Foundations and Methods from Mathematics to Neuroscience
Author: Colleen Crangle
Publisher:
Published: 2014
Total Pages: 277
ISBN-13: 9781575867465
DOWNLOAD EBOOK →Lanterna Rally
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Mathematical Foundations of Neuroscience
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.
Foundations and Methods from Mathematics to Neuroscience
Author: Colleen E. Crangle
Publisher: Stanford Univ Center for the Study
Published: 2015-01
Total Pages: 350
ISBN-13: 9781575867458
DOWNLOAD EBOOK →"Center for the Study of Language and Information, Leland Stanford Junior University."
Mathematics for Neuroscientists
Author: Fabrizio Gabbiani
Publisher: Academic Press
Published: 2017-02-04
Total Pages: 630
ISBN-13: 0128019069
DOWNLOAD EBOOK →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
Space, Time and Number in the Brain
Author: Stanislas Dehaene
Publisher: Academic Press
Published: 2011-07-13
Total Pages: 374
ISBN-13: 0123859492
DOWNLOAD EBOOK →The study of mathematical cognition and the ways in which the ideas of space, time and number are encoded in brain circuitry has become a fundamental issue for neuroscience. How such encoding differs across cultures and educational level is of further interest in education and neuropsychology. This rapidly expanding field of research is overdue for an interdisciplinary volume such as this, which deals with the neurological and psychological foundations of human numeric capacity. A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. The first comprehensive and authoritative volume dealing with neurological and psychological foundations of mathematical cognition Uniquely integrative volume at the frontier of a rapidly expanding interdisciplinary field Features outstanding and truly international scholarship, with chapters written by leading experts in a variety of fields
Mathematical 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
From Computer to Brain
Author: William W. Lytton
Publisher: Springer Science & Business Media
Published: 2007-05-08
Total Pages: 369
ISBN-13: 0387227334
DOWNLOAD EBOOK →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.
A New Foundation for Representation in Cognitive and Brain Science
Author: Jaime Gómez-Ramirez
Publisher: Springer Science & Business Media
Published: 2013-11-22
Total Pages: 213
ISBN-13: 9400777388
DOWNLOAD EBOOK →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.
Tutorials in Mathematical Biosciences I
Author: Alla Borisyuk
Publisher: Springer
Published: 2005-01-28
Total Pages: 179
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.
Computational Neuroscience and Cognitive Modelling
Author: Britt Anderson
Publisher: SAGE
Published: 2014-01-08
Total Pages: 241
ISBN-13: 1446297373
DOWNLOAD EBOOK →"For the neuroscientist or psychologist who cringes at the sight of mathematical formulae and whose eyes glaze over at terms like differential equations, linear algebra, vectors, matrices, Bayes’ rule, and Boolean logic, this book just might be the therapy needed." - Anjan Chatterjee, Professor of Neurology, University of Pennsylvania "Anderson provides a gentle introduction to computational aspects of psychological science, managing to respect the reader’s intelligence while also being completely unintimidating. Using carefully-selected computational demonstrations, he guides students through a wide array of important approaches and tools, with little in the way of prerequisites...I recommend it with enthusiasm." - Asohan Amarasingham, The City University of New York This unique, self-contained and accessible textbook provides an introduction to computational modelling neuroscience accessible to readers with little or no background in computing or mathematics. Organized into thematic sections, the book spans from modelling integrate and firing neurons to playing the game Rock, Paper, Scissors in ACT-R. This non-technical guide shows how basic knowledge and modern computers can be combined for interesting simulations, progressing from early exercises utilizing spreadsheets, to simple programs in Python. Key Features include: Interleaved chapters that show how traditional computing constructs are simply disguised versions of the spread sheet methods. Mathematical facts and notation needed to understand the modelling methods are presented at their most basic and are interleaved with biographical and historical notes for contex. Numerous worked examples to demonstrate the themes and procedures of cognitive modelling. An excellent text for postgraduate students taking courses in research methods, computational neuroscience, computational modelling, cognitive science and neuroscience. It will be especially valuable to psychology students.
