Author: Henry C. Tuckwell
Publisher: Cambridge University Press
ISBN: 9780511623202
Category : Mathematics
Languages : en
Pages : 265
Book Description
The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and nonspaceclamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.
Introduction to Theoretical Neurobiology: Volume 2, Nonlinear and Stochastic Theories
Author: Henry C. Tuckwell
Publisher: Cambridge University Press
ISBN: 9780511623202
Category : Mathematics
Languages : en
Pages : 265
Book Description
The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and nonspaceclamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.
Publisher: Cambridge University Press
ISBN: 9780511623202
Category : Mathematics
Languages : en
Pages : 265
Book Description
The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and nonspaceclamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.
Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and Dendritic Structure
Author: Henry C. Tuckwell
Publisher: Cambridge University Press
ISBN: 9780521022224
Category : Science
Languages : en
Pages : 304
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.
Publisher: Cambridge University Press
ISBN: 9780521022224
Category : Science
Languages : en
Pages : 304
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.
Introduction to theoretical neurobiology
Author: Henry Clavering Tuckwell
Publisher:
ISBN:
Category : Neural transmission
Languages : en
Pages : 0
Book Description
Publisher:
ISBN:
Category : Neural transmission
Languages : en
Pages : 0
Book Description
Stochastic Processes in the Neurosciences
Author: Henry C. Tuckwell
Publisher: SIAM
ISBN: 9781611970159
Category : Technology & Engineering
Languages : en
Pages : 134
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.
Publisher: SIAM
ISBN: 9781611970159
Category : Technology & Engineering
Languages : en
Pages : 134
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.
Stochastic Methods in Neuroscience
Author: Carlo Laing
Publisher: OUP Oxford
ISBN: 0191607983
Category : Mathematics
Languages : en
Pages : 417
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 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.
Publisher: OUP Oxford
ISBN: 0191607983
Category : Mathematics
Languages : en
Pages : 417
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 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.
Biological Kinetics
Author: Lee A. Segel
Publisher: Cambridge University Press
ISBN: 9780521391849
Category : Mathematics
Languages : en
Pages : 234
Book Description
This book demonstrates how an understanding of biological kinetics can lead to knowledge about the biological model being examined.
Publisher: Cambridge University Press
ISBN: 9780521391849
Category : Mathematics
Languages : en
Pages : 234
Book Description
This book demonstrates how an understanding of biological kinetics can lead to knowledge about the biological model being examined.
Handbook on Biological Networks
Author: Stefano Boccaletti
Publisher: World Scientific
ISBN: 9812838805
Category : Mathematics
Languages : en
Pages : 465
Book Description
Networked systems are all around us. The accumulated evidence of systems as complex as a cell cannot be fully understood by studying only their isolated constituents, giving rise to a new area of interest in research OCo the study of complex networks . In a broad sense, biological networks have been one of the most studied networks, and the field has benefited from many important contributions. By understanding and modeling the structure of a biological network, a better perception of its dynamical and functional behavior is to be expected. This unique book compiles the most relevant results and novel insights provided by network theory in the biological sciences, ranging from the structure and dynamics of the brain to cellular and protein networks and to population-level biology. Sample Chapter(s). Chapter 1: Introduction (61 KB). Contents: Networks at the Cellular Level: The Structural Network Properties of Biological Systems (M Brilli & P Li); Dynamics of Multicellular Synthetic Gene Networks (E Ullner et al.); Boolean Networks in Inference and Dynamic Modeling of Biological Systems at the Molecular and Physiological Level (J Thakar & R Albert); Complexity of Boolean Dynamics in Simple Models of Signaling Networks and in Real Genetic Networks (A D az-Guilera & R ulvarez-Buylla); Geometry and Topology of Folding Landscapes (L Bongini & L Casetti); Elastic Network Models for Biomolecular Dynamics: Theory and Application to Membrane Proteins and Viruses (T R Lezon et al.); Metabolic Networks (M C Palumbo et al.); Brain Networks: The Human Brain Network (O Sporns); Brain Network Analysis from High-Resolution EEG Signals (F De Vico Fallani & F Babiloni); An Optimization Approach to the Structure of the Neuronal layout of C elegans (A Arenas et al.); Cultured Neuronal Networks Express Complex Patterns of Activity and Morphological Memory (N Raichman et al.); Synchrony and Precise Timing in Complex Neural Networks (R-M Memmesheimer & M Timme); Networks at the Individual and Population Levels: Ideas for Moving Beyond Structure to Dynamics of Ecological Networks (D B Stouffer et al.); Evolutionary Models for Simple Biosystems (F Bagnoli); Evolution of Cooperation in Adaptive Social Networks (S Van Segbroeck et al.); From Animal Collectives and Complex Networks to Decentralized Motion Control Strategies (A Buscarino et al.); Interplay of Network State and Topology in Epidemic Dynamics (T Gross). Readership: Advanced undergraduates, graduate students and researchers interested in the study of complex networks in a wide range of biological processes and systems."
Publisher: World Scientific
ISBN: 9812838805
Category : Mathematics
Languages : en
Pages : 465
Book Description
Networked systems are all around us. The accumulated evidence of systems as complex as a cell cannot be fully understood by studying only their isolated constituents, giving rise to a new area of interest in research OCo the study of complex networks . In a broad sense, biological networks have been one of the most studied networks, and the field has benefited from many important contributions. By understanding and modeling the structure of a biological network, a better perception of its dynamical and functional behavior is to be expected. This unique book compiles the most relevant results and novel insights provided by network theory in the biological sciences, ranging from the structure and dynamics of the brain to cellular and protein networks and to population-level biology. Sample Chapter(s). Chapter 1: Introduction (61 KB). Contents: Networks at the Cellular Level: The Structural Network Properties of Biological Systems (M Brilli & P Li); Dynamics of Multicellular Synthetic Gene Networks (E Ullner et al.); Boolean Networks in Inference and Dynamic Modeling of Biological Systems at the Molecular and Physiological Level (J Thakar & R Albert); Complexity of Boolean Dynamics in Simple Models of Signaling Networks and in Real Genetic Networks (A D az-Guilera & R ulvarez-Buylla); Geometry and Topology of Folding Landscapes (L Bongini & L Casetti); Elastic Network Models for Biomolecular Dynamics: Theory and Application to Membrane Proteins and Viruses (T R Lezon et al.); Metabolic Networks (M C Palumbo et al.); Brain Networks: The Human Brain Network (O Sporns); Brain Network Analysis from High-Resolution EEG Signals (F De Vico Fallani & F Babiloni); An Optimization Approach to the Structure of the Neuronal layout of C elegans (A Arenas et al.); Cultured Neuronal Networks Express Complex Patterns of Activity and Morphological Memory (N Raichman et al.); Synchrony and Precise Timing in Complex Neural Networks (R-M Memmesheimer & M Timme); Networks at the Individual and Population Levels: Ideas for Moving Beyond Structure to Dynamics of Ecological Networks (D B Stouffer et al.); Evolutionary Models for Simple Biosystems (F Bagnoli); Evolution of Cooperation in Adaptive Social Networks (S Van Segbroeck et al.); From Animal Collectives and Complex Networks to Decentralized Motion Control Strategies (A Buscarino et al.); Interplay of Network State and Topology in Epidemic Dynamics (T Gross). Readership: Advanced undergraduates, graduate students and researchers interested in the study of complex networks in a wide range of biological processes and systems."
Stochastic Biomathematical Models
Author: Mostafa Bachar
Publisher: Springer
ISBN: 3642321577
Category : Mathematics
Languages : en
Pages : 216
Book Description
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.
Publisher: Springer
ISBN: 3642321577
Category : Mathematics
Languages : en
Pages : 216
Book Description
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.
Modeling in the Neurosciences
Author: R.R. Poznanski
Publisher: Routledge
ISBN: 1351430963
Category : Science
Languages : en
Pages : 562
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
Publisher: Routledge
ISBN: 1351430963
Category : Science
Languages : en
Pages : 562
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
Computational Neuroscience
Author: J.M. Bower
Publisher: Elsevier
ISBN: 9780444503077
Category : Computers
Languages : en
Pages : 1114
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.
Publisher: Elsevier
ISBN: 9780444503077
Category : Computers
Languages : en
Pages : 1114
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.