Mathematical Neuroscience Book

Mathematical Neuroscience


  • Author : Stanislaw Brzychczy
  • Publisher : Academic Press
  • Release Date : 2013-08-16
  • Genre: Mathematics
  • Pages : 208
  • ISBN 10 : 9780124104822

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Mathematical Neuroscience Excerpt :

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

Mathematics for Neuroscientists Book

Mathematics for Neuroscientists


  • Author : Fabrizio Gabbiani
  • Publisher : Academic Press
  • Release Date : 2017-03-21
  • Genre: Science
  • Pages : 628
  • ISBN 10 : 9780128019061

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Mathematics for Neuroscientists Excerpt :

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

Mathematical Foundations of Neuroscience Book

Mathematical Foundations of Neuroscience


  • Author : G. Bard Ermentrout
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-07-01
  • Genre: Mathematics
  • Pages : 422
  • ISBN 10 : 9780387877082

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Mathematical Foundations of Neuroscience Excerpt :

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.

Mathematical and Theoretical Neuroscience Book

Mathematical and Theoretical Neuroscience


  • Author : Giovanni Naldi
  • Publisher : Springer
  • Release Date : 2018-03-20
  • Genre: Mathematics
  • Pages : 253
  • ISBN 10 : 9783319682976

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Mathematical and Theoretical Neuroscience Excerpt :

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.

Theoretical Neuroscience Book
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Theoretical Neuroscience


  • Author : Peter Dayan
  • Publisher : MIT Press
  • Release Date : 2005-08-12
  • Genre: Medical
  • Pages : 477
  • ISBN 10 : 9780262541855

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Theoretical Neuroscience Excerpt :

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 activity of neurons. Part II discusses the modeling of neurons and neural circuits on the basis of cellular and synaptic biophysics. Part III analyzes the role of plasticity in development and learning. An appendix covers the mathematical methods used, and exercises are available on the book's Web site.

Neuroscience Book

Neuroscience


  • Author : Alwyn Scott
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-12-14
  • Genre: Science
  • Pages : 352
  • ISBN 10 : 9780387224633

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Neuroscience Excerpt :

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.

Mathematical Foundations of Neuroscience Book

Mathematical Foundations of Neuroscience


  • Author : G. Bard Ermentrout
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-07-08
  • Genre: Mathematics
  • Pages : 434
  • ISBN 10 : 9780387877075

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Mathematical Foundations of Neuroscience Excerpt :

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.

Computational Neuroscience Book

Computational Neuroscience


  • Author : Hanspeter A Mallot
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-05-23
  • Genre: Technology & Engineering
  • Pages : 135
  • ISBN 10 : 9783319008615

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Computational Neuroscience Excerpt :

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.

An Introduction to Modeling Neuronal Dynamics Book

An Introduction to Modeling Neuronal Dynamics


  • Author : Christoph Börgers
  • Publisher : Springer
  • Release Date : 2017-04-17
  • Genre: Mathematics
  • Pages : 457
  • ISBN 10 : 9783319511719

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An Introduction to Modeling Neuronal Dynamics Excerpt :

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 and functions of population rhythms in neuronal networks, and models of synaptic plasticity. An extensive online collection of Matlab programs generating the figures accompanies the book.

Fundamentals of Computational Neuroscience Book

Fundamentals of Computational Neuroscience


  • Author : Thomas Trappenberg
  • Publisher : Oxford University Press
  • Release Date : 2010
  • Genre: Mathematics
  • Pages : 417
  • ISBN 10 : 9780199568413

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Fundamentals of Computational Neuroscience Excerpt :

The new edition of Fundamentals of Computational Neuroscience build on the success and strengths of the first edition. Completely redesigned and revised, it introduces the theoretical foundations of neuroscience with a focus on the nature of information processing in the brain.

Dynamical Systems in Neuroscience Book

Dynamical Systems in Neuroscience


  • Author : Eugene M. Izhikevich
  • Publisher : MIT Press
  • Release Date : 2010-01-22
  • Genre: Medical
  • Pages : 459
  • ISBN 10 : 9780262514200

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Dynamical Systems in Neuroscience Excerpt :

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 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

Tutorials in Mathematical Biosciences I Book

Tutorials in Mathematical Biosciences I


  • Author : Alla Borisyuk
  • Publisher : Springer Science & Business Media
  • Release Date : 2005-02-18
  • Genre: Mathematics
  • Pages : 184
  • ISBN 10 : 3540238581

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Tutorials in Mathematical Biosciences I Excerpt :

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 connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.

Mathematics for Neuroscientists Book

Mathematics for Neuroscientists


  • Author : Fabrizio Gabbiani
  • Publisher : Academic Press
  • Release Date : 2010-09-16
  • Genre: Psychology
  • Pages : 498
  • ISBN 10 : 0080890490

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Mathematics for Neuroscientists Excerpt :

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. All mathematical concepts will be introduced from the simple to complex using the most widely used computing environment, Matlab. This book will provide a grounded introduction to the fundamental concepts of mathematics, neuroscience and their combined use, thus providing the reader with a springboard to cutting-edge research topics and fostering a tighter integration of mathematics and neuroscience for future generations of students. A very didactic and systematic introduction to mathematical concepts of importance for the analysis of data and the formulation of concepts based on experimental data in neuroscience Provides introductions to linear algebra, ordinary and partial differential equations, Fourier transforms, probabilities and stochastic processes Introduces numerical methods used to implement algorithms related to each mathematical concept Illustrates numerical methods by applying them to specific topics in neuroscience, including Hodgkin-Huxley equations, probabilities to describe stochastic release, stochastic processes to describe noise in neurons, Fourier transforms to describe the receptive fields of visual neurons Allows the mathematical novice to analyze their results in more sophisticated ways, and consider them in a broader theoretical framework

Computational Neuroscience Book

Computational Neuroscience


  • Author : Jianfeng Feng
  • Publisher : CRC Press
  • Release Date : 2003-10-20
  • Genre: Mathematics
  • Pages : 656
  • ISBN 10 : 9781135440466

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Computational Neuroscience Excerpt :

How does the brain work? After a century of research, we still lack a coherent view of how neurons process signals and control our activities. But as the field of computational neuroscience continues to evolve, we find that it provides a theoretical foundation and a set of technological approaches that can significantly enhance our understanding.

Waves in Neural Media Book

Waves in Neural Media


  • Author : Paul C. Bressloff
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-10-17
  • Genre: Mathematics
  • Pages : 436
  • ISBN 10 : 9781461488668

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Waves in Neural Media Excerpt :

​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 stochastic processes. Also covered in the text are exact methods of solution where applicable. Historically speaking, the propagation of action potentials has inspired new mathematics, particularly with regard to the PDE theory of waves in excitable media. More recently, continuum neural field models of large-scale brain networks have generated a new set of interesting mathematical questions with regard to the solution of nonlocal integro-differential equations. Advanced graduates, postdoctoral researchers and faculty working in mathematical biology, theoretical neuroscience, or applied nonlinear dynamics will find this book to be a valuable resource. The main prerequisites are an introductory graduate course on ordinary differential equations or partial differential equations, making this an accessible and unique contribution to the field of mathematical biology.