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AuthorSampath, G. author
TitleStochastic Models for Spike Trains of Single Neurons [electronic resource] / by G. Sampath, S. K. Srinivasan
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1977
Connect tohttp://dx.doi.org/10.1007/978-3-642-48302-8
Descript VIII, 190 p. online resource

SUMMARY

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 activĩ 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 1ndẽndent 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


CONTENT

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 โ{128}{148} 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 โ{128}{148} 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 โ{128}{148} 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 -- 10.2 Hyperpolarisation 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


Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes



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