correction bib

diff --git a/chaos-paper.bib b/chaos-paper.bib
index ff934154fecb0f3d3fecf216d37b7e5545759e64..54fd84ddc0f14fa327a065be8576acf1b25982be 100644 (file)
--- a/chaos-paper.bib
+++ b/chaos-paper.bib
@@ -108,7 +108,6 @@ year =              1998
                Xin Zhou},\r
   title     = {A Novel Wavelet Image Watermarking Scheme Combined with\r
                Chaos Sequence and Neural Network},\r
                Xin Zhou},\r
   title     = {A Novel Wavelet Image Watermarking Scheme Combined with\r
                Chaos Sequence and Neural Network},\r

-  booktitle = {ISNN (2)},\r

   year      = {2004},\r
   pages     = {663-668},\r
   ee        = {http://springerlink.metapress.com/openurl.asp?genre=article{\&}issn=0302-9743{\&}volume=3174{\&}spage=663},\r
   year      = {2004},\r
   pages     = {663-668},\r
   ee        = {http://springerlink.metapress.com/openurl.asp?genre=article{\&}issn=0302-9743{\&}volume=3174{\&}spage=663},\r


@@ -120,15 +119,13 @@ year =            1998
   editor    = {Fuliang Yin and\r
                Jun Wang and\r
                Chengan Guo},\r
   editor    = {Fuliang Yin and\r
                Jun Wang and\r
                Chengan Guo},\r

-  title     = {Advances in Neural Networks - ISNN 2004, International Symposium\r
+  title     = {Advances in Neural Networks - International Symposium\r

                on Neural Networks, Dalian, China, August 19-21, 2004, Proceedings,\r
                Part II},\r
                on Neural Networks, Dalian, China, August 19-21, 2004, Proceedings,\r
                Part II},\r

-  booktitle = {ISNN (2)},\r

   publisher = {Springer},\r
   series    = {Lecture Notes in Computer Science},\r
   volume    = {3174},\r
   year      = {2004},\r
   publisher = {Springer},\r
   series    = {Lecture Notes in Computer Science},\r
   volume    = {3174},\r
   year      = {2004},\r

-  isbn      = {3-540-22843-8},\r

   bibsource = {DBLP, http://dblp.uni-trier.de}\r
 }\r
 \r
   bibsource = {DBLP, http://dblp.uni-trier.de}\r
 }\r
 \r


@@ -214,7 +211,6 @@ keywords = "Image encryption"
  booktitle = {Proceedings of the 2009 international joint conference on Neural Networks},\r
  series = {IJCNN'09},\r
  year = {2009},\r
  booktitle = {Proceedings of the 2009 international joint conference on Neural Networks},\r
  series = {IJCNN'09},\r
  year = {2009},\r

- isbn = {978-1-4244-3549-4},\r

  location = {Atlanta, Georgia, USA},\r
  pages = {2723--2728},\r
  numpages = {6},\r
  location = {Atlanta, Georgia, USA},\r
  pages = {2723--2728},\r
  numpages = {6},\r


@@ -243,7 +239,7 @@ number={2},
 pages={ 587 - 590},\r
 keywords={ authentication; chaos based spread spectrum image steganography; chaotic encryption; chaotic modulation; covert communication; digital security schemes; home-office environment; in-band captioning; large-scale proliferation; tamperproofing; wireless products; chaotic communication; cryptography; data encapsulation; image processing; message authentication; modulation; spread spectrum communication;},\r
 doi={10.1109/TCE.2004.1309431},\r
 pages={ 587 - 590},\r
 keywords={ authentication; chaos based spread spectrum image steganography; chaotic encryption; chaotic modulation; covert communication; digital security schemes; home-office environment; in-band captioning; large-scale proliferation; tamperproofing; wireless products; chaotic communication; cryptography; data encapsulation; image processing; message authentication; modulation; spread spectrum communication;},\r
 doi={10.1109/TCE.2004.1309431},\r

-ISSN={0098-3063},}\r
+}\r

 \r
 @article{Zhang2005759,\r
 title = "An image encryption approach based on chaotic maps",\r
 \r
 @article{Zhang2005759,\r
 title = "An image encryption approach based on chaotic maps",\r


@@ -269,9 +265,8 @@ note = "{US} Patent 2,632,058, March 17 1953,(filed November 13 1947)"}
 @article{10.1109/CIMSiM.2010.36,\r
 author = {Jiri Holoska and Zuzana Oplatkova and Ivan Zelinka and Roman Senkerik},\r
 title = {Comparison between Neural Network Steganalysis and Linear Classification Method Stegdetect},\r
 @article{10.1109/CIMSiM.2010.36,\r
 author = {Jiri Holoska and Zuzana Oplatkova and Ivan Zelinka and Roman Senkerik},\r
 title = {Comparison between Neural Network Steganalysis and Linear Classification Method Stegdetect},\r

-journal ={Computational Intelligence, Modelling and Simulation, International Conference on},\r
+journal ={Computational Intelligence, Modelling and Simulation, International Conference on.},\r

 volume = {0},\r
 volume = {0},\r

-isbn = {978-0-7695-4262-1},\r

 year = {2010},\r
 pages = {15-20},\r
 doi = {http://doi.ieeecomputersociety.org/10.1109/CIMSiM.2010.36},\r
 year = {2010},\r
 pages = {15-20},\r
 doi = {http://doi.ieeecomputersociety.org/10.1109/CIMSiM.2010.36},\r


@@ -288,8 +283,8 @@ volume={},
 number={},\r
 pages={3352 -3357},\r
 keywords={Fisher linear discriminant;JPEG images;discrete cosine transforms;expanded Markov features;feature reduction;feature selection;polynomial fitting;principal component analysis;singular value decomposition;steganalysis;Markov processes;discrete cosine transforms;image coding;principal component analysis;singular value decomposition;steganography;},\r
 number={},\r
 pages={3352 -3357},\r
 keywords={Fisher linear discriminant;JPEG images;discrete cosine transforms;expanded Markov features;feature reduction;feature selection;polynomial fitting;principal component analysis;singular value decomposition;steganalysis;Markov processes;discrete cosine transforms;image coding;principal component analysis;singular value decomposition;steganography;},\r

-doi={10.1109/IJCNN.2008.4634274},\r
-ISSN={1098-7576},}\r
+doi={10.1109/IJCNN.2008.4634274}\r
+}\r

 \r
 @INPROCEEDINGS{guyeux10ter,\r
   author = {Bahi, Jacques and Guyeux, Christophe},\r
 \r
 @INPROCEEDINGS{guyeux10ter,\r
   author = {Bahi, Jacques and Guyeux, Christophe},\r


@@ -409,7 +404,6 @@ author = {Liu Shaohui and Yao Hongxun and Gao Wen},
 title = {Neural network based steganalysis in still images},\r
 journal ={Multimedia and Expo, IEEE International Conference on},\r
 volume = {2},\r
 title = {Neural network based steganalysis in still images},\r
 journal ={Multimedia and Expo, IEEE International Conference on},\r
 volume = {2},\r

-isbn = {0-7803-7965-9},\r

 year = {2003},\r
 pages = {509-512},\r
 doi = {http://doi.ieeecomputersociety.org/10.1109/ICME.2003.1221665},\r
 year = {2003},\r
 pages = {509-512},\r
 doi = {http://doi.ieeecomputersociety.org/10.1109/ICME.2003.1221665},\r

diff --git a/main.tex b/main.tex
index b72eb6d8ba43fb5945c7d9fd561aeddae914b5af..8e7f34b71c25b04a1da42419c9bd664974f2c412 100644 (file)
--- a/main.tex
+++ b/main.tex
@@ -58,6 +58,11 @@ IUT de Belfort-Montb\'eliard, BP 527, \\
 \date{\today}
 
 \newcommand{\CG}[1]{\begin{color}{red}\textit{#1}\end{color}}
 \date{\today}
 
 \newcommand{\CG}[1]{\begin{color}{red}\textit{#1}\end{color}}

+\newcommand{\JFC}[1]{\begin{color}{blue}\textit{#1}\end{color}}
+
+
+
+

 
 \begin{abstract}
 %% Text of abstract
 
 \begin{abstract}
 %% Text of abstract


@@ -134,7 +139,9 @@ which  is usually  assessed through  the computation  of  the Lyapunov
 exponent.  An alternative approach  is to consider a well-known neural
 network architecture: the  MultiLayer Perceptron (MLP). These networks
 are  suitable to model  nonlinear relationships  between data,  due to
 exponent.  An alternative approach  is to consider a well-known neural
 network architecture: the  MultiLayer Perceptron (MLP). These networks
 are  suitable to model  nonlinear relationships  between data,  due to

-their universal approximator capacity. Thus, this kind of networks can
+their universal approximator capacity.
+\JFC{Michel, peux-tu donner une ref la dessus}
+Thus, this kind of networks can

 be trained to model a physical  phenomenon known to be chaotic such as
 Chua's circuit  \cite{dalkiran10}.  Sometimes, a  neural network which
 is build by combining  transfer functions and initial conditions that are both
 be trained to model a physical  phenomenon known to be chaotic such as
 Chua's circuit  \cite{dalkiran10}.  Sometimes, a  neural network which
 is build by combining  transfer functions and initial conditions that are both


@@ -508,7 +515,9 @@ Fig.~\ref{Fig:perceptron}).
 
 The behavior of the neural network is such that when the initial state
 is  $x^0~\in~\mathds{B}^n$ and  a  sequence $(S^t)^{t  \in \Nats}$  is
 
 The behavior of the neural network is such that when the initial state
 is  $x^0~\in~\mathds{B}^n$ and  a  sequence $(S^t)^{t  \in \Nats}$  is

-given  as outside  input, then  the sequence  of  successive published
+given  as outside  input,
+\JFC{en dire davantage sur l'outside world}
+ then  the sequence  of  successive published

 output vectors $\left(x^t\right)^{t \in \mathds{N}^{\ast}}$ is exactly
 the  one produced  by  the chaotic  iterations  formally described  in
 Eq.~(\ref{eq:CIs}).  It  means that  mathematically if we  use similar
 output vectors $\left(x^t\right)^{t \in \mathds{N}^{\ast}}$ is exactly
 the  one produced  by  the chaotic  iterations  formally described  in
 Eq.~(\ref{eq:CIs}).  It  means that  mathematically if we  use similar


@@ -539,8 +548,8 @@ without any  convincing mathematical proof. We propose  an approach to
 overcome  this  drawback  for  a  particular  category  of  multilayer
 perceptrons defined below, and for the Devaney's formulation of chaos.
 In  spite of  this restriction,  we think  that this  approach  can be
 overcome  this  drawback  for  a  particular  category  of  multilayer
 perceptrons defined below, and for the Devaney's formulation of chaos.
 In  spite of  this restriction,  we think  that this  approach  can be

-extended to  a large variety  of neural networks.  We plan to  study a
-generalization of this approach in a future work.
+extended to  a large variety  of neural networks. 
+

 
 We consider a multilayer perceptron  of the following form: inputs
 are $n$ binary digits and  one integer value, while outputs are  $n$
 
 We consider a multilayer perceptron  of the following form: inputs
 are $n$ binary digits and  one integer value, while outputs are  $n$


@@ -556,6 +565,7 @@ connection to an input one.
   compute the new output one $\left(x^{t+1}_1,\dots,x^{t+1}_n\right)$.
   While  the remaining  input receives  a new  integer value  $S^t \in
   \llbracket1;n\rrbracket$, which is provided by the outside world.
   compute the new output one $\left(x^{t+1}_1,\dots,x^{t+1}_n\right)$.
   While  the remaining  input receives  a new  integer value  $S^t \in
   \llbracket1;n\rrbracket$, which is provided by the outside world.

+\JFC{en dire davantage sur l'outside world}

 \end{itemize}
 
 The topological  behavior of these  particular neural networks  can be
 \end{itemize}
 
 The topological  behavior of these  particular neural networks  can be


@@ -563,11 +573,15 @@ proven to be chaotic through the following process. Firstly, we denote
 by  $F:  \llbracket  1;n  \rrbracket \times  \mathds{B}^n  \rightarrow
 \mathds{B}^n$     the     function     that     maps     the     value
 $\left(s,\left(x_1,\dots,x_n\right)\right)    \in    \llbracket    1;n
 by  $F:  \llbracket  1;n  \rrbracket \times  \mathds{B}^n  \rightarrow
 \mathds{B}^n$     the     function     that     maps     the     value
 $\left(s,\left(x_1,\dots,x_n\right)\right)    \in    \llbracket    1;n

-\rrbracket      \times      \mathds{B}^n$      into     the      value
+\rrbracket      \times      \mathds{B}^n$   
+\JFC{ici, cela devait etre $S^t$ et pas $s$, nn ?}
+   into     the      value

 $\left(y_1,\dots,y_n\right)       \in       \mathds{B}^n$,       where
 $\left(y_1,\dots,y_n\right)$  is the  response of  the  neural network
 after    the    initialization     of    its    input    layer    with
 $\left(y_1,\dots,y_n\right)       \in       \mathds{B}^n$,       where
 $\left(y_1,\dots,y_n\right)$  is the  response of  the  neural network
 after    the    initialization     of    its    input    layer    with

-$\left(s,\left(x_1,\dots, x_n\right)\right)$.  Secondly, we define $f:
+$\left(s,\left(x_1,\dots, x_n\right)\right)$. 
+\JFC{ici, cela devait etre $S^t$ et pas $s$, nn ?}
+Secondly, we define $f:

 \mathds{B}^n       \rightarrow      \mathds{B}^n$       such      that
 $f\left(x_1,x_2,\dots,x_n\right)$ is equal to
 \begin{equation}
 \mathds{B}^n       \rightarrow      \mathds{B}^n$       such      that
 $f\left(x_1,x_2,\dots,x_n\right)$ is equal to
 \begin{equation}


@@ -614,9 +628,12 @@ if  and only  if,  for any  pair  of disjoint  open  sets $U$,$V  \neq
 \emptyset$, we can find some $n_0  \in \mathds{N}$ such that  for any $n$, 
 $n\geq n_0$, we have $f^n(U) \cap V \neq \emptyset$.
 \end{definition}
 \emptyset$, we can find some $n_0  \in \mathds{N}$ such that  for any $n$, 
 $n\geq n_0$, we have $f^n(U) \cap V \neq \emptyset$.
 \end{definition}

+\JFC{Donner un sens à ces definitions}
+

 
 

-As  proven in Ref.~\cite{gfb10:ip},  chaotic iterations  are expansive
-and  topologically mixing when  $f$ is  the vectorial  negation $f_0$.
+It has been proven in Ref.~\cite{gfb10:ip},  that chaotic iterations
+are expansive and  topologically mixing when  $f$ is  the
+vectorial  negation $f_0$.

 Consequently,  these  properties are  inherited  by the  CI-MLP($f_0$)
 recurrent neural network previously presented, which induce a greater
 unpredictability.  Any  difference on the  initial value of  the input
 Consequently,  these  properties are  inherited  by the  CI-MLP($f_0$)
 recurrent neural network previously presented, which induce a greater
 unpredictability.  Any  difference on the  initial value of  the input


@@ -624,8 +641,10 @@ layer is  in particular  magnified up to  be equal to  the expansivity
 constant.
 
 Let us then focus on the consequences for  a neural  network to  be chaotic
 constant.
 
 Let us then focus on the consequences for  a neural  network to  be chaotic

-according  to  Devaney's definition.  First  of  all, the  topological
-transitivity property implies indecomposability.
+according  to  Devaney's definition.  Intuitively, the  topological
+transitivity property implies indecomposability, which is formally defined 
+as follows:
+

 
 \begin{definition} \label{def10}
 A   dynamical   system   $\left(   \mathcal{X},  f\right)$   is   
 
 \begin{definition} \label{def10}
 A   dynamical   system   $\left(   \mathcal{X},  f\right)$   is   


@@ -784,7 +803,9 @@ such functions into a model amenable to be learned by an ANN.
   
 This  section  presents how  (not)  chaotic  iterations  of $G_f$  are
 translated  into  another  model  more  suited  to  artificial  neural
   
 This  section  presents how  (not)  chaotic  iterations  of $G_f$  are
 translated  into  another  model  more  suited  to  artificial  neural

-networks.  Formally, input and output vectors are pairs~$((S^t)^{t \in
+networks.  
+\JFC{détailler le more suited}
+Formally, input and output vectors are pairs~$((S^t)^{t \in

 \Nats},x)$ and $\left(\sigma((S^t)^{t \in \Nats}),F_{f}(S^0,x)\right)$
 as defined in~Eq.~(\ref{eq:Gf}).
 
 \Nats},x)$ and $\left(\sigma((S^t)^{t \in \Nats}),F_{f}(S^0,x)\right)$
 as defined in~Eq.~(\ref{eq:Gf}).
 


@@ -965,7 +986,7 @@ configuration is always expressed as  a natural number, whereas in the
 first one  the number  of inputs follows  the increase of  the boolean
 vectors coding configurations. In this latter case, the coding gives a
 finer information on configuration evolution.
 first one  the number  of inputs follows  the increase of  the boolean
 vectors coding configurations. In this latter case, the coding gives a
 finer information on configuration evolution.

-
+\JFC{Je n'ai pas compris le paragraphe precedent. Devrait être repris}

 \begin{table}[b]
 \caption{Prediction success rates for configurations expressed with Gray code}
 \label{tab2}
 \begin{table}[b]
 \caption{Prediction success rates for configurations expressed with Gray code}
 \label{tab2}