Author: Henry C. Tuckwell
Publisher: SIAM
ISBN: 9781611970159
Category : Technology & Engineering
Languages : en
Pages : 134
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Book Description
This monograph is centered on quantitative analysis of nerve-cell behavior. The work is foundational, with many higher order problems still remaining, especially in connection with neural networks. Thoroughly addressed topics include stochastic problems in neurobiology, and the treatment of the theory of related Markov processes.
Author: Henry C. Tuckwell
Publisher: SIAM
ISBN: 0898712327
Category : Technology & Engineering
Languages : en
Pages : 128
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Book Description
This monograph is centered on quantitative analysis of nerve-cell behavior. The work is foundational, with many higher order problems still remaining, especially in connection with neural networks. Thoroughly addressed topics include stochastic problems in neurobiology, and the treatment of the theory of related Markov processes.
Author: Carlo Laing
Publisher: Oxford University Press
ISBN: 0199235074
Category : Mathematics
Languages : en
Pages : 399
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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 parameterestimation; 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.
Author: Fabrizio Gabbiani
Publisher: Academic Press
ISBN: 0128019069
Category : Mathematics
Languages : en
Pages : 630
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Book Description
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
Author: J.M. Bower
Publisher: Elsevier
ISBN: 9780444503077
Category : Computers
Languages : en
Pages : 1114
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Book Description
This volume includes papers originally presented at the 7th annual Computational Neuroscience Meeting (CNS'98) held in July of 1998 at the Fess Parker Doubletree Inn in Santa Barbara, California. The CNS meetings bring together computational neuroscientists representing many different fields and backgrounds as well as many different experimental preparations and theoretical approaches. The papers published here range from pure experimental neurobiology, to neuro-ethology, mathematics, physics, and engineering. In all cases the research described is focused on understanding how nervous systems compute. The actual subjects of the research include a highly diverse number of preparations, modeling approaches, and analysis techniques. Accordingly, this volume reflects the breadth and depth of current research in computational neuroscience taking place throughout the world.
Author: R.R. Poznanski
Publisher: Routledge
ISBN: 1351430971
Category : Computers
Languages : en
Pages : 556
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Book Description
With contributions from more than 40 renowned experts, Modeling in the Neurosciences: From Ionic Channels to Neural Networks is essential for those interested in neuronal modeling and quantitative neiroscience. Focusing on new mathematical and computer models, techniques and methods, this monograph represents a cohesive and comprehensive treatment
Author: M. Reza Rahimi Tabar
Publisher: Springer
ISBN: 3030184722
Category : Science
Languages : en
Pages : 290
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Book Description
This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.
Author: Jianfeng Feng
Publisher: CRC Press
ISBN: 0203494466
Category : Mathematics
Languages : en
Pages : 649
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Book Description
How does the brain work? After a century of research, we still lack a coherent view of how neurons process signals and control our activities. But as the field of computational neuroscience continues to evolve, we find that it provides a theoretical foundation and a set of technological approaches that can significantly enhance our understanding.
Author: Vincenzo Capasso
Publisher: Springer Nature
ISBN: 3030696537
Category : Mathematics
Languages : en
Pages : 574
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Book Description
This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields. Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations. An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularly the applications explored in the second half of the book.
Author: Uwe Windhorst
Publisher: Springer Science & Business Media
ISBN: 9783540644606
Category : Medical
Languages : en
Pages : 1360
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Book Description
This manual provides an overview of the techniques used in modern neuroscience research. The emphasis is on showing how different techniques can optimally be combined in the study of problems that arise at some levels of nervous system organization. It is a working tool for the scientist in the laboratory and clinic, providing detailed step-by-step protocols with tips and recommendations. Most chapters or protocols are organized such that they can be used independently of one another. Cross-references between the chapters, a glossary, a list of suppliers and appendices provide further help.
