Stochastic Models for Spike Trains of Single Neurons PDF Download
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Author: S.K. Srinivasan
Publisher: Springer Science & Business Media
ISBN: 364248302X
Category : Mathematics
Languages : en
Pages : 197
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Book Description
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.
Author: S.K. Srinivasan
Publisher: Springer Science & Business Media
ISBN: 364248302X
Category : Mathematics
Languages : en
Pages : 197
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Book Description
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.
Author: Wulfram Gerstner
Publisher: Cambridge University Press
ISBN: 1107060834
Category : Computers
Languages : en
Pages : 591
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Book Description
This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.
Author: G. Sampath
Publisher:
ISBN:
Category : Action potentials (Electrophysiology)
Languages : en
Pages : 470
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Book Description
Author: Zhe Chen
Publisher: Cambridge University Press
ISBN: 1107079195
Category : Computers
Languages : en
Pages : 397
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Book Description
An authoritative and in-depth treatment of state space methods, with a range of applications in neural and clinical data.
Author: Wulfram Gerstner
Publisher: Cambridge University Press
ISBN: 9780521890793
Category : Computers
Languages : en
Pages : 498
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Book Description
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.
Author: Sonja Grün
Publisher: Springer Science & Business Media
ISBN: 1441956751
Category : Medical
Languages : en
Pages : 447
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Book Description
Solid and transparent data analysis is the most important basis for reliable interpretation of experiments. The technique of parallel spike train recordings using multi-electrode arrangements has been available for many decades now, but only recently gained wide popularity among electro physiologists. Many traditional analysis methods are based on firing rates obtained by trial-averaging, and some of the assumptions for such procedures to work can be ignored without serious consequences. The situation is different for correlation analysis, the result of which may be considerably distorted if certain critical assumptions are violated. The focus of this book is on concepts and methods of correlation analysis (synchrony, patterns, rate covariance), combined with a solid introduction into approaches for single spike trains, which represent the basis of correlations analysis. The book also emphasizes pitfalls and potential wrong interpretations of data due to violations of critical assumptions.
Author: Henry Markram
Publisher: Frontiers E-books
ISBN: 2889190439
Category :
Languages : en
Pages : 575
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Book Description
Hebb's postulate provided a crucial framework to understand synaptic alterations underlying learning and memory. Hebb's theory proposed that neurons that fire together, also wire together, which provided the logical framework for the strengthening of synapses. Weakening of synapses was however addressed by "not being strengthened", and it was only later that the active decrease of synaptic strength was introduced through the discovery of long-term depression caused by low frequency stimulation of the presynaptic neuron. In 1994, it was found that the precise relative timing of pre and postynaptic spikes determined not only the magnitude, but also the direction of synaptic alterations when two neurons are active together. Neurons that fire together may therefore not necessarily wire together if the precise timing of the spikes involved are not tighly correlated. In the subsequent 15 years, Spike Timing Dependent Plasticity (STDP) has been found in multiple brain brain regions and in many different species. The size and shape of the time windows in which positive and negative changes can be made vary for different brain regions, but the core principle of spike timing dependent changes remain. A large number of theoretical studies have also been conducted during this period that explore the computational function of this driving principle and STDP algorithms have become the main learning algorithm when modeling neural networks. This Research Topic will bring together all the key experimental and theoretical research on STDP.
Author: A. V. Holden
Publisher: Springer Science & Business Media
ISBN: 3642463452
Category : Mathematics
Languages : en
Pages : 378
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Book Description
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.
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: Leandro Pardo
Publisher: Springer
ISBN: 3642208533
Category : Technology & Engineering
Languages : en
Pages : 498
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Book Description
Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately. This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations. Several researchers, colleagues, friends and students of Professor María Luisa Menéndez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work.
