November 29, 2020

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Mathematical Neuroscience

Mathematical Neuroscience
Author : Stanislaw Brzychczy,Roman R. Poznanski
Publisher : Academic Press
Release Date : 2013-08-16
Category : Mathematics
Total pages :208
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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

Tutorials in Mathematical Biosciences I

Tutorials in Mathematical Biosciences I
Author : Alla Borisyuk,G. Bard Ermentrout,Avner Friedman,David H. Terman
Publisher : Springer
Release Date : 2005-01-28
Category : Mathematics
Total pages :170
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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 Foundations of Neuroscience

Mathematical Foundations of Neuroscience
Author : G. Bard Ermentrout,David H. Terman
Publisher : Springer Science & Business Media
Release Date : 2010-07-01
Category : Mathematics
Total pages :422
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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

Mathematical and Theoretical Neuroscience
Author : Giovanni Naldi,Thierry Nieus
Publisher : Springer
Release Date : 2018-03-20
Category : Mathematics
Total pages :253
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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.

Mathematics for Neuroscientists

Mathematics for Neuroscientists
Author : Fabrizio Gabbiani,Steven James Cox
Publisher : Academic Press
Release Date : 2017-03-21
Category : Science
Total pages :628
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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

Exam Prep for: Mathematical Neuroscience

Exam Prep for: Mathematical Neuroscience
Author : Anonim
Publisher : Unknown
Release Date : 2020
Category :
Total pages :129
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Neuroscience

Neuroscience
Author : Alwyn Scott
Publisher : Springer Science & Business Media
Release Date : 2007-12-14
Category : Science
Total pages :352
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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.

Stochastic Methods in Neuroscience

Stochastic Methods in Neuroscience
Author : Carlo Laing,Gabriel J Lord
Publisher : Oxford University Press
Release Date : 2010
Category : Mathematics
Total pages :370
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Computational or mathematical neuroscience is a research area currently of great interest, due to, amongst other factors, rapid increases in computing power, increases in the ability to record large amounts of neurophysiological data, and a realisation amongst both neuroscientists and mathematicians that each can benefit from collaborating with the other. This text will concentrate on the intersection between stochastic dynamics and neuroscience, presenting aseries of self-contained chapters on major aspects of noise and neuroscience, each written by an expert in their particular field. These range over Markov chain models for ion channel release, stochastically forced single neurons and population of neurons, statistical methods for parameter estimation,and the numerical approximation these models. Aimed at graduates and researchers in computational neuroscience and stochastic systems, each chapter will give an overview of a particular topic, including its history, important results in the area and future challenges.

Mathematical Modelling in Motor Neuroscience: State of the Art and Translation to the Clinic, Gaze Orienting Mechanisms and Disease

Mathematical Modelling in Motor Neuroscience: State of the Art and Translation to the Clinic, Gaze Orienting Mechanisms and Disease
Author : Anonim
Publisher : Academic Press
Release Date : 2019-07-18
Category : Science
Total pages :426
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Mathematical Modelling in Motor Neuroscience: State of the Art and Translation to the Clinic, Gaze Orienting Mechanisms and Disease, Volume 249, the latest release in the Progress in Brain Research series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of topics, including Sequential Bayesian updating, Maps and Sensorimotor Transformations for Eye-Head Gaze Shifts: Role of the Midbrain Superior Colliculus, Modeling Gaze Position-Dependent Opsoclonus, Eye Position-Dependent Opsoclonus in Mild Traumatic Brain Injury, Saccades in Parkinson's disease -- hypometric, slow, and maladaptive, Brainstem Neural Circuits for Fixation and Generation of Saccadic Eye Movements, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Progress in Brain Research series Includes the latest information on mathematical modeling in motor neuroscience

Theoretical Neuroscience

Theoretical Neuroscience
Author : Peter Dayan,L. F. Abbott
Publisher : Computational Neuroscience Series
Release Date : 2001
Category : Medical
Total pages :460
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The construction and analysis of mathematical and computational models of neural systems.

From Computer to Brain

From Computer to Brain
Author : William W. Lytton
Publisher : Springer Science & Business Media
Release Date : 2007-05-08
Category : Mathematics
Total pages :364
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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.

The Oxford Handbook of Numerical Cognition

The Oxford Handbook of Numerical Cognition
Author : Roi Kadosh,Ann Dowker
Publisher : OUP Oxford
Release Date : 2015-07-30
Category : Psychology
Total pages :1144
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How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.

Computational Neuroscience

Computational Neuroscience
Author : Eric L. Schwartz
Publisher : MIT Press
Release Date : 1993-08-26
Category : Medical
Total pages :441
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The thirty original contributions in this book provide a working definition of"computational neuroscience" as the area in which problems lie simultaneously within computerscience and neuroscience. They review this emerging field in historical and philosophical overviewsand in stimulating summaries of recent results. Leading researchers address the structure of thebrain and the computational problems associated with describing and understanding this structure atthe synaptic, neural, map, and system levels.The overview chapters discuss the early days of thefield, provide a philosophical analysis of the problems associated with confusion between brainmetaphor and brain theory, and take up the scope and structure of computationalneuroscience.Synaptic-level structure is addressed in chapters that relate the properties ofdendritic branches, spines, and synapses to the biophysics of computation and provide a connectionbetween real neuron architectures and neural network simulations.The network-level chapters take upthe preattentive perception of 3-D forms, oscillation in neural networks, the neurobiologicalsignificance of new learning models, and the analysis of neural assemblies and local learningrides.Map-level structure is explored in chapters on the bat echolocation system, cat orientationmaps, primate stereo vision cortical cognitive maps, dynamic remapping in primate visual cortex, andcomputer-aided reconstruction of topographic and columnar maps in primates.The system-level chaptersfocus on the oculomotor system VLSI models of early vision, schemas for high-level vision,goal-directed movements, modular learning, effects of applied electric current fields on corticalneural activity neuropsychological studies of brain and mind, and an information-theoretic view ofanalog representation in striate cortex.Eric L. Schwartz is Professor of Brain Research and ResearchProfessor of Computer Science, Courant Institute of Mathematical Sciences, New York UniversityMedical Center. Computational Neuroscience is included in the System Development FoundationBenchmark Series.

Fundamentals of Computational Neuroscience

Fundamentals of Computational Neuroscience
Author : Thomas Trappenberg
Publisher : Oxford University Press
Release Date : 2010
Category : Mathematics
Total pages :390
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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.

Tutorials in Mathematical Biosciences I

Tutorials in Mathematical Biosciences I
Author : Alla Borisyuk,G. Bard Ermentrout,Avner Friedman,David H. Terman
Publisher : Springer Science & Business Media
Release Date : 2005-02-18
Category : Mathematics
Total pages :170
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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.