Introduction to Theoretical Neurobiology: Linear cable theory and dendritic structure PDF Download
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Author: Henry Clavering Tuckwell
Publisher:
ISBN:
Category : Mathematical models
Languages : en
Pages : 0
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Book Description
Author: Henry Clavering Tuckwell
Publisher:
ISBN:
Category : Mathematical models
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Henry Clavering Tuckwell
Publisher: Cambridge University Press
ISBN: 0521350964
Category : Mathematical models
Languages : en
Pages : 307
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Book Description
Explaining the basic properties of a neuron, this volume develops mathematical theories for the way neurons respond to the various stimuli they receive. It contains descriptions and analyses of the principal mathematical models, providing a brief review of the basic neuroanatomical and neurophysiological facts with the mathematical theories.
Author: Henry C. Tuckwell
Publisher: Cambridge University Press
ISBN: 9780521022224
Category : Science
Languages : en
Pages : 304
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Book Description
The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron--an electrically active nerve cell--and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principle mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two some familiarity with differential equations and linear algebra is desirable.
Author: Helge Holden
Publisher: American Mathematical Soc.
ISBN: 0821875744
Category : Mathematics
Languages : en
Pages : 409
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Book Description
This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions. There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particu
Author: R.R. Poznanski
Publisher: Routledge
ISBN: 1351430963
Category : Science
Languages : en
Pages : 562
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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: Dorian Florescu
Publisher: Springer
ISBN: 3319570811
Category : Technology & Engineering
Languages : en
Pages : 148
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Book Description
This work is motivated by the ongoing open question of how information in the outside world is represented and processed by the brain. Consequently, several novel methods are developed. A new mathematical formulation is proposed for the encoding and decoding of analog signals using integrate-and-fire neuron models. Based on this formulation, a novel algorithm, significantly faster than the state-of-the-art method, is proposed for reconstructing the input of the neuron. Two new identification methods are proposed for neural circuits comprising a filter in series with a spiking neuron model. These methods reduce the number of assumptions made by the state-of-the-art identification framework, allowing for a wider range of models of sensory processing circuits to be inferred directly from input-output observations. A third contribution is an algorithm that computes the spike time sequence generated by an integrate-and-fire neuron model in response to the output of a linear filter, given the input of the filter encoded with the same neuron model.
Author: Greg Conradi Smith
Publisher: Cambridge University Press
ISBN: 1108686613
Category : Science
Languages : en
Pages : 395
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Book Description
What every neuroscientist should know about the mathematical modeling of excitable cells. Combining empirical physiology and nonlinear dynamics, this text provides an introduction to the simulation and modeling of dynamic phenomena in cell biology and neuroscience. It introduces mathematical modeling techniques alongside cellular electrophysiology. Topics include membrane transport and diffusion, the biophysics of excitable membranes, the gating of voltage and ligand-gated ion channels, intracellular calcium signalling, and electrical bursting in neurons and other excitable cell types. It introduces mathematical modeling techniques such as ordinary differential equations, phase plane, and bifurcation analysis of single-compartment neuron models. With analytical and computational problem sets, this book is suitable for life sciences majors, in biology to neuroscience, with one year of calculus, as well as graduate students looking for a primer on membrane excitability and calcium signalling.
Author: Jaap Pelt
Publisher: Elsevier
ISBN: 0444818197
Category : Medical
Languages : en
Pages : 463
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Book Description
This book concentrates on the organizational level of neurons and neuronal networks under the unifying theme "The Self-Organizing Brain - From Growth Cones to Functional Networks". Such a theme is attractive because it incorporates all phases in the emergence of complexity and (adaptive) organization, as well as involving processes that remain operative in the mature state. The order of the sections follows successive levels of organization from neuronal growth cones, neurite formation, neuronal morphology and signal processing to network development, network dynamics and, finally, to the formation of functional circuits.
Author: Thomas M. McKenna
Publisher: Academic Press
ISBN: 1483296067
Category : Computers
Languages : en
Pages : 663
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Book Description
This book contains twenty-two original contributions that provide a comprehensive overview of computational approaches to understanding a single neuron structure. The focus on cellular-level processes is twofold. From a computational neuroscience perspective, a thorough understanding of the information processing performed by single neurons leads to an understanding of circuit- and systems-level activity. From the standpoint of artificial neural networks (ANNs), a single real neuron is as complex an operational unit as an entire ANN, and formalizing the complex computations performed by real neurons is essential to the design of enhanced processor elements for use in the next generation of ANNs.The book covers computation in dendrites and spines, computational aspects of ion channels, synapses, patterned discharge and multistate neurons, and stochastic models of neuron dynamics. It is the most up-to-date presentation of biophysical and computational methods.
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.
