Neural Networks and Qualitative Physics
A Viability Approach
By (author) Jean-Pierre Aubin
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Neural Networks and Qualitative Physics by Jean-Pierre Aubin
Book DescriptionThis book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a 'learning algorithm' of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints. This book will be of value to anyone with an interest in neural networks and cognitive systems.
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Book DetailsISBN: 9780521445320
(228mm x 152mm x 21mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 29-Mar-1996
Country of Publication: United Kingdom
Books By Author Jean-Pierre Aubin
Neural Networks and Qualitative Physics, Paperback (August 2011)
This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics.
Mathematical Methods of Game and Economic Theory, Paperback (February 2008)
This text begins with optimization theory and convex analysis, followed by topics in game theory and mathematical economics, and concluding with an introduction to nonlinear analysis and control theory. 1982 edition.
Approximation of Elliptic Boundary-Value Problems, Paperback (March 2007)
A marriage of the finite-differences method with variational methods for solving boundary-value problems, this self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis.
Applied Nonlinear Analysis, Paperback (December 2006)» View all books by Jean-Pierre Aubin
This introductory text offers simple presentations of the fundamentals of nonlinear analysis, with direct proofs and clear applications. Topics include smooth/nonsmooth functions, convex/nonconvex variational problems, economics, and mechanics. 1984 edition.
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