Numerical resolution of moderately high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality for the classical numerical methods including finite difference, finite element and spectral methods. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by tracking the deterministic motion, random jump, resampling and reweighting of particles. Real-valued weighted particles are adopted by SPM to approximate the high-dimensional solution, which automatically adjusts the point distribution to intimate the relevant feature of the solution. A piecewise constant reconstruction with virtual uniform grid is employed to evaluate the nonlinear terms, which fully exploits the intrinsic adaptive characteristic of SPM. Combining both, SPM can achieve the goal of adaptive sampling in time. Numerical experiments on the 6-D Allen-Cahn equation and the 7- D Hamiltonian-Jacobi-Bellman equation demonstrate the potential of SPM in solving moderately high-dimensional nonlinear PDEs efficiently while maintaining an acceptable accuracy
The ability to segment moving objects from three-dimensional (3D) LiDAR scans is critical to advancing autonomous driving technology, facilitating core tasks like localization, collision avoidance, and path planning. In this paper, we introduce a novel deep neural network designed to enhance the performance of 3D LiDAR point cloud moving object segmentation (MOS) through the integration of image gradient information and the principle of motion consistency. Our method processes sequential range images, employing depth pixel difference convolution (DPDC) to improve the efficacy of dilated convolutions, thus boosting spatial information extraction from range images. Additionally, we incorporate Bayesian filtering to impose posterior constraints on predictions, enhancing the accuracy of motion segmentation. To handle the issue of uneven object scales in range images, we develop a novel edge-aware loss function and use a progressive training strategy to further boost performance. Our method is validated on the SemanticKITTI-based LiDAR MOS benchmark, where it significantly outperforms current state-of-the-art (SOTA) methods, all while working directly on two-dimensional (2D) range images without requiring mapping.
The proliferation and spread of antibiotic-resistant bacteria (ARB) significantly threaten human health and ecosystem. Periodate (PI) based advanced oxidation process has potentials for water purification but limited by complex activators or activation process. Herein, we demonstrated that H2O2 could be used to activate PI, achieving efficient ARB disinfection performance. Particularly, we found that the PI/H2O2 system (0.1 mM for both oxidants) could inactivate ARB (Escherichia coli) within 35 min. The intracellular defense system attacked by HO· radicals generated in the disinfection system, resulting in the inactivation of ARB. Antibiotic resistance genes (ARGs) released with the lysis of cell membrane could be further degraded by HO· radicals. Moreover, we found that the PI/H2O2 system was effective to inactivate ARB in a broad range of ionic strengths, with coexisting common ions and humic acid, as well as in four typical actual water bodies. The PI/H2O2 system could also efficiently disinfect other types of bacteria and degrade typical organic contaminants. In addition, under sunlight irradiation, the ARB inactivation performance of the PI/H2O2 system could be greatly improved. This study provided a practical and efficient way for decontaminating ARB/ARGs-polluted water.
