Mathematical Neuroscience PDF Download
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| Author | : Stanislaw Brzychczy |
| Publisher | : Academic Press |
| Total Pages | : 201 |
| Release | : 2013-08-16 |
| Genre | : Mathematics |
| ISBN | : 0124104827 |
Download Mathematical Neuroscience Book in PDF, ePub and Kindle
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
| Author | : G. Bard Ermentrout |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2010-07-01 |
| Genre | : Mathematics |
| ISBN | : 0387877088 |
Download Mathematical Foundations of Neuroscience Book in PDF, ePub and Kindle
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.
| Author | : Fabrizio Gabbiani |
| Publisher | : Academic Press |
| Total Pages | : 630 |
| Release | : 2017-02-04 |
| Genre | : Mathematics |
| ISBN | : 0128019069 |
Download Mathematics for Neuroscientists Book in PDF, ePub and Kindle
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
| Author | : Giovanni Naldi |
| Publisher | : Springer |
| Total Pages | : 255 |
| Release | : 2018-03-20 |
| Genre | : Mathematics |
| ISBN | : 3319682970 |
Download Mathematical and Theoretical Neuroscience Book in PDF, ePub and Kindle
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.
| Author | : Alwyn Scott |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 362 |
| Release | : 2007-12-14 |
| Genre | : Science |
| ISBN | : 0387224637 |
Download Neuroscience Book in PDF, ePub and Kindle
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.
| Author | : Alla Borisyuk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 184 |
| Release | : 2005-02-18 |
| Genre | : Mathematics |
| ISBN | : 9783540238584 |
Download Tutorials in Mathematical Biosciences I Book in PDF, ePub and Kindle
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.
| Author | : Eugene M. Izhikevich |
| Publisher | : MIT Press |
| Total Pages | : 459 |
| Release | : 2010-01-22 |
| Genre | : Medical |
| ISBN | : 0262514206 |
Download Dynamical Systems in Neuroscience Book in PDF, ePub and Kindle
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 author's website, www.izhikevich.com.
| Author | : G. Bard Ermentrout |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2010-07-08 |
| Genre | : Mathematics |
| ISBN | : 038787707X |
Download Mathematical Foundations of Neuroscience Book in PDF, ePub and Kindle
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.
| Author | : Colleen Crangle |
| Publisher | : Center for the Study of Language and Information Publica Tion |
| Total Pages | : 0 |
| Release | : 2014 |
| Genre | : Logic, Symbolic and mathematical |
| ISBN | : 9781575867441 |
Download Foundations and Methods from Mathematics to Neuroscience Book in PDF, ePub and Kindle
During his long and continuing scholarly career, Patrick Suppes contributed significantly both to the sciences and to their philosophies. The volume consists of papers by an international group of Suppes colleagues, collaborators, and students in many of the areas of his expertise, building on or adding to his insights. Michael Friedman offers an overview of Suppes accomplishments and of his unique perspective on the relation between science and philosophy. Paul Humphreys, Stephen Hartmann, and Tom Ryckman present essays in the philosophy of physics. Jens-Erik Fenstad, Harvey Friedman, and Jaako Hintikka consider problems in the foundations of mathematics, while the late Duncan Luce, Jean-Claude Falmagne, Brian Skyrms, and Hannes Leitgeb have contributed essays in theory of measurement, decision theory and probability. Foundations of economics and political theory are addressed by Adolfo Garcia de la Sienra, Russell Hardin, and Kenneth Arrow. Psychology, language, and philosophy of language are addressed by Elizabeth Loftus, Anne Fagot-Largeault, Willem Levelt, Dagfinn Follesdal, and Marcos Perreau-Guimares and some of Suppes most recent research in neurobiology is addressed in essays by Colleen Crangle, Acadio de Barros and Claudio Carvalhes. Finally Nancy Cartwright and Alexandre Marcelles consider the alignment (or misalignment) of method and policy. Each of the essays is accompanied by a response from Suppes."
| Author | : Alla Borisyuk |
| Publisher | : Springer |
| Total Pages | : 179 |
| Release | : 2005-01-28 |
| Genre | : Mathematics |
| ISBN | : 3540315446 |
Download Tutorials in Mathematical Biosciences I Book in PDF, ePub and Kindle
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.
