Statistical approach in search for optimal signal in simple olfactory neuronal models

Ergodicity and parameter estimates in auditory neural circuits

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.

Efficiency of rate and latency coding with respect to metabolic cost and time

Recent studies on the theoretical performance of latency and rate code in single neurons have revealed that the ultimate accuracy is affected in a nontrivial way by aspects such as the level of spontaneous activity of presynaptic neurons, amount of neuronal noise or the duration of the time window used to determine the firing rate. This study explores how the optimal decoding performance and the corresponding conditions change when the energy expenditure of a neuron in order to spike and maintain the resting membrane potential is accounted for. It is shown that a nonzero amount of spontaneous activity remains essential for both the latency and the rate coding. Moreover, the optimal level of spontaneous activity does not change so much with respect to the intensity of the applied stimulus. Furthermore, the efficiency of the temporal and the rate code converge to an identical finite value if the neuronal activity is observed for an unlimited period of time.