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Mathematical Neuroscience

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Mathematical Neuroscience

Mathematical Neuroscience Book
Author : Stanislaw Brzychczy,Roman R. Poznanski
Publisher : Academic Press
Release : 2013-08-16
ISBN : 0124104827
Language : En, Es, Fr & De

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Book Description :

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

Exam Prep for Mathematical Neuroscience

Exam Prep for  Mathematical Neuroscience Book
Author : Anonim
Publisher : Unknown
Release : 2021-04-13
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Tutorials in Mathematical Biosciences I

Tutorials in Mathematical Biosciences I Book
Author : Alla Borisyuk,G. Bard Ermentrout,Avner Friedman,David H. Terman
Publisher : Springer
Release : 2005-01-28
ISBN : 3540315446
Language : En, Es, Fr & De

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Book Description :

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

Mathematics for Neuroscientists Book
Author : Fabrizio Gabbiani,Steven James Cox
Publisher : Academic Press
Release : 2010-09-16
ISBN : 9780080890494
Language : En, Es, Fr & De

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Book Description :

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

Mathematical Foundations of Neuroscience

Mathematical Foundations of Neuroscience Book
Author : G. Bard Ermentrout,David H. Terman
Publisher : Springer Science & Business Media
Release : 2010-07-01
ISBN : 0387877088
Language : En, Es, Fr & De

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Book Description :

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.

Tutorials in Mathematical Biosciences I

Tutorials in Mathematical Biosciences I Book
Author : Alla Borisyuk,G. Bard Ermentrout,Avner Friedman,David H. Terman
Publisher : Springer Science & Business Media
Release : 2005-02-18
ISBN : 9783540238584
Language : En, Es, Fr & De

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Book Description :

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.

Mathematical and Theoretical Neuroscience

Mathematical and Theoretical Neuroscience Book
Author : Giovanni Naldi,Thierry Nieus
Publisher : Springer
Release : 2018-03-20
ISBN : 3319682970
Language : En, Es, Fr & De

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Book Description :

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.

Artificial Intelligence and Robotics

Artificial Intelligence and Robotics Book
Author : Peter J. Bentley
Publisher : Johns Hopkins University Press
Release : 2020-09-08
ISBN : 1421439727
Language : En, Es, Fr & De

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Book Description :

Broken down into ten simple lessons and written by leading experts in their field, the books reveal the ten most important takeaways from those areas of science you've always wanted to know more about.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2008
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Reviews book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

From Computer to Brain

From Computer to Brain Book
Author : William W. Lytton
Publisher : Springer Science & Business Media
Release : 2007-05-08
ISBN : 0387227334
Language : En, Es, Fr & De

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Book Description :

Biology undergraduates, medical students and life-science graduate students often have limited mathematical skills. Similarly, physics, math and engineering students have little patience for the detailed facts that make up much of biological knowledge. 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 in an appendix and providing basic explanations without becoming bogged down in unnecessary details. The book will be suitable for undergraduates and beginning graduate students taking a computational neuroscience course and also to anyone with an interest in the uses of the computer in modeling the nervous system.

Stochastic Methods in Neuroscience

Stochastic Methods in Neuroscience Book
Author : Carlo Laing,Gabriel J Lord
Publisher : OUP Oxford
Release : 2009-09-24
ISBN : 0191607983
Language : En, Es, Fr & De

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Book Description :

Great interest is now being shown in computational and mathematical neuroscience, fuelled in part by the rise in computing power, the ability to record large amounts of neurophysiological data, and advances in stochastic analysis. These techniques are leading to biophysically more realistic models. It has also become clear that both neuroscientists and mathematicians profit from collaborations in this exciting research area. Graduates and researchers in computational neuroscience and stochastic systems, and neuroscientists seeking to learn more about recent advances in the modelling and analysis of noisy neural systems, will benefit from this comprehensive overview. The series of self-contained chapters, each written by experts in their field, covers key topics such as: Markov chain models for ion channel release; stochastically forced single neurons and populations of neurons; statistical methods for parameter estimation; and the numerical approximation of these stochastic models. Each chapter gives an overview of a particular topic, including its history, important results in the area, and future challenges, and the text comes complete with a jargon-busting index of acronyms to allow readers to familiarize themselves with the language used.

Tutorials in Mathematical Biosciences IV

Tutorials in Mathematical Biosciences IV Book
Author : Avner Friedman
Publisher : Springer
Release : 2007-11-21
ISBN : 9783540743286
Language : En, Es, Fr & De

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Book Description :

This book offers an introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. It reviews the concept and methodologies of phylogenetic trees, introduces ecological models, examines a broad range of ongoing research in population dynamics, and deals with gene frequencies under the action of migration and selection. The book features computational schemes, illustrations, and mathematical theorems.

Scientiae Mathematicae Japonicae

Scientiae Mathematicae Japonicae Book
Author : Anonim
Publisher : Unknown
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Dynamical Systems in Neuroscience

Dynamical Systems in Neuroscience Book
Author : Eugene M. Izhikevich
Publisher : MIT Press
Release : 2007
ISBN : 0262090430
Language : En, Es, Fr & De

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Book Description :

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.

Atti del Congresso internazionale dei matematici

Atti del     Congresso internazionale dei matematici     Book
Author : Anonim
Publisher : Unknown
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Selected Topics of P adic Mathematical Physics and Analysis

Selected Topics of P adic Mathematical Physics and Analysis Book
Author : Anonim
Publisher : Unknown
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Theoretical Neuroscience

Theoretical Neuroscience Book
Author : Peter Dayan
Publisher : Mit Press
Release : 2005
ISBN : 9780262541855
Language : En, Es, Fr & De

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Book Description :

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

The Mathematical Scientist

The Mathematical Scientist Book
Author : Anonim
Publisher : Unknown
Release : 2001
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Network

Network Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Assistantships and Graduate Fellowships in the Mathematical Sciences

Assistantships and Graduate Fellowships in the Mathematical Sciences Book
Author : Anonim
Publisher : Unknown
Release : 2001
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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