Mathematics for Neuroscientists

Author: Fabrizio Gabbiani
Publisher: Academic Press
ISBN: 0128019069
Format: PDF, Kindle
Download Now
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

Mathematics for Neuroscientists

Author: Fabrizio Gabbiani
Publisher: Academic Press
ISBN: 9780080890494
Format: PDF, Docs
Download Now
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

Mathematics for Neuroscientists

Author: Fabrizio Gabbiani
Publisher: Academic Press
ISBN: 9780128018958
Format: PDF, ePub
Download Now
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

Author: G. Bard Ermentrout
Publisher: Springer Science & Business Media
ISBN: 0387877088
Format: PDF, ePub
Download Now
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.

Signal Processing for Neuroscientists

Author: Wim van Drongelen
Publisher: Academic Press
ISBN: 012810483X
Format: PDF
Download Now
Signal Processing for Neuroscientists, Second Edition provides an introduction to signal processing and modeling for those with a modest understanding of algebra, trigonometry and calculus. With a robust modeling component, this book describes modeling from the fundamental level of differential equations all the way up to practical applications in neuronal modeling. It features nine new chapters and an exercise section developed by the author. Since the modeling of systems and signal analysis are closely related, integrated presentation of these topics using identical or similar mathematics presents a didactic advantage and a significant resource for neuroscientists with quantitative interest. Although each of the topics introduced could fill several volumes, this book provides a fundamental and uncluttered background for the non-specialist scientist or engineer to not only get applications started, but also evaluate more advanced literature on signal processing and modeling. Includes an introduction to biomedical signals, noise characteristics, recording techniques, and the more advanced topics of linear, nonlinear and multi-channel systems analysis Features new chapters on the fundamentals of modeling, application to neuronal modeling, Kalman filter, multi-taper power spectrum estimation, and practice exercises Contains the basics and background for more advanced topics in extensive notes and appendices Includes practical examples of algorithm development and implementation in MATLAB Features a companion website with MATLAB scripts, data files, figures and video lectures

MATLAB for Neuroscientists

Author: Pascal Wallisch
Publisher: Academic Press
ISBN: 0123838371
Format: PDF, ePub
Download Now
MATLAB for Neuroscientists serves as the only complete study manual and teaching resource for MATLAB, the globally accepted standard for scientific computing, in the neurosciences and psychology. This unique introduction can be used to learn the entire empirical and experimental process (including stimulus generation, experimental control, data collection, data analysis, modeling, and more), and the 2nd Edition continues to ensure that a wide variety of computational problems can be addressed in a single programming environment. This updated edition features additional material on the creation of visual stimuli, advanced psychophysics, analysis of LFP data, choice probabilities, synchrony, and advanced spectral analysis. Users at a variety of levels—advanced undergraduates, beginning graduate students, and researchers looking to modernize their skills—will learn to design and implement their own analytical tools, and gain the fluency required to meet the computational needs of neuroscience practitioners. The first complete volume on MATLAB focusing on neuroscience and psychology applications Problem-based approach with many examples from neuroscience and cognitive psychology using real data Illustrated in full color throughout Careful tutorial approach, by authors who are award-winning educators with strong teaching experience

Dynamical Systems in Neuroscience

Author: Eugene M. Izhikevich
Publisher: MIT Press
ISBN: 0262090430
Format: PDF, Docs
Download Now
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: 3319008617
Format: PDF, Mobi
Download Now
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.

A New Foundation for Representation in Cognitive and Brain Science

Author: Jaime Gómez Ramirez
Publisher: Springer Science & Business Media
ISBN: 9400777388
Format: PDF, ePub, Mobi
Download Now
The purpose of the book is to advance in the understanding of brain function by defining a general framework for representation based on category theory. The idea is to bring this mathematical formalism into the domain of neural representation of physical spaces, setting the basis for a theory of mental representation, able to relate empirical findings, uniting them into a sound theoretical corpus. The innovative approach presented in the book provides a horizon of interdisciplinary collaboration that aims to set up a common agenda that synthesizes mathematical formalization and empirical procedures in a systemic way. Category theory has been successfully applied to qualitative analysis, mainly in theoretical computer science to deal with programming language semantics. Nevertheless, the potential of category theoretic tools for quantitative analysis of networks has not been tackled so far. Statistical methods to investigate graph structure typically rely on network parameters. Category theory can be seen as an abstraction of graph theory. Thus, new categorical properties can be added into network analysis and graph theoretic constructs can be accordingly extended in more fundamental basis. By generalizing networks using category theory we can address questions and elaborate answers in a more fundamental way without waiving graph theoretic tools. The vital issue is to establish a new framework for quantitative analysis of networks using the theory of categories, in which computational neuroscientists and network theorists may tackle in more efficient ways the dynamics of brain cognitive networks. The intended audience of the book is researchers who wish to explore the validity of mathematical principles in the understanding of cognitive systems. All the actors in cognitive science: philosophers, engineers, neurobiologists, cognitive psychologists, computer scientists etc. are akin to discover along its pages new unforeseen connections through the development of concepts and formal theories described in the book. Practitioners of both pure and applied mathematics e.g., network theorists, will be delighted with the mapping of abstract mathematical concepts in the terra incognita of cognition.

Fundamentals of Computational Neuroscience

Author: Thomas Trappenberg
Publisher: Oxford University Press
ISBN: 0199568413
Format: PDF
Download Now
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.