X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hdrcouchot.git/blobdiff_plain/dd837d463f86ebb399eb1cac274139e98815fdd1..1863b8b84356fa645dafb42dc9fe4028d825e54f:/chaosANN.tex?ds=sidebyside

diff --git a/chaosANN.tex b/chaosANN.tex
index 1754b80..cdcd912 100644
--- a/chaosANN.tex
+++ b/chaosANN.tex
@@ -152,34 +152,19 @@ $\left(x_1^0,\dots,x_n^0\right)$   et $S   \in    [n]^{\mathds{N}}$,
 il produit exactement les mÃªme sorties que les itÃ©rations de  $F_{f_u}$ avec une 
 condition initiale $\left((x_1^0,\dots,  x_n^0),S\right)  \in  \mathds{B}^n \times [n]^{\mathds{N}}$.
 Les itÃ©rations de $F_{f_u}$ 
-sont donc un modÃ¨le formel de ce genre de rÃ©seau de neurones.
-Pour vÃ©rifier s'il est chaotique, il suffit ainsi 
+sont donc un modÃ¨le formel de cette classe de rÃ©seau de neurones.
+Pour vÃ©rifier si un de ces reprÃ©sentants est chaotique, il suffit ainsi 
 de vÃ©rifier si le graphe d'itÃ©rations
 $\textsc{giu}(f)$ est fortement connexe.
 
 
-\section{Suitability of Feedforward Neural Networks 
-for Predicting Chaotic and Non-chaotic Behaviors}
-
-In  the context  of computer  science  different topic  areas have  an
-interest       in       chaos,       as       for       steganographic
-techniques~\cite{1309431,Zhang2005759}.    Steganography  consists  in
-embedding a  secret message within  an ordinary one, while  the secret
-extraction takes place once  at destination.  The reverse ({\it i.e.},
-automatically detecting the presence  of hidden messages inside media)
-is  called   steganalysis.   Among  the   deployed  strategies  inside
-detectors,          there         are          support         vectors
-machines~\cite{Qiao:2009:SM:1704555.1704664},                   neural
-networks~\cite{10.1109/ICME.2003.1221665,10.1109/CIMSiM.2010.36},  and
-Markov   chains~\cite{Sullivan06steganalysisfor}.    Most   of   these
-detectors  give quite  good results  and are  rather  competitive when
-facing steganographic  tools.  However, to  the best of  our knowledge
-none of the considered information hiding schemes fulfills the Devaney
-definition  of chaos~\cite{Devaney}.  Indeed,  one can  wonder whether
-detectors  continue to  give good  results when  facing  truly chaotic
-schemes.  More  generally, there remains the open  problem of deciding
-whether artificial intelligence is suitable for predicting topological
-chaotic behaviors.
+\section{Un rÃ©seau de neurones peut-il approximer un 
+des itÃ©ration unaires chaotiques?}
+
+Cette section s'intÃ©resse Ã  Ã©tudier le comportement d'un rÃ©seau de neurones 
+face Ã  des itÃ©rations unaires chaotiques, comme dÃ©finies Ã  
+la section~\ref{sec:TIPE12}.
+
 
 \subsection{Representing Chaotic Iterations for Neural Networks} 
 \label{section:translation}
