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Author: G. Bard Ermentrout
Publisher: Springer Science & Business Media
Published: 2010-07-08
Total Pages: 434
ISBN-13: 038787707X
DOWNLOAD EBOOK →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: Stanislaw Brzychczy
Publisher: Academic Press
Published: 2013-08-16
Total Pages: 201
ISBN-13: 0124104827
DOWNLOAD EBOOK →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: Alla Borisyuk
Publisher: Springer
Published: 2005-01-28
Total Pages: 170
ISBN-13: 3540315446
DOWNLOAD EBOOK →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: Giovanni Naldi
Publisher: Springer
Published: 2018-03-20
Total Pages: 253
ISBN-13: 3319682970
DOWNLOAD EBOOK →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
Published: 2007-12-14
Total Pages: 362
ISBN-13: 0387224637
DOWNLOAD EBOOK →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: Rhonda Douglas Brown
Publisher: Springer
Published: 2018-04-13
Total Pages: 146
ISBN-13: 3319764098
DOWNLOAD EBOOK →This book examines the neuroscience of mathematical cognitive development from infancy into emerging adulthood, addressing both biological and environmental influences on brain development and plasticity. It begins by presenting major theoretical frameworks for designing and interpreting neuroscience studies of mathematical cognitive development, including developmental evolutionary theory, developmental systems approaches, and the triple-code model of numerical processing. The book includes chapters that discuss findings from studies using neuroscience research methods to examine numerical and visuospatial cognition, calculation, and mathematical difficulties and exceptionalities. It concludes with a review of mathematical intervention programs and recommendations for future neuroscience research on mathematical cognitive development. Featured neuroscience research methods include: Functional Magnetic Resonance Imaging (fMRI). Diffusion Tensor Imaging (DTI). Event Related Potentials (ERP). Transcranial Magnetic Stimulation (TMS). Neuroscience of Mathematical Cognitive Development is an essential resource for researchers, clinicians and related professionals, and graduate students in child and school psychology, neuroscience, educational psychology, neuropsychology, and mathematics education.
Author: Fabrizio Gabbiani
Publisher: Academic Press
Published: 2010-09-16
Total Pages: 505
ISBN-13: 0080890490
DOWNLOAD EBOOK →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
Author: Inmaculada Méndez
Publisher: Frontiers Media SA
Published: 2024-03-07
Total Pages: 174
ISBN-13: 2832545866
DOWNLOAD EBOOK →Author: Alla Borisyuk
Publisher: Springer Science & Business Media
Published: 2005-02-18
Total Pages: 184
ISBN-13: 9783540238584
DOWNLOAD EBOOK →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: Yoko Yamaguchi
Publisher: Springer Science & Business Media
Published: 2013-04-08
Total Pages: 799
ISBN-13: 9400747926
DOWNLOAD EBOOK →Within our knowledge, the series of the International Conference on Cognitive Neurodynamics (ICCN) is the only conference series dedicating to cognitive neurodynamis. This volume is the proceedings of the 3rd International Conference on Cognitive Neurodynamics held in 2011, which reviews the progress in this field since the 1st ICCN - 2007. The topics include: Neural coding and realistic neural network dynamics, Neural population dynamics, Firing Oscillations and Patterns in Neuronal Networks, Brain imaging, EEG, MEG, Sensory and Motor Dynamics, Global cognitive function, Multi-scalar Neurodynamics - from Physiology to Systems Theory, Neural computing, Emerging Technologies for Brain Computer Interfaces, Neural dynamics of brain disorders.
