Theoretical Neuroscience

Author: Peter Dayan
Publisher: Mit Press
ISBN: 0262541858
Release Date: 2005
Genre: Medical

The construction and analysis of mathematical and computational models of neural systems.

Fundamentals of Computational Neuroscience

Author: Thomas Trappenberg
Publisher: Oxford University Press
ISBN: 9780199568413
Release Date: 2010
Genre: Mathematics

The new edition of Fundamentals of Computational Neuroscience build on the success and strengths of the first edition. It introduces the theoretical foundations of neuroscience with a focus on the nature of information processing in the brain. The book covers the introduction and motivation of simplified models of neurons that are suitable for exploring information processing in large brain-like networks. Additionally, it introduces several fundamental networkarchitectures and discusses their relevance for information processing in the brain, giving some examples of models of higher-order cognitive functions to demonstrate the advanced insight that can begained with such studies.

Dynamical Systems in Neuroscience

Author: Eugene M. Izhikevich
Publisher: MIT Press
ISBN: 9780262090438
Release Date: 2007
Genre: Medical

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 learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.

Computational Neuroscience

Author: Hanspeter Mallot
Publisher: Springer Science & Business Media
ISBN: 9783319008615
Release Date: 2013-05-23
Genre: Computers

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 networks. The required mathematical concepts are kept as intuitive and simple as possible throughout the book, making it fully accessible to readers who are less familiar with mathematics. Overall, Computational Neuroscience - A First Course represents an essential reference guide for all neuroscientists who use computational methods in their daily work, as well as for any theoretical scientist approaching the field of computational neuroscience.

Principles of Computational Modelling in Neuroscience

Author: David Sterratt
Publisher: Cambridge University Press
ISBN: 9781139500791
Release Date: 2011-06-30
Genre: Medical

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 the effects of neuronal morphology, synapses, ion channels and intracellular signalling. The principle of abstraction is explained through chapters on simplifying models, and how simplified models can be used in networks. This theme is continued in a final chapter on modelling the development of the nervous system. Requiring an elementary background in neuroscience and some high school mathematics, this textbook is an ideal basis for a course on computational neuroscience.

Biophysics of Computation

Author: Christof Koch
Publisher: Oxford University Press
ISBN: 9780195181999
Release Date: 2004-10-28
Genre: Medical

Neural network research often builds on the fiction that neurons are simple linear threshold units, completely neglecting the highly dynamic and complex nature of synapses, dendrites, and voltage-dependent ionic currents. Biophysics of Computation: Information Processing in Single Neurons challenges this notion, using richly detailed experimental and theoretical findings from cellular biophysics to explain the repertoire of computational functions available to single neurons. The author shows how individual nerve cells can multiply, integrate, or delay synaptic inputs and how information can be encoded in the voltage across the membrane, in the intracellular calcium concentration, or in the timing of individual spikes.Key topics covered include the linear cable equation; cable theory as applied to passive dendritic trees and dendritic spines; chemical and electrical synapses and how to treat them from a computational point of view; nonlinear interactions of synaptic input in passive and active dendritic trees; the Hodgkin-Huxley model of action potential generation and propagation; phase space analysis; linking stochastic ionic channels to membrane-dependent currents; calcium and potassium currents and their role in information processing; the role of diffusion, buffering and binding of calcium, and other messenger systems in information processing and storage; short- and long-term models of synaptic plasticity; simplified models of single cells; stochastic aspects of neuronal firing; the nature of the neuronal code; and unconventional models of sub-cellular computation.Biophysics of Computation: Information Processing in Single Neurons serves as an ideal text for advanced undergraduate and graduate courses in cellular biophysics, computational neuroscience, and neural networks, and will appeal to students and professionals in neuroscience, electrical and computer engineering, and physics.

Neural Engineering

Author: Chris Eliasmith
Publisher: MIT Press
ISBN: 0262550601
Release Date: 2004-08
Genre: Medical

A synthesis of current approaches to adapting engineering tools to the study of neurobiological systems.

Mathematics for Neuroscientists

Author: Fabrizio Gabbiani
Publisher: Academic Press
ISBN: 9780128019061
Release Date: 2017-03-21
Genre: Science

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 on extracellular potentials, motion detection and neurovascular coupling Revised selection of exercises with solutions More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts

Neural Control Engineering

Author: Steven J. Schiff
Publisher: MIT Press
ISBN: 9780262015370
Release Date: 2012
Genre: Medical

How powerful new methods in nonlinear control engineering can be applied to neuroscience, from fundamental model formulation to advanced medical applications.

Mathematical Foundations of Neuroscience

Author: G. Bard Ermentrout
Publisher: Springer Science & Business Media
ISBN: 9780387877082
Release Date: 2010-07-01
Genre: Mathematics

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 and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.

From Computer to Brain

Author: William W. Lytton
Publisher: Springer Science & Business Media
ISBN: 0387955267
Release Date: 2002-10-01
Genre: Computers

Teaching computational neuroscience as an integrated discipline requires that both groups be brought forward onto common ground. This book does this by making ancillary material available and by providing basic explanations without the unnecessary details. The book is ideal for students taking a computational neuroscience course and also to anyone with an interest in the uses of the computer in modeling the nervous system. A companion website includes extensive interactive resources.

Mathematical Neuroscience

Author: Stanislaw Brzychczy
Publisher: Academic Press
ISBN: 9780124104822
Release Date: 2013-08-16
Genre: Mathematics

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

The Computational Brain

Author: Patricia S. Churchland
Publisher: MIT Press
ISBN: 9780262339667
Release Date: 2016-10-28
Genre: Science

Before The Computational Brain was published in 1992, conceptual frameworks for brain function were based on the behavior of single neurons, applied globally. In The Computational Brain, Patricia Churchland and Terrence Sejnowski developed a different conceptual framework, based on large populations of neurons. They did this by showing that patterns of activities among the units in trained artificial neural network models had properties that resembled those recorded from populations of neurons recorded one at a time. It is one of the first books to bring together computational concepts and behavioral data within a neurobiological framework. Aimed at a broad audience of neuroscientists, computer scientists, cognitive scientists, and philosophers, The Computational Brain is written for both expert and novice. This anniversary edition offers a new preface by the authors that puts the book in the context of current research.This approach influenced a generation of researchers. Even today, when neuroscientists can routinely record from hundreds of neurons using optics rather than electricity, and the 2013 White House BRAIN initiative heralded a new era in innovative neurotechnologies, the main message of The Computational Brain is still relevant.

Tutorial on Neural Systems Modeling

Author: Thomas J. Anastasio
Publisher: Sinauer Associates Incorporated
ISBN: 0878933395
Release Date: 2010
Genre: Medical

For students of neuroscience and cognitive science who wish to explore the functioning of the brain further, but lack an extensive background in computer programming or maths, this new book makes neural systems modelling truly accessible. Short, simple MATLAB computer programs give readers all the experience necessary to run their own simulations.