Optimum signal in a diffusion leaky integrate-and-fire neuronal model

An optimum signal in the Ornstein-Uhlenbeck neuronal model is determined on the basis of interspike interval data. Two criteria are proposed for this purpose. The first, the classical one, is based on searching for maxima of the slope of the frequency transfer function. The second one uses maximum of the Fisher information, which is, under certain conditions, the inverse variance of the best possible estimator. The Fisher information is further normalized with respect to the time required to make the observation on which the signal estimation is performed. Three variants of the model are investigated. Beside the basic one, we use the version obtained by inclusion of the refractory period. Finally, we investigate such a version of the model in which signal and the input parameter of the model are in a nonlinear relationship. The results show that despite qualitative similarity between the criteria, there is substantial quantitative difference. As a common feature, we found that in the Ornstein-Uhlenbeck model with increasing noise the optimum signal decreases and the coding range gets broader.     

Phenotypic traits evolution and morphological traits associated with echolocation calls in cryptic horseshoe bats (Rhinolophidae)

Bats provide an excellent casestudy for studying evolution due to their remarkable flight and echolocation capabilities. In this study, we sought to understand the phenotypic evolution of key traits in Rhinolophidae (horseshoe bats) using phylogenetic comparative methods. We aimed to test the phylogenetic signals of traits, and evaluated the best-fit evolutionary models given the data for each trait considering different traits may evolve under different models (i.e., Brownian Motion [BM], Ornstein-Uhlenbeck [OU], and Early Burst [EB]) and reconstruct ancestral character states. We examined how phenotypic characters are associated with echolocation calls and minimum detectable prey size. We measured 34 traits of 10 Asian rhinolophids species (187 individuals). We found that the majority of traits showed a high phylogenetic signal based on Blomberg′s K and Pagel′s λ, but each trait may evolve under different evolutionary models. Sella traits were shown to evolve under stabilizing selection based on OU models, indicating sella traits have the tendency to move forward along the branches toward some medial value in equilibrium. Our findings highlight the importance of sella characters in association with echolocation call emissions in Rhinolophidae, as calls are important for spatial cognition and also influence dietary preferences. Minimum detectable prey size in Rhinolophidae was associated with call frequency, bandwidth, call duration, wingspan, and wing surface area. Ultimately, understanding trait evolution requires sensitivity due to the differential selective pressures which may apply to different characteristics.     

The parameters of the stochastic leaky integrate-and-fire neuronal model

Five parameters of one of the most common neuronal models, the diffusion leaky integrate-and-fire model, also known as the Ornstein-Uhlenbeck neuronal model, were estimated on the basis of intracellular recording. These parameters can be classified into two categories. Three of them (the membrane time constant, the resting potential and the firing threshold) characterize the neuron itself. The remaining two characterize the neuronal input. The intracellular data were collected during spontaneous firing, which in this case is characterized by a Poisson process of interspike intervals. Two methods for the estimation were applied, the regression method and the maximum-likelihood method. Both methods permit to estimate the input parameters and the membrane time constant in a short time window (a single interspike interval). We found that, at least in our example, the regression method gave more consistent results than the maximum-likelihood method. The estimates of the input parameters show the asymptotical normality, which can be further used for statistical testing, under the condition that the data are collected in different experimental situations. The model neuron, as deduced from the determined parameters, works in a subthreshold regimen. This result was confirmed by both applied methods. The subthreshold regimen for this model is characterized by the Poissonian firing. This is in a complete agreement with the observed interspike interval data. Action Editor: Nicolas Brunel     

A Stochastic Epidemic Model with Seasonal Variations in Infection Rate

In this paper we consider a modification of Bailey's stochastic model for the spread of an epidemic when there are seasonal variations in infection rate. The resulting nonlinear model is analyzed by employing the diffusion approximation technique. We have shown that for a large population the process, on suitable scaling and normalization, converges to a non-stationary Ornstein-Uhlenbeck process. Consequently the number of infectives has in the steady state a gaussian distribution.