Alain Yger's Books

Multidimensional Residue Theory and Applications

By: Alekos Vidras,Alain Yger

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Multidimensional Residue Theory and Applications

By: Alekos Vidras,Alain Yger

Residue theory is an active area of complex analysis with connections and applications to fields as diverse as partial differential and integral equations, computer algebra, arithmetic or diophantine geometry, and mathematical physics. Multidimensional Residue Theory and Applications defines and studies multidimensional residues via analytic continuation for holomorphic bundle-valued current maps. This point of view offers versatility and flexibility to the tools and constructions proposed, allowing these residues to be defined and studied outside the classical case of complete intersection. The book goes on to show how these residues are algebraic in nature, and how they relate and apply to a wide range of situations, most notably to membership problems, such as the Briançon–Skoda theorem and Hilbert's Nullstellensatz, to arithmetic intersection theory and to tropical geometry. This book will supersede the existing literature in this area, which dates back more than three decades. It will be appreciated by mathematicians and graduate students in multivariate complex analysis. But thanks to the gentle treatment of the one-dimensional case in Chapter 1 and the rich background material in the appendices, it may also be read by specialists in arithmetic, diophantine, or tropical geometry, as well as in mathematical physics or computer algebra.

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Page Count

556

Publisher

American Mathematical Society

Published Date

ISBN 10

1470471124

ISBN 13

9781470471125

Thalamocortical Assemblies

Sleep Spindles, Slow Waves and Epileptic Discharges

By: Alain Destexhe,Terrence Sejknowski

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Thalamocortical Assemblies

Sleep Spindles, Slow Waves and Epileptic Discharges

By: Alain Destexhe,Terrence Sejknowski

During sleep, the mammalian brain generates an orderly progression of low frequency oscillations as the brain moves from sleep onset into deep sleep. This book explores the underlying neural mechanisms involved in generating these oscillations through interacting neural assemblies in the thalamus and the cortex. Sleep spindles are involved in the consolidation of experiences in long-term memory during sleep. Written by two leading experts in the field, this book integrates the properties of ion channels, synaptic interactions, and intrinsic cellular mechanisms into biophysical models of neural oscillations in local circuits and distributed networks. In particular, the book focuses on sleep spindles and how they are highjacked by epileptic seizures Reissued in paperback after being unavailable for many years, this revised edition of Thalamocortical Assemblies includes updates to each chapter, highlighting developments since its first publication. The book will be valuable to neuroscientists, neurobiologists, physiologists and computational researchers interested in sleep and memory processes.

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Page Count

510

Publisher

Oxford University Press

Published Date

ISBN 10

019886499X

ISBN 13

9780198864998

Neuronal Noise

By: Alain Destexhe,Michelle Rudolph-Lilith

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Neuronal Noise

By: Alain Destexhe,Michelle Rudolph-Lilith

Neuronal Noise combines experimental, theoretical and computational results to show how noise is inherent to neuronal activity, and how noise can be important for neuronal computations. The book covers many aspects of noise in neurons, with an emphasis on the largest source of noise: synaptic noise. It provides students and young researchers with an overview of the important methods and concepts that have emerged from research in this area. It also provides the specialist with a summary of the large body of sometimes contrasting experimental data, and different theories proposed to explore the computational power that various forms of "noise" can confer to neurons.

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Page Count

468

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387790209

ISBN 13

9780387790206

Book's by Alain Yger

Multidimensional Residue Theory and Applications

Multidimensional Residue Theory and Applications

Thalamocortical Assemblies

Thalamocortical Assemblies

Neuronal Noise

Neuronal Noise

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