Mathematical Neuroscience

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9780124114685: Mathematical Neuroscience

Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables - such as synaptic or firing rate activity in populations of neurons - and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience. It combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain. It introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling.

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Review:

"Brzychczy,. Krak w and Poznanski.present methods of nonlinear functional analysis and their application to neuroscience. This is the first book, they say, to compile methods of nonlinear analysis to better understand the dynamics associated with solutions of infinite systems of equations. It would be suitable as a textbook for a one-semester graduate course in mathematical neuroscience for neuroscience students seeking tools and mathematics students looking for applications."--Reference & Research Book News, December 2013

About the Author:

Roman R. Poznanski develops theories in neuroscience with mathematics. He recently co-authored the book, "Mathematical Neuroscience." His passion remains to pinpoint and crack open complex problems holding back our understanding of how the brain works. He is adamant, that a new Einstein in neuroscience will one day produce a complete theory of the brain, not as a hodgepodge of models, but as an integrative theory expressed in terms of modern mathematics. He has over 20 years experience as a theoretician and modeller in the neurosciences. He has edited several contemporary books: Biophysical Neural Networks (2001) and Modeling in the Neurosciences (1999, 2005). He is currently a visiting professor at the Rockefeller University.

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Book Description Elsevier Science Publishing Co Inc, United States, 2013. Hardback. Book Condition: New. 236 x 194 mm. Language: English . Brand New Book. Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables - such as synaptic or firing rate activity in populations of neurons - and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience. It combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain. It introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling. Bookseller Inventory # AA59780124114685

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Book Description Elsevier Science Publishing Co Inc. Hardback. Book Condition: new. BRAND NEW, Mathematical Neuroscience, Stanislaw Brzychczy, Roman R. Poznanski, Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables - such as synaptic or firing rate activity in populations of neurons - and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience. It combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain. It introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling. Bookseller Inventory # B9780124114685

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Book Description Elsevier Science Publishing Co Inc, United States, 2013. Hardback. Book Condition: New. 236 x 194 mm. Language: English . Brand New Book. Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables-such as synaptic or firing rate activity in populations of neurons -and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. Bookseller Inventory # AA59780124114685

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Book Description Hardback. Book Condition: New. Not Signed; Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techni. book. Bookseller Inventory # ria9780124114685_rkm

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