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Stochastic Models for Spike Trains of Single Neurons

  • G. Sampath
  • S. K. Srinivasan

Part of the Lecture Notes in Biomathematics book series (LNBM, volume 16)

Table of contents

  1. Front Matter
    Pages I-VII
  2. G. Sampath, S. K. Srinivasan
    Pages 1-3
  3. G. Sampath, S. K. Srinivasan
    Pages 4-13
  4. G. Sampath, S. K. Srinivasan
    Pages 14-18
  5. G. Sampath, S. K. Srinivasan
    Pages 19-25
  6. G. Sampath, S. K. Srinivasan
    Pages 26-42
  7. G. Sampath, S. K. Srinivasan
    Pages 43-66
  8. G. Sampath, S. K. Srinivasan
    Pages 67-88
  9. G. Sampath, S. K. Srinivasan
    Pages 89-101
  10. G. Sampath, S. K. Srinivasan
    Pages 102-134
  11. G. Sampath, S. K. Srinivasan
    Pages 135-168
  12. G. Sampath, S. K. Srinivasan
    Pages 169-177
  13. Back Matter
    Pages 178-192

About this book

Introduction

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.

Keywords

Aktionspotential Biomathematik Erregung (Physiol.) Nervenzelle Stochastisches Modell equation function

Authors and affiliations

  • G. Sampath
    • 1
  • S. K. Srinivasan
    • 1
  1. 1.Dept. of MathematicsIndian Institute of TechnologyMadrasIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-48302-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1977
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-08257-6
  • Online ISBN 978-3-642-48302-8
  • Series Print ISSN 0341-633X
  • Buy this book on publisher's site