Publication details

Ergodicity and parameter estimates in auditory neural circuits


TÓTH Peter Gabriel MARŠÁLEK Petr POKORA Ondřej

Year of publication 2018
Type Article in Periodical
Magazine / Source Biological Cybernetics
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords auditory pathway; ergodic theory; ergodicity; circular statistics; interspike interval; probability distribution function; sensory modality; spike train; spike timing jitter; vector strength
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Description This paper discusses ergodic properties and circular statistical characteristics in neuronal spike trains. Ergodicity means that the average taken over a long time period and over smaller population should equal to the average in less time and larger population. Objectives are to show simple examples of design and validation of a neuronal model, where the ergodicity assumption helps finding correspondence between variables and parameters. Methods used are analytical and numerical computations, numerical models of phenomenological spiking neurons and neuronal circuits. Results obtained using these methods are the following. They are: formula to calculate vector strength of neural spike timing in dependence of the spike train parameters, description of parameters of spike train variability and model of output spiking density based on assumption of the computation realized by sound localization neural circuit. Theoretical results are illustrated by references to experimental data. Examples of neurons, where spike trains have and have not the ergodic property are then discussed.
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