Stochastic Models for Spike Trains of Single Neurons

1. Front Matter

   Pages I-VII

   PDF

2. Introduction

   • G. Sampath, S. K. Srinivasan

   Pages 1-3

3. Some Basic Neurophysiology

   • G. Sampath, S. K. Srinivasan

   Pages 4-13

4. Signals in the Nervous System

   • G. Sampath, S. K. Srinivasan

   Pages 14-18

5. Stochastic Modelling of Single Neuron Spike Trains

   • G. Sampath, S. K. Srinivasan

   Pages 19-25

6. Superposition Models

   • G. Sampath, S. K. Srinivasan

   Pages 26-42

7. Deletion Models

   • G. Sampath, S. K. Srinivasan

   Pages 43-66

8. Diffusion Models

   • G. Sampath, S. K. Srinivasan

   Pages 67-88

9. Counter Models

   • G. Sampath, S. K. Srinivasan

   Pages 89-101

10. Discrete State Models

    • G. Sampath, S. K. Srinivasan

    Pages 102-134

11. Continuous State Models

    • G. Sampath, S. K. Srinivasan

    Pages 135-168

12. Real Neurons and Mathematical Models

    • G. Sampath, S. K. Srinivasan

    Pages 169-177

13. Back Matter

    Pages 178-192

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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.

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

• Dept. of Mathematics, Indian Institute of Technology, Madras, India

  G. Sampath, S. K. Srinivasan

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