Sistem tasarımı ve kriptografik yöntemler için kritik bir öneme sahip olan rassal sayı üretimi; işlem gücü yüksek bilgisayarların ortaya çıkmasıyla güvenlik açısından daha da ön plana çıkmaktadır. Bu problemin çözülmesi fiziksel işleyiş ile üretimini hedefleyen gerçek üreteçleri kullanılabileceği gibi yazılım tabanlı olduğu uygulanması kolay sözde (SRSÜ) de kullanılabilmektedir. SRSÜ, genellikl...

We study the geometric ergodicity and long-time behavior of Random Batch Method for interacting particle systems, which exhibits superior numerical performance in recent large-scale scientific computing experiments. show that both system (IPS) random batch (RB–IPS), distribution laws converge to their respective invariant distributions exponentially, convergence rate does not depend on number p...

The Random Batch Method proposed in our previous work (Jin et al. J Comput Phys, 2020) is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as model of the system which particles interact, at discrete time, with randomly selected mini-batch particles. In this paper, we investigate limit number N→∞. Unlike classical mean field where law...

This work deals with the Monte Carlo method for stationary device simulation, known as the Single-Particle Monte Carlo method. A thorough mathematical analysis of this method clearly identifies the independent, identically distributed random variables of the simulated process. Knowledge of these random variables allows usage of straight-forward estimates of the stochastic error. The presented m...

A new parameter estimation algorithm based on improved particle swarm optimizer is proposed to improve the precision and recall rate of conditional random fields model. Aggregation degree of particle swarm is utilized to control particle swarm optimizer’s early local convergence, the relative change ratio of log-likelihood between iterations is employed to end its iterations, and the inertia fa...

The main purpose of this paper is to solve an inverse random differential equation problem using evolutionary algorithms. Particle Swarm Algorithm and Genetic Algorithm are two algorithms that are used in this paper. In this paper, we solve the inverse problem by solving the inverse random differential equation using Crank-Nicholson's method. Then, using the particle swarm optimization algorith...

In this paper, we introduce a random particle blob method for the Keller-Segel equation (with dimension d ≥ 2) and establish a rigorous convergence analysis.