In this paper, a new one-dimensional fractional chaotic map is proposed and an image encryption scheme based on parallel DNA coding is designed by using the chaotic map. The mathematical model of the new chaotic system combines a sine map and a fract...

Accurate and real-time forecasting of the price of oil plays an important role in the world economy. Research interest in forecasting this type of time series has increased considerably in recent decades, since, due to the characteristics of the time...

In this paper, we present a comprehensive mathematical analysis of the hallucination phenomenon in generative pretrained transformer (GPT) models. We rigorously define and measure hallucination and creativity using concepts from probability theory an...

We develop an approach for two-player constraint zero-sum and nonzero-sum stochastic differential games, which are modeled by Markov regime-switching jump-diffusion processes. We provide the relations between a usual stochastic optimal control settin...

In this paper, we deduce a predator–prey model with discrete time in the interior of R+2 using a new discrete method to study its local dynamics and Neimark–Sacker bifurcation. Compared with continuous models, discrete ones have many uniq...

Despite the availability and ease of collecting a large amount of free, unlabeled data, the expensive and time-consuming labeling process is still an obstacle to labeling a sufficient amount of training data, which is essential for building supervise...