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Artificial Neural Networks take a loose inspiration from the brain to perform classification and signal processing tasks. They are arrays of simple identical cells, the neurons, which are nonlinear systems: this is the point of view under which they are approached in this book, that will be devoted to two models whose neurons are only locally connected.
The metdods used to study such arrays reflect the inter-disciplinarity of fields in which they are infolved (mathematics, physics, electronics, signal processing, biology). The equivalent level of maturity of the research on this topic in almost all these disciplines makes a sharing of the techniques fruitful and a scattering of the progresses among them attractive. The first model is the Cellular Network, which is an array of dynamical systems, performing nonlinear preprocessing operations (mainly on images) and well suited for an analog VLSI implementation thanks to the local character of the connections. Two modes of propagation of the information signal, intrdoduced as initial condition of the system, are possible: local diffusion and global propagation, from which many fundamental properties are deduced.
The second ntwork is the Kohonen Self-Organizing Map. The aconvergence of this learning algoritm is linked to the properties of global propagation and local diffusion.
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The methods used to study such arrays reflect the inter-disciplinarity of fields in which they are involved (mathematics, physics, electronics, signal processing, biology). The equivalent level of maturity of the research on this topic in almost all these disciplines makes a cross-fertilization of the techniques and a scattering of the progress achieved among them attractive. The first model is the Cellular Neural Network, which is an array of dynamical systems, performing nonlinear preprocessing operations (mainly on images) and well suited for an analog VLSI implementation thanks to the local character of the connections. Two modes of propagation of the information signal, introduced as initial condition of the system, are possible: local diffusion and global propagation, from which many fundamental properties are deduced. The second network is the Kohonen Self-Organizing Map. The convergence of this learning algorithm is linked to the properties of global propagation and local diffusion.
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Préface - introduction - Symmetric nearest-neighbor coupling - Anti-symmetric nearest-neighbor coupling - One-sided nearest-neighbor coupling - Local diffusion - Global propagation - Isotropic two-dimensional coupling - Self-organization - Conclusion.
"Highly original, deep, and profound results. This work represents a major scientific achievement that will no doubt become a classic reference on the foundation of locally-coupled nonlinear networks"
. Leon O. Chua, University of California, Berkeley..
"... Possible wide-spread interdiciplinar applications, timeliness of the subject, important and original scientific and engineering contributions presented in the work, excellent quality of mathematical contributions, very good, clear and logical presentation of the results .."
. Prof. M. J. Ogorzalek, University of Mining and Metallurgy, Krakow
"Le livre est passionnant et il contient des chapitres qui sont de nature à intéresser le biologiste théoricien. Non seulement celui qui étudie des modèles cérébraux, mais aussi celui qui analyse l'emergence des formes sur les pelages de mammifères (Turing, Murray...). L'ouvrage peut être utilisé comme une introduction aux systèmes autoorganisés et aux réseaux neuronaux, mais il ouvre aussi très vite sur des pistes conduisant à des recherches avancées.
D. Lambert "
Revue des Questions Scientifiques
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