Stochastic Methods in Neuroscience
Title | Stochastic Methods in Neuroscience PDF eBook |
Author | Carlo Laing |
Publisher | Oxford University Press |
Total Pages | 399 |
Release | 2010 |
Genre | Mathematics |
ISBN | 0199235074 |
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.
Stochastic Processes in the Neurosciences
Title | Stochastic Processes in the Neurosciences PDF eBook |
Author | Henry C. Tuckwell |
Publisher | SIAM |
Total Pages | 134 |
Release | 1989-01-01 |
Genre | Technology & Engineering |
ISBN | 9781611970159 |
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.
Stochastic Neuron Models
Title | Stochastic Neuron Models PDF eBook |
Author | Priscilla E. Greenwood |
Publisher | Springer |
Total Pages | 82 |
Release | 2016-02-02 |
Genre | Mathematics |
ISBN | 3319269119 |
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain Research Centre at the University of British Columbia.
Stochastic Biomathematical Models
Title | Stochastic Biomathematical Models PDF eBook |
Author | Mostafa Bachar |
Publisher | Springer |
Total Pages | 216 |
Release | 2012-10-19 |
Genre | Mathematics |
ISBN | 3642321577 |
Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.
Phase Resetting in Medicine and Biology
Title | Phase Resetting in Medicine and Biology PDF eBook |
Author | Peter A. Tass |
Publisher | Springer |
Total Pages | 0 |
Release | 1999-05-21 |
Genre | Science |
ISBN | 9783540656975 |
This book presents a new theoretical approach to phase resetting and stimulation-induced synchronization and desynchronization in a population of oscillators. The author uses stochastic methods from statistical mechanics and applies his theory to models of practical importance in physiology and neuroscience. The book is accessible to readers not familiar with the mathematical formalism. The author also proposes improvements to stimulation techniques as used by neurologists and neurosurgeons in the context of Parkinson's disease and MEG/EEG data analysis.
Mathematics for Neuroscientists
Title | Mathematics for Neuroscientists PDF eBook |
Author | Fabrizio Gabbiani |
Publisher | Academic Press |
Total Pages | 630 |
Release | 2017-02-04 |
Genre | Mathematics |
ISBN | 0128019069 |
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
Neuronal Stochastic Variability: Influences on Spiking Dynamics and Network Activity
Title | Neuronal Stochastic Variability: Influences on Spiking Dynamics and Network Activity PDF eBook |
Author | Mark D. McDonnell |
Publisher | Frontiers Media SA |
Total Pages | 158 |
Release | 2016-07-18 |
Genre | Neurosciences. Biological psychiatry. Neuropsychiatry |
ISBN | 2889198847 |
Stochastic fluctuations are intrinsic to and unavoidable at every stage of neural dynamics. For example, ion channels undergo random conformational changes, neurotransmitter release at synapses is discrete and probabilistic, and neural networks are embedded in spontaneous background activity. The mathematical and computational tool sets contributing to our understanding of stochastic neural dynamics have expanded rapidly in recent years. New theories have emerged detailing the dynamics and computational power of the balanced state in recurrent networks. At the cellular level, novel stochastic extensions to the classical Hodgkin-Huxley model have enlarged our understanding of neuronal dynamics and action potential initiation. Analytical methods have been developed that allow for the calculation of the firing statistics of simplified phenomenological integrate-and-fire models, taking into account adaptation currents or temporal correlations of the noise. This Research Topic is focused on identified physiological/internal noise sources and mechanisms. By "internal", we mean variability that is generated by intrinsic biophysical processes. This includes noise at a range of scales, from ion channels to synapses to neurons to networks. The contributions in this Research Topic introduce innovative mathematical analysis and/or computational methods that relate to empirical measures of neural activity and illuminate the functional role of intrinsic noise in the brain.