In vivo cortical neurons are known to exhibit highly irregular spike patterns. Because the intervals between successive spikes fluctuate greatly, irregular neuronal firing makes it difficult to estimate instantaneous firing rates accurately. If, however, the irregularity of spike timing is decoupled from rate modulations, the estimate of firing rate can be improved. Here, we introduce a novel c...

We study the stationary distribution of the number of busy servers in a GI/GI/∞ system in which the service-time distribution is identical to the interarrival-time distribution, and obtain several representations for the variance. As a result we can verify an expression for the variance, conjectured by Rajaratnam and Takawira (IEEE Trans. Vehicular Technol. 50 (2001) 954-970), when the common d...

In modeling internet traffic there have been little attention on skewness. Shifted gamma distribution is a simple traffic model which is long-range dependent and its marginal distribution exhibits specific skewness. Using this model, we give some analytical results on the impact of skewness on the queueing performance such as mean delay and overflow probability. We also investigate the feasibil...

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a hetero...

Active Brownian motion with intermittent direction reversals is common in bacteria like Myxococcus xanthus and Pseudomonas putida. We show that, for such a two dimensions, the presence of timescales set by rotational diffusion constant ${D}_{R}$ reversal rate $\ensuremath{\gamma}$ gives rise to four distinct dynamical regimes: (I) $t\ensuremath{\ll}min({\ensuremath{\gamma}}^{\ensuremath{-}1},{D...

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

although knowing the time of the occurrence of the earthquakes is vital and helpful, unfortunately it is still unpredictable. by the way there is an urgent need to find a method to foresee this catastrophic event. there are a lot of methods for forecasting the time of earthquake occurrence. another method for predicting that is to know probability density function of time interval between earth...

in this paper, the effect of size on melting temperature of metallic nanoparticles (au, pb and bi) is theoretically simulated and explained. in this regard, the cause of difference in various experimental data is introduced, which is the difference between nanoparticles’ grain gaussian distribution. this volume-depended model with the help of the gaussian distribution can describe the relation ...