STOCHASTIC MECHANISM OF BROADENING SPECTRAL DENSITY OF SYNCHROTRON RADIATION OF RELATIVISTIC ELECTRON

The consideration is based on the study of the spectral profile of the synchrotron radiation (SR) line of a relativistic electron orbiting in a circular orbit in the uniform magnetic field. Fast stochastic fluctuations accompanying the motion of the electron during emission of SR quanta lead to the formation of spectral contour of each SR harmonic and it’s broadening. It is shown that the joint broadening of the set of harmonics causes broadening of the SR spectrum as the whole. The results of numerical calculations on the formation of the final SR spectral density of a relativistic electron are presented. In order to obtain precision characteristics, the formation of SR density in the frequency range exceeding the critical frequency has been studied.

A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models

It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data

Seeing, fast and slow: the effects of processing time on perceptual bias

Fast and slow decisions exhibit distinct behavioral properties, such as the presence of decision bias in faster but not slower responses. This dichotomy is currently explained by assuming that distinct cognitive processes map to separate brain mechanisms. Here, we suggest an alternative, single-process account based on the stochastic properties of decision processes. Our experimental results show perceptual biases in a variety of tasks (specifically: learned priors, tilt illusion, and tilt aftereffect) that were much reduced with increasing reaction time. To account for this, we consider a simple yet general explanation: prior and noisy decision-related evidence are integrated serially, with evidence and noise accumulating over time (as in the standard drift diffusion model). With time, owing to noise accumulation, the prior effect is predicted to diminish. This illustrates that a clear behavioral separation – presence vs. absence of bias – may reflect a simple stochastic mechanism.HighlightsPerceptual and decisional biases are reduced in slower decisions.Simple mechanistic single-process account for slow bias-free decisions.Signal detection theory criterion is ~zero in decision times>median.