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Mathematical Neuroscience

Mathematical Neuroscience
  • Author : Stanislaw Brzychczy
  • Publsiher : Academic Press
  • Release : 16 August 2013
  • ISBN : 0124104827
  • Pages : 208 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKMathematical Neuroscience

Summary:
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


Mathematical Neuroscience

Mathematical Neuroscience
  • Author : Stanislaw Brzychczy,Roman R. Poznanski
  • Publisher : Academic Press
  • Release : 16 August 2013
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

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Mathematics for Neuroscientists

Mathematics for Neuroscientists
  • Author : Fabrizio Gabbiani,Steven James Cox
  • Publisher : Academic Press
  • Release : 21 March 2017
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

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Mathematical Foundations of Neuroscience

Mathematical Foundations of Neuroscience
  • Author : G. Bard Ermentrout,David H. Terman
  • Publisher : Springer Science & Business Media
  • Release : 01 July 2010
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

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Mathematical and Theoretical Neuroscience

Mathematical and Theoretical Neuroscience
  • Author : Giovanni Naldi,Thierry Nieus
  • Publisher : Springer
  • Release : 20 March 2018
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.

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Neuroscience

Neuroscience
  • Author : Alwyn Scott
  • Publisher : Springer Science & Business Media
  • Release : 14 December 2007
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.

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Network Neuroscience

Network Neuroscience
  • Author : Flavio Fröhlich
  • Publisher : Academic Press
  • Release : 20 September 2016
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

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Computational Neuroscience

Computational Neuroscience
  • Author : Hanspeter A Mallot
  • Publisher : Springer Science & Business Media
  • Release : 23 May 2013
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

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Theoretical Neuroscience

Theoretical Neuroscience
  • Author : Peter Dayan,Laurence F. Abbott
  • Publisher : MIT Press
  • Release : 12 August 2005
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

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An Introduction to Modeling Neuronal Dynamics

An Introduction to Modeling Neuronal Dynamics
  • Author : Christoph Börgers
  • Publisher : Springer
  • Release : 17 April 2017
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

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Mathematical Foundations of Neuroscience

Mathematical Foundations of Neuroscience
  • Author : G. Bard Ermentrout,David H. Terman
  • Publisher : Springer Science & Business Media
  • Release : 08 July 2010
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.

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Principles of Computational Modelling in Neuroscience

Principles of Computational Modelling in Neuroscience
  • Author : David Sterratt,Bruce Graham,Andrew Gillies,David Willshaw
  • Publisher : Cambridge University Press
  • Release : 30 June 2011
GET THIS BOOKPrinciples of Computational Modelling in Neuroscience

The nervous system is made up of a large number of interacting elements. To understand how such a complex system functions requires the construction and analysis of computational models at many different levels. This book provides a step-by-step account of how to model the neuron and neural circuitry to understand the nervous system at all levels, from ion channels to networks. Starting with a simple model of the neuron as an electrical circuit, gradually more details are added to include

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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 : 18 February 2005
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

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Dynamical Systems in Neuroscience

Dynamical Systems in Neuroscience
  • Author : Eugene M. Izhikevich
  • Publisher : MIT Press
  • Release : 22 January 2010
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

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Waves in Neural Media

Waves in Neural Media
  • Author : Paul C. Bressloff
  • Publisher : Springer Science & Business Media
  • Release : 17 October 2013
GET THIS BOOKWaves in Neural Media

​Waves in Neural Media: From Single Neurons to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The work provides a pedagogical account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. These include regular and singular perturbation methods, weakly nonlinear analysis, Evans functions and wave stability, homogenization theory and averaging, and

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Stochastic Methods in Neuroscience

Stochastic Methods in Neuroscience
  • Author : Carlo Laing,Gabriel J Lord
  • Publisher : Oxford University Press
  • Release : 20 August 2022
GET THIS BOOKStochastic Methods in Neuroscience

Computational or mathematical neuroscience is a research area currently of great interest, due to, amongst other factors, rapid increases in computing power, increases in the ability to record large amounts of neurophysiological data, and a realisation amongst both neuroscientists and mathematicians that each can benefit from collaborating with the other. This text will concentrate on the intersection between stochastic dynamics and neuroscience, presenting aseries of self-contained chapters on major aspects of noise and neuroscience, each written by an expert in

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