X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/chaos1.git/blobdiff_plain/9e6c76e39059d7f227f7ed48ad71195374a2f2a5..8c453843ba5ef7f01a7a202686584c36cc7201c5:/main.tex

diff --git a/main.tex b/main.tex
index de92eaa..0ce8df0 100644
--- a/main.tex
+++ b/main.tex
@@ -1072,13 +1072,13 @@ Chaotic/non chaotic & \multicolumn{3}{c|}{Output = Strategy} \\
 
 In  this paper,  we have  established an  equivalence  between chaotic
 iterations,  according to  the Devaney's  definition of  chaos,  and a
-class  of  multilayer perceptron  neural  networks.  Firstly, we  have
+class  of multilayer  perceptron  neural networks.   Firstly, we  have
 described how to build a neural network that can be trained to learn a
-given chaotic map function.  Then,  we found a condition that allow to
-check whether the iterations induced by a function are chaotic or not,
-and thus  if a chaotic map  is obtained. Thanks to  this condition our
-approach is not limited to a particular function. In the dual case, we
-show  that  checking  if  a  neural network  is  chaotic  consists  in
+given chaotic map function. Secondly,  we found a condition that allow
+to check whether  the iterations induced by a  function are chaotic or
+not, and thus  if a chaotic map is obtained.  Thanks to this condition
+our  approach is not  limited to  a particular  function. In  the dual
+case, we show that checking if a neural network is chaotic consists in
 verifying  a property  on an  associated  graph, called  the graph  of
 iterations.   These results  are valid  for recurrent  neural networks
 with a  particular architecture.  However,  we believe that  a similar
@@ -1092,10 +1092,7 @@ implemented  in a  new steganographic  method  \cite{guyeux10ter}.  As
 steganographic   detectors  embed  tools   like  neural   networks  to
 distinguish between  original and stego contents, our  studies tend to
 prove that such  detectors might be unable to  tackle with chaos-based
-information hiding schemes.  Furthermore, iterations such that not all
-of  the  components  are updated  at  each  step  are very  common  in
-biological  and  physics mechanisms.   Therefore,  one can  reasonably
-wonder whether neural networks should be applied in these contexts.
+information  hiding  schemes.
 
 In  future  work we  intend  to  enlarge  the comparison  between  the
 learning   of  truly   chaotic  and   non-chaotic   behaviors.   Other
@@ -1104,8 +1101,7 @@ be investigated  too, to  discover which tools  are the  most relevant
 when facing a truly chaotic phenomenon.  A comparison between learning
 rate  success  and  prediction  quality will  be  realized.   Concrete
 consequences in biology, physics, and computer science security fields
-will be  stated.  Lastly,  thresholds separating systems  depending on
-the ability to learn their dynamics will be established.
+will be  stated.
 
 % \appendix{}