Mathematical Neuroscience

Book Mathematical Neuroscience Cover

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  • Publisher : Academic Press
  • Release : 16 August 2013
  • ISBN : 9780124104822
  • Page : 208 pages
  • Rating : 4.5/5 from 103 voters

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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 Combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain Introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling

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Mathematical Neuroscience

Mathematical Neuroscience
  • Author : Stanislaw Brzychczy,Roman R. Poznanski
  • Publisher : Academic Press
  • Release Date : 2013-08-16
  • ISBN : 9780124104822
GET THIS BOOKMathematical 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

Mathematics for Neuroscientists

Mathematics for Neuroscientists
  • Author : Fabrizio Gabbiani,Steven James Cox
  • Publisher : Academic Press
  • Release Date : 2017-03-21
  • ISBN : 9780128019061
GET THIS BOOKMathematics for Neuroscientists

Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory. Fully revised material and corrected text Additional chapters

Mathematical Foundations of Neuroscience

Mathematical Foundations of Neuroscience
  • Author : G. Bard Ermentrout,David H. Terman
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-07-01
  • ISBN : 9780387877082
GET THIS BOOKMathematical Foundations of Neuroscience

This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve

Mathematical and Theoretical Neuroscience

Mathematical and Theoretical Neuroscience
  • Author : Giovanni Naldi,Thierry Nieus
  • Publisher : Springer
  • Release Date : 2018-03-20
  • ISBN : 9783319682976
GET THIS BOOKMathematical and Theoretical Neuroscience

This volume gathers contributions from theoretical, experimental and computational researchers who are working on various topics in theoretical/computational/mathematical neuroscience. The focus is on mathematical modeling, analytical and numerical topics, and statistical analysis in neuroscience with applications. The following subjects are considered: mathematical modelling in Neuroscience, analytical and numerical topics; statistical analysis in Neuroscience; Neural Networks; Theoretical Neuroscience. The book is addressed to researchers involved in mathematical models applied to neuroscience.

An Introduction to Modeling Neuronal Dynamics

An Introduction to Modeling Neuronal Dynamics
  • Author : Christoph Börgers
  • Publisher : Springer
  • Release Date : 2017-04-17
  • ISBN : 9783319511719
GET THIS BOOKAn Introduction to Modeling Neuronal Dynamics

This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology. Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins

Dynamical Systems in Neuroscience

Dynamical Systems in Neuroscience
  • Author : Eugene M. Izhikevich
  • Publisher : MIT Press
  • Release Date : 2010-01-22
  • ISBN : 9780262514200
GET THIS BOOKDynamical Systems in Neuroscience

Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to

Mathematical Foundations of Neuroscience

Mathematical Foundations of Neuroscience
  • Author : G. Bard Ermentrout,David H. Terman
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-07-08
  • ISBN : 9780387877075
GET THIS BOOKMathematical Foundations of Neuroscience

Arising from several courses taught by the authors, this book provides a needed overview illustrating how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience.

Neuroscience

Neuroscience
  • Author : Alwyn Scott
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-12-14
  • ISBN : 9780387224633
GET THIS BOOKNeuroscience

This book will be of interest to anyone who wishes to know what role mathematics can play in attempting to comprehend the dynamics of the human brain. It also aims to serve as a general introduction to neuromathematics. The book gives the reader a qualitative understanding and working knowledge of useful mathematical applications to the field of neuroscience. The book is readable by those who have little knowledge of mathematics for neuroscience but are committed to begin acquiring such knowledge.

Network Neuroscience

Network Neuroscience
  • Author : Flavio Fröhlich
  • Publisher : Academic Press
  • Release Date : 2016-09-20
  • ISBN : 9780128015865
GET THIS BOOKNetwork Neuroscience

Studying brain networks has become a truly interdisciplinary endeavor, attracting students and seasoned researchers alike from a wide variety of academic backgrounds. What has been lacking is an introductory textbook that brings together the different fields and provides a gentle introduction to the major concepts and findings in the emerging field of network neuroscience. Network Neuroscience is a one-stop-shop that is of equal use to the neurobiologist, who is interested in understanding the quantitative methods employed in network neuroscience, and

Theoretical Neuroscience

Theoretical Neuroscience
  • Author : Peter Dayan,Laurence F. Abbott
  • Publisher : MIT Press
  • Release Date : 2005-08-12
  • ISBN : 9780262541855
GET THIS BOOKTheoretical Neuroscience

Theoretical neuroscience provides a quantitative basis for describing what nervous systems do, determining how they function, and uncovering the general principles by which they operate. This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory. The book is divided into three parts. Part I discusses the relationship between sensory stimuli and neural responses, focusing on the representation of information by the spiking

Computational Neuroscience

Computational Neuroscience
  • Author : Hanspeter A Mallot
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-05-23
  • ISBN : 9783319008615
GET THIS BOOKComputational Neuroscience

Computational Neuroscience - A First Course provides an essential introduction to computational neuroscience and equips readers with a fundamental understanding of modeling the nervous system at the membrane, cellular, and network level. The book, which grew out of a lecture series held regularly for more than ten years to graduate students in neuroscience with backgrounds in biology, psychology and medicine, takes its readers on a journey through three fundamental domains of computational neuroscience: membrane biophysics, systems theory and artificial neural

Tutorials in Mathematical Biosciences I

Tutorials in Mathematical Biosciences I
  • Author : Alla Borisyuk,G. Bard Ermentrout,Avner Friedman,David H. Terman
  • Publisher : Springer Science & Business Media
  • Release Date : 2005-02-18
  • ISBN : 3540238581
GET THIS BOOKTutorials in Mathematical Biosciences I

This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic

Mathematics for Neuroscientists

Mathematics for Neuroscientists
  • Author : Fabrizio Gabbiani,Steven James Cox
  • Publisher : Academic Press
  • Release Date : 2010-09-16
  • ISBN : 0080890490
GET THIS BOOKMathematics for Neuroscientists

Virtually all scientific problems in neuroscience require mathematical analysis, and all neuroscientists are increasingly required to have a significant understanding of mathematical methods. There is currently no comprehensive, integrated introductory book on the use of mathematics in neuroscience; existing books either concentrate solely on theoretical modeling or discuss mathematical concepts for the treatment of very specific problems. This book fills this need by systematically introducing mathematical and computational tools in precisely the contexts that first established their importance for neuroscience.

An Introduction to Mathematical Cognition

An Introduction to Mathematical Cognition
  • Author : Camilla Gilmore,Silke M. Göbel,Matthew Inglis
  • Publisher : Routledge
  • Release Date : 2018-06-13
  • ISBN : 9781317410102
GET THIS BOOKAn Introduction to Mathematical Cognition

The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems,

Models of the Mind

Models of the Mind
  • Author : Grace Lindsay
  • Publisher : Bloomsbury Publishing
  • Release Date : 2021-03-04
  • ISBN : 9781472966452
GET THIS BOOKModels of the Mind

The human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate – and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it.