Stochastic Neuron Models

Stochastic Neuron Models

Author: Priscilla E. Greenwood

Publisher: Springer

Published: 2016-02-02

Total Pages: 82

ISBN-13: 3319269119

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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.


Book Synopsis Stochastic Neuron Models by : Priscilla E. Greenwood

Download or read book Stochastic Neuron Models written by Priscilla E. Greenwood and published by Springer. This book was released on 2016-02-02 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Models for Spike Trains of Single Neurons

Stochastic Models for Spike Trains of Single Neurons

Author: S.K. Srinivasan

Publisher: Springer Science & Business Media

Published: 2013-03-13

Total Pages: 197

ISBN-13: 364248302X

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1 Some basic neurophysiology 4 The neuron 1. 1 4 1. 1. 1 The axon 7 1. 1. 2 The synapse 9 12 1. 1. 3 The soma 1. 1. 4 The dendrites 13 13 1. 2 Types of neurons 2 Signals in the nervous system 14 2. 1 Action potentials as point events - point processes in the nervous system 15 18 2. 2 Spontaneous activi~ in neurons 3 Stochastic modelling of single neuron spike trains 19 3. 1 Characteristics of a neuron spike train 19 3. 2 The mathematical neuron 23 4 Superposition models 26 4. 1 superposition of renewal processes 26 4. 2 Superposition of stationary point processe- limiting behaviour 34 4. 2. 1 Palm functions 35 4. 2. 2 Asymptotic behaviour of n stationary point processes superposed 36 4. 3 Superposition models of neuron spike trains 37 4. 3. 1 Model 4. 1 39 4. 3. 2 Model 4. 2 - A superposition model with 40 two input channels 40 4. 3. 3 Model 4. 3 4. 4 Discussion 41 43 5 Deletion models 5. 1 Deletion models with 1nd~endent interaction of excitatory and inhibitory sequences 44 VI 5. 1. 1 Model 5. 1 The basic deletion model 45 5. 1. 2 Higher-order properties of the sequence of r-events 55 5. 1. 3 Extended version of Model 5. 1 - Model 60 5. 2 5. 2 Models with dependent interaction of excitatory and inhibitory sequences - MOdels 5. 3 and 5.


Book Synopsis Stochastic Models for Spike Trains of Single Neurons by : S.K. Srinivasan

Download or read book Stochastic Models for Spike Trains of Single Neurons written by S.K. Srinivasan and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1 Some basic neurophysiology 4 The neuron 1. 1 4 1. 1. 1 The axon 7 1. 1. 2 The synapse 9 12 1. 1. 3 The soma 1. 1. 4 The dendrites 13 13 1. 2 Types of neurons 2 Signals in the nervous system 14 2. 1 Action potentials as point events - point processes in the nervous system 15 18 2. 2 Spontaneous activi~ in neurons 3 Stochastic modelling of single neuron spike trains 19 3. 1 Characteristics of a neuron spike train 19 3. 2 The mathematical neuron 23 4 Superposition models 26 4. 1 superposition of renewal processes 26 4. 2 Superposition of stationary point processe- limiting behaviour 34 4. 2. 1 Palm functions 35 4. 2. 2 Asymptotic behaviour of n stationary point processes superposed 36 4. 3 Superposition models of neuron spike trains 37 4. 3. 1 Model 4. 1 39 4. 3. 2 Model 4. 2 - A superposition model with 40 two input channels 40 4. 3. 3 Model 4. 3 4. 4 Discussion 41 43 5 Deletion models 5. 1 Deletion models with 1nd~endent interaction of excitatory and inhibitory sequences 44 VI 5. 1. 1 Model 5. 1 The basic deletion model 45 5. 1. 2 Higher-order properties of the sequence of r-events 55 5. 1. 3 Extended version of Model 5. 1 - Model 60 5. 2 5. 2 Models with dependent interaction of excitatory and inhibitory sequences - MOdels 5. 3 and 5.

Neuronal Dynamics

Neuronal Dynamics

Author: Wulfram Gerstner

Publisher: Cambridge University Press

Published: 2014-07-24

Total Pages: 591

ISBN-13: 1107060834

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


Book Synopsis Neuronal Dynamics by : Wulfram Gerstner

Download or read book Neuronal Dynamics written by Wulfram Gerstner and published by Cambridge University Press. This book was released on 2014-07-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.

Stochastic Models of Neural Networks

Stochastic Models of Neural Networks

Author: Claudio Turchetti

Publisher: IOS Press

Published: 2004

Total Pages: 202

ISBN-13: 9784274906268

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Book Synopsis Stochastic Models of Neural Networks by : Claudio Turchetti

Download or read book Stochastic Models of Neural Networks written by Claudio Turchetti and published by IOS Press. This book was released on 2004 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Neuronal Stochastic Variability: Influences on Spiking Dynamics and Network Activity

Neuronal Stochastic Variability: Influences on Spiking Dynamics and Network Activity

Author: Mark D. McDonnell

Publisher: Frontiers Media SA

Published: 2016-07-18

Total Pages: 158

ISBN-13: 2889198847

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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.


Book Synopsis Neuronal Stochastic Variability: Influences on Spiking Dynamics and Network Activity by : Mark D. McDonnell

Download or read book Neuronal Stochastic Variability: Influences on Spiking Dynamics and Network Activity written by Mark D. McDonnell and published by Frontiers Media SA. This book was released on 2016-07-18 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Neural Networks

Neural Networks

Author: Berndt Müller

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 340

ISBN-13: 3642577601

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Neural Networks presents concepts of neural-network models and techniques of parallel distributed processing in a three-step approach: - A brief overview of the neural structure of the brain and the history of neural-network modeling introduces to associative memory, preceptrons, feature-sensitive networks, learning strategies, and practical applications. - The second part covers subjects like statistical physics of spin glasses, the mean-field theory of the Hopfield model, and the "space of interactions" approach to the storage capacity of neural networks. - The final part discusses nine programs with practical demonstrations of neural-network models. The software and source code in C are on a 3 1/2" MS-DOS diskette can be run with Microsoft, Borland, Turbo-C, or compatible compilers.


Book Synopsis Neural Networks by : Berndt Müller

Download or read book Neural Networks written by Berndt Müller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural Networks presents concepts of neural-network models and techniques of parallel distributed processing in a three-step approach: - A brief overview of the neural structure of the brain and the history of neural-network modeling introduces to associative memory, preceptrons, feature-sensitive networks, learning strategies, and practical applications. - The second part covers subjects like statistical physics of spin glasses, the mean-field theory of the Hopfield model, and the "space of interactions" approach to the storage capacity of neural networks. - The final part discusses nine programs with practical demonstrations of neural-network models. The software and source code in C are on a 3 1/2" MS-DOS diskette can be run with Microsoft, Borland, Turbo-C, or compatible compilers.

Spiking Neuron Models

Spiking Neuron Models

Author: Wulfram Gerstner

Publisher: Cambridge University Press

Published: 2002-08-15

Total Pages: 498

ISBN-13: 9780521890793

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Neurons in the brain communicate by short electrical pulses, the so-called action potentials or spikes. How can we understand the process of spike generation? How can we understand information transmission by neurons? What happens if thousands of neurons are coupled together in a seemingly random network? How does the network connectivity determine the activity patterns? And, vice versa, how does the spike activity influence the connectivity pattern? These questions are addressed in this 2002 introduction to spiking neurons aimed at those taking courses in computational neuroscience, theoretical biology, biophysics, or neural networks. The approach will suit students of physics, mathematics, or computer science; it will also be useful for biologists who are interested in mathematical modelling. The text is enhanced by many worked examples and illustrations. There are no mathematical prerequisites beyond what the audience would meet as undergraduates: more advanced techniques are introduced in an elementary, concrete fashion when needed.


Book Synopsis Spiking Neuron Models by : Wulfram Gerstner

Download or read book Spiking Neuron Models written by Wulfram Gerstner and published by Cambridge University Press. This book was released on 2002-08-15 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neurons in the brain communicate by short electrical pulses, the so-called action potentials or spikes. How can we understand the process of spike generation? How can we understand information transmission by neurons? What happens if thousands of neurons are coupled together in a seemingly random network? How does the network connectivity determine the activity patterns? And, vice versa, how does the spike activity influence the connectivity pattern? These questions are addressed in this 2002 introduction to spiking neurons aimed at those taking courses in computational neuroscience, theoretical biology, biophysics, or neural networks. The approach will suit students of physics, mathematics, or computer science; it will also be useful for biologists who are interested in mathematical modelling. The text is enhanced by many worked examples and illustrations. There are no mathematical prerequisites beyond what the audience would meet as undergraduates: more advanced techniques are introduced in an elementary, concrete fashion when needed.

Deterministic and Stochastic Dynamics of Multi-Variable Neuron Models

Deterministic and Stochastic Dynamics of Multi-Variable Neuron Models

Author: Azadeh Khajeh alijani

Publisher: LAP Lambert Academic Publishing

Published: 2012

Total Pages: 188

ISBN-13: 9783659217746

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Neurons are the basic elements of the networks that constitute the computational units of the brain. They dynamically transform input information into sequences of electrical pulses. Therefore it is crucial to understand this transformation and identify simple neuron models which accurately reproduce the known features of biological neurons. This book addresses three different features of neurons. We start by exploring the effect of subthreshold resonance on the response of a periodically forced neuron and show qualitatively distinct responses including mode locking and chaos. Then we will consider an experimentally verified model with realistic spike-generating mechanism and study the effect of filtered synaptic fluctuations on the firing-rate response of the neuron. Finally, a model is studied that incorporates threshold variability of neurons. We determine the modulation of the input-output properties of the model due to oscillatory inputs and in the presence of synaptic fluctuations. This book would be useful to understand the above properties of neurons and to learn some mathematical methods in analyzing deterministic and stochastic neuron models.


Book Synopsis Deterministic and Stochastic Dynamics of Multi-Variable Neuron Models by : Azadeh Khajeh alijani

Download or read book Deterministic and Stochastic Dynamics of Multi-Variable Neuron Models written by Azadeh Khajeh alijani and published by LAP Lambert Academic Publishing. This book was released on 2012 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neurons are the basic elements of the networks that constitute the computational units of the brain. They dynamically transform input information into sequences of electrical pulses. Therefore it is crucial to understand this transformation and identify simple neuron models which accurately reproduce the known features of biological neurons. This book addresses three different features of neurons. We start by exploring the effect of subthreshold resonance on the response of a periodically forced neuron and show qualitatively distinct responses including mode locking and chaos. Then we will consider an experimentally verified model with realistic spike-generating mechanism and study the effect of filtered synaptic fluctuations on the firing-rate response of the neuron. Finally, a model is studied that incorporates threshold variability of neurons. We determine the modulation of the input-output properties of the model due to oscillatory inputs and in the presence of synaptic fluctuations. This book would be useful to understand the above properties of neurons and to learn some mathematical methods in analyzing deterministic and stochastic neuron models.

Stochastic Biomathematical Models

Stochastic Biomathematical Models

Author: Mostafa Bachar

Publisher: Springer

Published: 2012-10-19

Total Pages: 216

ISBN-13: 3642321577

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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.


Book Synopsis Stochastic Biomathematical Models by : Mostafa Bachar

Download or read book Stochastic Biomathematical Models written by Mostafa Bachar and published by Springer. This book was released on 2012-10-19 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrimination and Control in Stochastic Neuron Models

Discrimination and Control in Stochastic Neuron Models

Author: Jing Kang

Publisher:

Published: 2009

Total Pages: 0

ISBN-13:

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Book Synopsis Discrimination and Control in Stochastic Neuron Models by : Jing Kang

Download or read book Discrimination and Control in Stochastic Neuron Models written by Jing Kang and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: