Mathematics For Neuroscientists
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Mathematics For Neuroscientists
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Author : Fabrizio Gabbiani
language : en
Publisher: Academic Press
Release Date : 2017-02-04
Mathematics For Neuroscientists written by Fabrizio Gabbiani and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-04 with Mathematics categories.
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
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Author : G. Bard Ermentrout
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-01
Mathematical Foundations Of Neuroscience written by G. Bard Ermentrout and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Mathematics categories.
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.
Dynamical Systems In Neuroscience
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Author : Eugene M. Izhikevich
language : en
Publisher: MIT Press
Release Date : 2007
Dynamical Systems In Neuroscience written by Eugene M. Izhikevich and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Differentiable dynamical systems categories.
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
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Author : Hanspeter A Mallot
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-23
Computational Neuroscience written by Hanspeter A Mallot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-23 with Technology & Engineering categories.
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.
Nonlinear Dynamics In Computational Neuroscience
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Author : Fernando Corinto
language : en
Publisher: Springer
Release Date : 2018-06-19
Nonlinear Dynamics In Computational Neuroscience written by Fernando Corinto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-19 with Technology & Engineering categories.
This book provides an essential overview of computational neuroscience. It addresses a broad range of aspects, from physiology to nonlinear dynamical approaches to understanding neural computation, and from the simulation of brain circuits to the development of engineering devices and platforms for neuromorphic computation. Written by leading experts in such diverse fields as neuroscience, physics, psychology, neural engineering, cognitive science and applied mathematics, the book reflects the remarkable advances that have been made in the field of computational neuroscience, an emerging discipline devoted to the study of brain functions in terms of the information-processing properties of the structures forming the nervous system. The contents build on the workshop “Nonlinear Dynamics in Computational Neuroscience: from Physics and Biology to ICT,” which was held in Torino, Italy in September 2015.
Network Neuroscience
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Author : Flavio Fröhlich
language : en
Publisher: Academic Press
Release Date : 2016-09-20
Network Neuroscience written by Flavio Fröhlich and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-20 with Medical categories.
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 to the physicist or engineer, who is interested in neuroscience applications of mathematical and engineering tools. The book spans 27 chapters that cover everything from individual cells all the way to complex network disorders such as depression and autism spectrum disorders. An additional 12 toolboxes provide the necessary background for making network neuroscience accessible independent of the reader's background. Dr. Flavio Frohlich wrote this book based on his experience of mentoring dozens of trainees in the Frohlich Lab, from undergraduate students to senior researchers. The Frohlich lab pursues a unique and integrated vision that combines computer simulations, animal model studies, human studies, and clinical trials with the goal of developing novel brain stimulation treatments for psychiatric disorders. The book is based on a course he teaches at UNC that has attracted trainees from many different departments, including neuroscience, biomedical engineering, psychology, cell biology, physiology, neurology, and psychiatry. Dr. Frohlich has consistently received rave reviews for his teaching. With this book he hopes to make his integrated view of neuroscience available to trainees and researchers on a global scale. His goal is to make the book the training manual for the next generation of (network) neuroscientists, who will be fusing biology, engineering, and medicine to unravel the big questions about the brain and to revolutionize psychiatry and neurology. - Easy-to-read, comprehensive introduction to the emerging field of network neuroscience - Includes 27 chapters packed with information on topics from single neurons to complex network disorders such as depression and autism - Features 12 toolboxes serve as primers to provide essential background knowledge in the fields of biology, mathematics, engineering, and physics
Statistical Techniques For Neuroscientists
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Author : Young K. Truong
language : en
Publisher: CRC Press
Release Date : 2024-10-14
Statistical Techniques For Neuroscientists written by Young K. Truong and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-14 with Mathematics categories.
An ideal introduction to statistical neurocomputing, this book examines current statistical methods for solving emerging problems in neuroscience. These methods have been applied to data involving multichannel neural spike train, spike sorting, blind source separation, functional and effective neural connectivity, spatiotemporal modeling, and mu
Math For Scientists
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Author : Natasha Maurits
language : en
Publisher: Springer
Release Date : 2017-08-26
Math For Scientists written by Natasha Maurits and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-26 with Mathematics categories.
This book reviews math topics relevant to non-mathematics students and scientists, but which they may not have seen or studied for a while. These math issues can range from reading mathematical symbols, to using complex numbers, dealing with equations involved in calculating medication equivalents, the General Linear Model (GLM) used in e.g. neuroimaging analysis, finding the minimum of a function, independent component analysis, or filtering approaches. Almost every student or scientist, will at some point run into mathematical formulas or ideas in scientific papers that may be hard to understand, given that formal math education may be some years ago. In this book we will explain the theory behind many of these mathematical ideas and expressions and provide readers with the tools to better understand them. We will revisit high school mathematics and extend and relate this to the mathematics you need to understand the math you may encounter in the course of your research. This book will help you understand the math and formulas in the scientific papers you read. To achieve this goal, each chapter mixes theory with practical pen-and-paper exercises such that you (re)gain experience with solving math problems yourself. Mnemonics will be taught whenever possible. To clarify the math and help readers apply it, each chapter provides real-world and scientific examples.
Spikes
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Author : Fred Rieke
language : en
Publisher: MIT Press (MA)
Release Date : 1997
Spikes written by Fred Rieke and has been published by MIT Press (MA) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Medical categories.
Intended for neurobiologists with an interest in mathematical analysis of neural data as well as the growing number of physicists and mathematicians interested in information processing by "real" nervous systems, Spikes provides a self-contained review of relevant concepts in information theory and statistical decision theory.