From 8c453843ba5ef7f01a7a202686584c36cc7201c5 Mon Sep 17 00:00:00 2001 From: Michel Salomon Date: Sat, 8 Oct 2011 15:44:17 +0200 Subject: [PATCH] Conclusion raccourcie et biblio corrigee --- chaos-paper.bib | 7 +++---- main.tex | 20 ++++++++------------ 2 files changed, 11 insertions(+), 16 deletions(-) diff --git a/chaos-paper.bib b/chaos-paper.bib index 120e1fe..bdc8bb1 100644 --- a/chaos-paper.bib +++ b/chaos-paper.bib @@ -285,7 +285,7 @@ doi={10.1109/IJCNN.2008.4634274} } @INPROCEEDINGS{guyeux10ter, - author = {Bahi, Jacques and Guyeux, Christophe}, + author = {Bahi, Jacques M. and Guyeux, Christophe}, title = {A new chaos-based watermarking algorithm}, booktitle = {SECRYPT'10, International Conference on Security and Cryptography}, @@ -348,7 +348,7 @@ and Cryptography}, } @INPROCEEDINGS{gfb10:ip, - author = {Guyeux, Christophe and Friot, Nicolas and Bahi, Jacques}, + author = {Guyeux, Christophe and Friot, Nicolas and Bahi, Jacques M.}, title = {Chaotic iterations versus Spread-spectrum: chaos and stego security}, booktitle = {IIH-MSP'10, 6-th International Conference on Intelligent Information Hiding and Multimedia Signal Processing}, @@ -414,10 +414,9 @@ inhal = {no}, domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, equipe = {and}, classement = {ACTI}, -author = {Bahi, Jacques and Guyeux, Christophe and Salomon, Michel}, +author = {Bahi, Jacques M. and Guyeux, Christophe and Salomon, Michel}, title = {Building a Chaotic Proven Neural Network}, booktitle = {ICCANS 2011, IEEE Int. Conf. on Computer Applications and Network Security}, -pages = {***--***}, address = {Maldives, Maldives}, month = may, year = 2011, 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{} -- 2.39.5