mathematics for neuroscientists

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Mathematics For Neuroscientists

Author : Fabrizio Gabbiani
ISBN : 9780128019061
Genre : Science
File Size : 85. 23 MB
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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

Mathematical Foundations Of Neuroscience

Author : G. Bard Ermentrout
ISBN : 9780387877082
Genre : Mathematics
File Size : 76. 82 MB
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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 Neuroscience

Author : Stanislaw Brzychczy
ISBN : 9780124104822
Genre : Mathematics
File Size : 20. 23 MB
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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

Theoretical Neuroscience

Author : Peter Dayan
ISBN : 0262541858
Genre : Medical
File Size : 20. 9 MB
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The construction and analysis of mathematical and computational models of neural systems.

Invited Lectures From The 13th International Congress On Mathematical Education

Author : Gabriele Kaiser
ISBN : 9783319721705
Genre : Education
File Size : 36. 67 MB
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This book is Open Access under a CC BY 4.0 license. The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

Signal Processing For Neuroscientists

Author : Wim van Drongelen
ISBN : 9780128104835
Genre : Science
File Size : 31. 11 MB
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Signal Processing for Neuroscientists, Second Edition provides an introduction to signal processing and modeling for those with a modest understanding of algebra, trigonometry and calculus. With a robust modeling component, this book describes modeling from the fundamental level of differential equations all the way up to practical applications in neuronal modeling. It features nine new chapters and an exercise section developed by the author. Since the modeling of systems and signal analysis are closely related, integrated presentation of these topics using identical or similar mathematics presents a didactic advantage and a significant resource for neuroscientists with quantitative interest. Although each of the topics introduced could fill several volumes, this book provides a fundamental and uncluttered background for the non-specialist scientist or engineer to not only get applications started, but also evaluate more advanced literature on signal processing and modeling. Includes an introduction to biomedical signals, noise characteristics, recording techniques, and the more advanced topics of linear, nonlinear and multi-channel systems analysis Features new chapters on the fundamentals of modeling, application to neuronal modeling, Kalman filter, multi-taper power spectrum estimation, and practice exercises Contains the basics and background for more advanced topics in extensive notes and appendices Includes practical examples of algorithm development and implementation in MATLAB Features a companion website with MATLAB scripts, data files, figures and video lectures

Educational Neuroscience

Author : Kathryn E. Patten
ISBN : 9781444345803
Genre : Education
File Size : 21. 70 MB
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Educational Neuroscience provides an overview of the wide range of recent initiatives in educational neuroscience, examining a variety of methodological concerns, issues, and directions. Encourages interdisciplinary perspectives in educational neuroscience Contributions from leading researchers examine key issues relating to educational neuroscience and mind, brain, and education more generally Promotes a theoretical and empirical base for the subject area Explores a range of methods available to researchers Identifies agencies, organizations, and associations facilitating development in the field Reveals a variety of on-going efforts to establish theories, models, methods, ethics, and a common language

Stochastic Methods In Neuroscience

Author : Carlo Laing
ISBN : 9780191607981
Genre : Mathematics
File Size : 69. 51 MB
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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.

Dynamical Systems In Neuroscience

Author : Eugene M. Izhikevich
ISBN : 9780262090438
Genre : Medical
File Size : 25. 15 MB
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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.

Neuroscience For Clinicians

Author : C. Alexander Simpkins
ISBN : 9781461448426
Genre : Psychology
File Size : 42. 10 MB
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This book fills the need for an introductory text that opens the field up to the beginner and takes them to higher-level thinking about neuroscience. Neuroscience has captured the interest of students, professionals, and the general public. In fact it is so new, that there are very few books that gather it together in one text. Neuroscience is an amalgamation of many fields: psychology, cognitive science, chemistry, biology, engineering, philosophy, mathematics, and statistics. People who are new to the discipline have to be able to find their way through all of these fields together. In addition, they need to understand the highly technical lexicon, modeling methods, and theoretical assumptions used to describe brain structure, function, and the interaction between them. This book helps readers navigate the conventions used to describe the brain that developed through the years. The authors crystallize the complex modeling methods and technologies so that readers understand what they are saying and how to use them. They address the important underlying principles and important issues of neuroscience, with the debates and discussions that are ongoing as the field evolves. They also include many salient fine-grained details so that the book is not just an overview, but also a useful guide for many levels of readers.

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