In this paper we propose a faster
+version which is also proven to be chaotic with the Devaney formulation.
+
+Although graphics processing units (GPU) was initially designed to accelerate
+the manipulation of image, they are nowadays commonly used in many scientific
+applications. Therefore, it is important to be able to generate pseudo-random
+numbers in a GPU when a scientific application runs in a GPU. That is why we
+also provie an efficient PRNG for GPU respecting based on IC.
+
+
+
+
Interet des itérations chaotiques pour générer des nombre alea\\
Interet de générer des nombres alea sur GPU
-\alert{RC, un petit state-of-the-art sur les PRNGs sur GPU ?}
-...
+\section{Related works}
+
+In this section we review some GPU based PRNGs.
+\alert{RC, un petit state-of-the-art sur les PRNGs sur GPU ?}
+
\section{Basic Recalls}
\label{section:BASIC RECALLS}
This section is devoted to basic definitions and terminologies in the fields of
faster, does not deflate their topological chaos properties.
\subsection{Proofs of Chaos of the General Formulation of the Chaotic Iterations}
-
+\label{deuxième def}
Let us consider the discrete dynamical systems in chaotic iterations having
the general form:
\section{Experiments}
-Differents experiments have been performed in order to measure the generation
+Different experiments have been performed in order to measure the generation
speed.
\begin{figure}[t]
\begin{center}
\section{The relativity of disorder}
\label{sec:de la relativité du désordre}
+In the next two sections, we investigate the impact of the choices that have
+lead to the definitions of measures in Sections \ref{sec:chaotic iterations} and \ref{deuxième def}.
+
\subsection{Impact of the topology's finenesse}
Let us firstly introduce the following notations.
