Mathematical Aspects of Hodgkin-Huxley Neural Theory


Book Description

This book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work.







Neuronal Dynamics


Book Description

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.




Methods of Mathematical Modelling and Computation for Complex Systems


Book Description

This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.







Neural Information Processing


Book Description

The five volume set LNCS 7663, LNCS 7664, LNCS 7665, LNCS 7666 and LNCS 7667 constitutes the proceedings of the 19th International Conference on Neural Information Processing, ICONIP 2012, held in Doha, Qatar, in November 2012. The 423 regular session papers presented were carefully reviewed and selected from numerous submissions. These papers cover all major topics of theoretical research, empirical study and applications of neural information processing research. The 5 volumes represent 5 topical sections containing articles on theoretical analysis, neural modeling, algorithms, applications, as well as simulation and synthesis.




From Molecules to Networks


Book Description

An understanding of the nervous system at virtually any level of analysis requires an understanding of its basic building block, the neuron. The third edition of From Molecules to Networks provides the solid foundation of the morphological, biochemical, and biophysical properties of nerve cells. In keeping with previous editions, the unique content focus on cellular and molecular neurobiology and related computational neuroscience is maintained and enhanced. All chapters have been thoroughly revised for this third edition to reflect the significant advances of the past five years. The new edition expands on the network aspects of cellular neurobiology by adding new coverage of specific research methods (e.g., patch-clamp electrophysiology, including applications for ion channel function and transmitter release; ligand binding; structural methods such as x-ray crystallography). Written and edited by leading experts in the field, the third edition completely and comprehensively updates all chapters of this unique textbook and insures that all references to primary research represent the latest results. - The first treatment of cellular and molecular neuroscience that includes an introduction to mathematical modeling and simulation approaches - 80% updated and new content - New Chapter on "Biophysics of Voltage-Gated Ion Channels" - New Chapter on "Synaptic Plasticity" - Includes a chapter on the Neurobiology of Disease - Highly referenced, comprehensive and quantitative - Full color, professional graphics throughout - All graphics are available in electronic version for teaching purposes




Mathematics for Neuroscientists


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




Computational Electrophysiology


Book Description

Biological systems inherently possess much ambiguity or uncertainty. Computational electrophysiology is the one area, from among the vast and rapidly growing discipline of computational and systems biology, in which computational or mathematical models have succeeded. This textbook provides a practical and quick guide to both computational electrophysiology and numerical bifurcation analysis. Bifurcation analysis is a very powerful tool for the analysis of such highly nonlinear biological systems. Bifurcation theory provides a way to analyze the effect of a parameter change on a system and to detect a critical parameter value when the qualitative nature of the system changes. Included in this work are many examples of numerical computations of bifurcation analysis of various models as well as mathematical models with different abstraction levels from neuroscience and electrophysiology. This volume will benefit graduate and undergraduate students as well as researchers in diverse fields of science.




Modeling in the Neurosciences


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