Volume 22, Issue 2

Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this paper, we propose to quantify how changes in the spatial dependence structure affect the Riemannian metric tensor that equips the model's parametric space. Defining Fisher curves, we measure the variations in each component of the metric tensor when visiting different entropic states of the system. Simulations show that the geometric deformations induced by the metric tensor in case of a decrease in the inverse temperature are not reversible for an increase of the same amount, provided there is significant variation in the system's entropy: the process of taking a system from a lower entropy state A to a higher entropy state B and then bringing it back to A, induces a natural intrinsic one-way direction of evolution. In this context, Fisher curves resemble mathematical models of hysteresis in which the natural orientation is pointed by an arrow of time.

The paper is devoted to the complexity analysis of binary floating point pseudorandom generators. We start with a stochastic model of a “usual” pseudorandom generator (PRNG). Then integer outputs of this generator are transformed into i.i.d. random variables, agreed with an abstract binary floating point system. Additionally, these random variables are approximately uniformly distributed on the interval [0,1]. Therefore, they can interpreted as (random) outputs of a binary floating point pseudorandom generator (flPRNG). The simulation complexity of such a transformation is defined as the average number of PRNG's outputs necessary to produce the unique output of flPRNG. Several transformations with minimal or approximately minimal complexities are presented and discussed.

We suggest random walk on semi-infinite cylinders methods for solving interior and exterior diffusion problems with different types of boundary conditions which include mixed Dirichlet, Neumann, and Robin boundary conditions on different parts of the boundary. Based on probabilistic interpretation of the diffusion process, stochastic simulation algorithms take into account specific features of each boundary condition to optimally adjust the Markov chain distribution on the relevant boundary parts. In contrast to the conventional direct trajectory tracking method, the new method avoids to simulate the diffusion trajectories. Instead, it exploits exact probabilities of different events like the first passage, splitting, and survival probabilities inside the semi-infinite cylinders, depending on the domain and its boundary structure. Applications to diffusion imaging methods like the cathodoluminescence (CL) and electron beam induced current (EBIC) semiconductor analysis techniques performed in scanning electron and transmission microscopes, are discussed.

Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carlo method, which uses low-discrepancy sequences, instead of pseudorandom numbers, in simulation. Low-discrepancy sequences from different distributions can be obtained by the inverse transformation method, just like for pseudorandom numbers. In this paper, we present an acceptance-rejection algorithm for low-discrepancy sequences. We prove a convergence result, and present error bounds. We then use this acceptance-rejection algorithm to develop quasi-Monte Carlo versions of some well-known algorithms to generate beta and gamma distributions, and investigate the efficiency of these algorithms numerically. We also consider the simulation of the variance gamma model, a model used in computational finance, where the generation of these probability distributions are needed. Our results show that the acceptance-rejection technique can result in significant improvements in computing time over the inverse transformation method in the context of low-discrepancy sequences.

Sputtering is characterized by a sputtering yield ratio which depends on several conditions, in particular the incident ions energy to the cathode, in normal incidence and when considers the angle α of the incident ions. Our investigations may be considered in first step to calculate the sputtering yield of three metals: copper, silver, and aluminum collide with argon, xenon, oxygen and nitrogen ions using highly developed software called SRIM (Stopping and Range of Ions in Matter) with normal incidence, then with varied angles in future works. The results obtained are compared with those obtained using the analytical models based on the Monte Carlo method proposed by researchers as Sigmund and Yamamaura in order to validate models.