Stochastic Models for Spike Trains of Single Neurons

by S.K. Srinivasan, Gopalan Sampath

Overview

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 Shastic 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.

Product Details

ISBN-13:	9783540082576
Publisher:	Springer Berlin Heidelberg
Publication date:	08/01/1977
Series:	Lecture Notes in Biomathematics , #16
Edition description:	Softcover reprint of the original 1st ed. 1977
Pages:	190
Product dimensions:	6.69(w) x 9.61(h) x 0.02(d)

Table of Contents

1 Some basic neurophysiology.- 1.1 The neuron.- 1.2 Types of neurons.- 2 Signals in the nervous system.- 2.1 Action potentials as point events — point processes in the nervous system.- 2.2 Spontaneous activity in neurons.- 3 Shastic modelling of single neuron spike trains.- 3.1 Characteristics of a neuron spike train.- 3.2 The mathematical neuron.- 4 Superposition models.- 4.1 Superposition of renewal processes.- 4.2 Superposition of stationary point processes — limiting behaviour.- 4.3 Superposition models of neuron spike trains.- 4.4 Discussion.- 5 Deletion models.- 5.1 Deletion models with independent interaction of excitatory and inhibitory sequences.- 5.2 Models with dependent interaction of excitatory and inhibitory sequences — Models 5.3 and 5.4.- 5.3 Discussion.- 6 Diffusion models.- 6.1 The diffusion equation.- 6.2 Diffusion models for neuron firing sequences.- 6.3 Discussion.- 7 Counter models.- 7.1 Theory of counters.- 7.2 Counter model extensions of deletion models with independent interaction of e-and i-events.- 7.3 Counter model extensions of deletion models with dependent interaction of e-and i-events.- 7.4 Counter models with threshold behaviour 100 7.4.1 Model 7.6.- 7.5 Discussion.- 8 Discrete state models.- 8.1 Birth and death processes.- 8.2 Models with excitatoiy inputs only.- 8.3 Models with independent interaction of e-events and i-events.- 8.4 Models with dependent interaction of input sequaices.- 8.5 Discussion.- 9 Continuous state models.- 9.1 Cumulative processes.- 9.2 Models with only one input sequence.- 9.3 Models with independent interaction of e-and i-events.- 9.4 Models with dependent interaction of e- and i-events.- 9.5 Discussion.- 10 Real neurons and mathematical models.- 10.1 Decay of the membrane potential.- 10.2Hyperpolarisation of the membrane.- 10.3 Refractoriness and threshold.- 10.4 Spatial summation.- 10.5 Other properties of neurons.- 10.6 The neuron as a black box.- 10.7 Spike trains and renewal processes.- 10.8 Conclusion.- References.