Stochastic Models for Spike Trains of Single Neurons

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 Stochastic 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