Ergodicity and parameter estimates in auditory neural circuits

Abstract

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 the average in less time and larger population. The objectives are to show simple examples of design and validation of a neuronal model, where the ergodicity assumption helps find correspondence between variables and parameters. The 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: a formula to calculate vector strength of neural spike timing dependent on 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 do not have the ergodic property are then discussed.

On the precision of neural computation with interaural time differences in the medial superior olive

“…As the lower bound we can also use circular normal density function, the difference is negligible, not shown. The conditions, when it is possible to interchange the estimated probability density functions of regular normal (Gaussian) and circular normal densities are discussed in detail in [Toth et al, 2018]. Comparison of time constants and sound periods in the model presented here will answer a tentative question: What is the highest slope of the ITD interpolation curve, such that it gives the resolution of well known minimum audible angle in the midline (ITD = 0), which is 4 • in angular degrees?…”

“…Two estimate errors are present in this Figure . The first is the mismatch between the use of Gaussian (normal) probability density function, as it is used in the experimental literature, and a circular statistics. More details of the circular statistics use in the sound localization context are explained in the article on the ergodic assumption by [Toth et al, 2018]. The first error is shown here as the green curve.…”

“…Towards the analytical descriptions it is important to note that other periodic functions can be used as the ITD readout curves. In [Toth et al, 2018] we have compared the Sine function with the circular beta density, circular normal density, and other alternative functions. To impose periodic and infinite boundaries to the problem, regular normal density and circular normal density have been used and tested in previous versions of our model.…”

“…Historical comments on Jeffress papers are summarized by Cariani in Scholarpedia [Cariani, 2011]. A plausible explanation of the microsecond precision of the MSO circuit describes the neural computation by leading edges of action potentials and post-synaptic potentials, [Marsalek, 2000], [Toth et al, 2018].…”