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.
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.
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:
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.
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.
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.
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.
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:
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.
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.
Download or read book Stochastic Methods in Neuroscience written by Carlo Laing and published by Oxford University Press. This book was released on 2010 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stimulus Coding and Synchrony in Stochastic Neuron Models written by Jakub Cieniak and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A stochastic leaky integrate-and-fire neuron model was implemented in this study to simulate the spiking activity of the electrosensory "P-unit" receptor neurons of the weakly electric fish Apteronotus leptorhynchus. In the context of sensory coding, these cells have been previously shown to respond in experiment to natural random narrowband signals with either a linear or nonlinear coding scheme, depending on the intrinsic firing rate of the cell in the absence of external stimulation. It was hypothesised in this study that this duality is due to the relation of the stimulus to the neuron's excitation threshold. This hypothesis was validated with the model by lowering the threshold of the neuron or increasing its intrinsic noise, or randomness, either of which made the relation between firing rate and input strength more linear. Furthermore, synchronous P-unit firing to a common input also plays a role in decoding the stimulus at deeper levels of the neural pathways. Synchronisation and desynchronisation between multiple model responses for different types of natural communication signals were shown to agree with experimental observations. A novel result of resonance-induced synchrony enhancement of P-units to certain communication frequencies was also found.
Download or read book Advanced Models of Neural Networks written by Gerasimos G. Rigatos and published by Springer. This book was released on 2014-08-27 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete study on neural structures exhibiting nonlinear and stochastic dynamics, elaborating on neural dynamics by introducing advanced models of neural networks. It overviews the main findings in the modelling of neural dynamics in terms of electrical circuits and examines their stability properties with the use of dynamical systems theory. It is suitable for researchers and postgraduate students engaged with neural networks and dynamical systems theory.
Download or read book Stochastic Phase Dynamics in Neuron Models and Spike Time Reliability written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The present thesis is concerned with the stochastic phase dynamics of neuron models and spike time reliability. It is well known that noise exists in all natural systems, and some beneficial effects of noise, such as coherence resonance and noise-induced synchrony, have been observed. However, it is usually difficult to separate the effect of the nonlinear system itself from the effect of noise on the system's phase dynamics. In this thesis, we present a stochastic theory to investigate the stochastic phase dynamics of a nonlinear system. The method we use here, called ``the stochastic multi-scale method'', allows a stochastic phase description of a system, in which the contributions from the deterministic system itself and from the noise are clearly seen. Firstly, we use this method to study the noise-induced coherence resonance of a single quiescent ``neuron" (i.e. an oscillator) near a Hopf bifurcation. By calculating the expected values of the neuron's stochastic amplitude and phase, we derive analytically the dependence of the frequency of coherent oscillations on the noise level for different types of models. These analytical results are in good agreement with numerical results we obtained. The analysis provides an explanation for the occurrence of a peak in coherence measured at an intermediate noise level, which is a defining feature of the coherence resonance. Secondly, this work is extended to study the interaction and competition of the coupling and noise on the synchrony in two weakly coupled neurons. Through numerical simulations, we demonstrate that noise-induced mixed-mode oscillations occur due to the existence of multistability states for the deterministic oscillators with weak coupling. We also use the standard multi-scale method to approximate the multistability states of a normal form of such a weakly coupled system. Finally we focus on the spike time reliability that refers to the phenomenon: the repetitive application of a stochastic stimulus t.
Download or read book Signal Transmission in Stochastic Neuron Models with Non white Or Non Gaussian Noise written by Felix Droste and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Models of the Stochastic Activity of Neurones written by A. V. Holden and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes have grown from a series of seminars given at Leeds between 1972 and 1975. They represent an attempt to gather together the different kinds of model which have been proposed to account for the stochastic activity of neurones, and to provide an introduction to this area of mathematical biology. A striking feature of the electrical activity of the nervous system is that it appears stochastic: this is apparent at all levels of recording, ranging from intracellular recordings to the electroencephalogram. The chapters start with fluctuations in membrane potential, proceed through single unit and synaptic activity and end with the behaviour of large aggregates of neurones: L have chgaen this seque~~e\/~~';uggest that the interesting behaviourr~f :the nervous system - its individuality, variability and dynamic forms - may in part result from the stochastic behaviour of its components. I would like to thank Dr. Julio Rubio for reading and commenting on the drafts, Mrs. Doris Beighton for producing the final typescript and Mr. Peter Hargreaves for preparing the figures.
Download or read book The Noisy Brain written by Edmund T. Rolls and published by . This book was released on 2010-01-28 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The activity of neurons in the brain is noisy in that the neuronal firing times are random for a given mean rate. The Noisy Brain shows that this is fundamental to understanding many aspects of brain function, including probabilistic decision-making, perception, memory recall, short-term memory, attention, and even creativity. There are many applications too of this understanding, to for example memory and attentional disorders, aging, schizophrenia, and obsessive-compulsive disorder.
