Yulan Lu

M. H. Song, Y. L. Lu, M. Z. Liu

Recently, Martin Hutzenthaler pointed out that the explicit Euler method fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with superlinearly growing and globally one sided Lipschitz drift coefficient. Afterwards, he proposed an explicit and easily implementable Euler method, i.e tamed Euler method, for such an SDE and showed that this method converges strongly with order of one half. In this paper, we use the tamed Euler method to solve the stochastic differential equations with piecewise continuous arguments (SEPCAs) with superlinearly growing coefficients and prove that this method is convergent with strong order one half.

Zishan Xu, Yifu Guo, Yuquan Lu et al.

Traditional video reasoning segmentation methods rely on supervised fine-tuning, which limits generalization to out-of-distribution scenarios and lacks explicit reasoning. To address this, we propose \textbf{VideoSeg-R1}, the first framework to introduce reinforcement learning into video reasoning segmentation. It adopts a decoupled architecture that formulates the task as joint referring image segmentation and video mask propagation. It comprises three stages: (1) A hierarchical text-guided frame sampler to emulate human attention; (2) A reasoning model that produces spatial cues along with explicit reasoning chains; and (3) A segmentation-propagation stage using SAM2 and XMem. A task difficulty-aware mechanism adaptively controls reasoning length for better efficiency and accuracy. Extensive evaluations on multiple benchmarks demonstrate that VideoSeg-R1 achieves state-of-the-art performance in complex video reasoning and segmentation tasks. The code will be publicly available at https://github.com/euyis1019/VideoSeg-R1.

M. H. Song, Y. L. Lu, M. Z. Liu

In this paper, we study the polynomial stability of analytical solution and convergence of the semi-implicit Euler method for non-linear stochastic pantograph differential equations. Firstly, the sufficient conditions for solutions to grow at a polynomial rate in the sense of mean-square and almost surely are obtained. Secondly, the consistence and convergence of this method are proved. Furthermore, the orders of consistence (in the sense of average and mean-square) and convergence are given, respectively.