Band 28, Heft 3

Random numbers are used in a variety of applications including simulation, sampling, and cryptography. Fortunately, there exist many well-established methods of random number generation. An example of a well-known pseudorandom number generator is the lagged-Fibonacci generator (LFG). Marsaglia showed that the lagged-Fibonacci generator using addition failed some of his DIEHARD statistical tests, while it passed all when longer lags were used. This paper presents a scrambler that takes bits from a pseudorandom number generator and outputs (hopefully) improved pseudorandom numbers. The scrambler is based on a modified Feistel function, a method used in the generation of cryptographic random numbers, and multiplication by a chosen multiplier. We show that this scrambler improves the quality of pseudorandom numbers by applying it to the additive LFG with small lags. The scrambler performs well based on its performance with the TestU01 suite of randomness tests. The TestU01 suite of randomness tests is more comprehensive than the DIEHARD tests. In fact, the specific suite of tests we used from TestU01 includes the DIEHARD tests The scrambling of the LFG is so successful that scrambled LFGs with small lags perform as well as unscrambled LFGs with long lags. This comes at the cost of a doubling of execution time, and provides users with generators with small memory footprints that can provide parallel generators like the LFGs in the SPRNG parallel random number generation package.

The present study addresses the sensitivity analysis of particle concentration dispersion in the turbulent flow. A stochastic spectral model of turbulence is used to simulate the particle transfer. Sensitivity analysis is performed by estimations of Morris and Sobol indices. This study allows to define the significant and nonsignificant model parameters. It also gives an idea of the qualitative behavior of the stochastic model used.

Markov chain Monte Carlo (MCMC) methods are important in a variety of statistical applications that require sampling from intractable probability distributions. Among the most common MCMC algorithms is the Gibbs sampler. When an MCMC algorithm is used, it is important to have an idea of how long it takes for the chain to become “close” to its stationary distribution. In many cases, there is high autocorrelation in the output of the chain, so the output needs to be thinned so that an approximate random sample from the desired probability distribution can be obtained by taking a state of the chain every h steps in a process called h -thinning. This manuscript extends the work of [D. A. Spade, Estimating drift and minorization coefficients for Gibbs sampling algorithms, Monte Carlo Methods Appl. 27 2021, 3, 195–209] by presenting a computational approach to obtaining an approximate upper bound on the mixing time of the h -thinned Gibbs sampler.

In numerous industrial and related activities, the sums of the values of, frequently, unequal size samples are systematically recorded, for several purposes such as legal or quality control reasons. For the typical case where the individual values are not or no longer known, we address the point estimation, with confidence intervals, of the standard deviation (and mean) of the individual items, from those sums alone. The estimation may be useful also to corroborate estimates from previous statistical process control. An everyday case of a sum is the total weight of a set of items, such as a load of bags on a truck, which is used illustratively. For the parameters mean and standard deviation of the distribution, assumed Gaussian, we derive point estimates, which lead to weighted statistics, and we derive confidence intervals. For the latter, starting with a tentative reduction to equal size samples, we arrive at a solid conjecture for the mean, and a proposal for the standard deviation. All results are verifiable by direct computation or by simulation in a general and effective way. These computations can be run on public web pages of ours, namely for possible industrial use.

In this paper, we study the multiple recombination exciton–photon–exciton process governed by a coupled system of the drift-diffusion-recombination equation and the integral radiative transfer equation. We develop a random walk on spheres algorithm for solving this system of equations. The algorithm directly simulates the transient drift-diffusion process of exciton’s motion. Then, at a random time the exciton recombines to a photon that moves in accordance with the radiative transfer equation, which in turn may recombine to an exciton etc. This algorithm is applied to calculate fluxes of excitons and photons as functions of time, and some other characteristics of the process. Calculations have also been carried out to validate the constructed model.

The paper describes a sensitivity function calculation method for few-view X-ray computed tomography of strongly absorbing objects. It is based on a probabilistic interpretation of energy transport through the object from a source to a detector. A PRIZMA code package is used to track photons. The code is developed at FSUE “RFNC–VNIITF named after Academ. E. I. Zababakhin” and implements a stochastic Monte Carlo method. The value of the sensitivity function in a discrete cell of the reconstruction region is assumed to be directly proportional to the fraction of photon trajectories which cross the cell from all those recorded by the detector. The method’s efficiency is validated through a numerical experiment on the reconstruction of a section of a spherical heavy-metal phantom with an air cavity and a density difference of 25 Ṫhe proposed method is shown to outperform the method based on projection approximation in case of reconstruction from 9 views.