{"product_id":"neural-networks-and-qualitative-physics-jean-pierre-aubin-9781107402843","title":"Neural Networks and Qualitative Physics: A Viability Approach","description":"This 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Jean-Pierre Aubin\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1107402840\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781107402843\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Cambridge University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/11\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 302\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.89lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.63d","brand":"Jean-Pierre Aubin","offers":[{"title":"Paperback","offer_id":46250458022143,"sku":"9781107402843","price":72.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_f5a95c3e-ada0-466e-a60a-df1cab394b8c.jpg?v=1729600380","url":"https:\/\/www.whiterainbookhouse.com\/products\/neural-networks-and-qualitative-physics-jean-pierre-aubin-9781107402843","provider":"WR Book House","version":"1.0","type":"link"}