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Aiming at the problems of blind sampling points and slow planning speed of path planning Rapidly-exploring Random Trees algorithm, an effective region sampling Levy Rapidly-exploring Random Trees algorithm (LRRT*) is proposed based on the improved Levy flight strategy. Divide the entire path planning process into two stages: quickly finding the initial path and optimizing the path. Goal oriented strategy is used to explore the path when finding the initial path quickly. The Levy flight strategy is used to regenerate nodes after obstacles are encountered to improve the quality of the expansion points. They can quickly plan a collision-free path. In the phase of optimizing the initial path using the effective region sampling method, each sampling is only sampled around the initial path. Meanwhile, node rejection strategy is introduced to reduce the number of collision detection and accelerate the convergence speed. In 2D and 3D environments, the LRRT* algorithm reduces the initial path planning time by 17.6% and 91.9% respectively compared to the RRT* algorithm, and shortens the average planning time by 12.3% and 65.5%, and the path smoothness is 3.4% and 79.4% shorter respectively. Applying the LRRT algorithm to a robotic arm allows for the planning of collision-free paths.

The higher-order Hermite–Gaussian (HG) modes exhibit complex spatial distributions and find a wide range of applications in fields such as quantum information processing, optical communications, and precision measurements. In recent years, the advancement of deep learning has emerged as an effective approach for generating higher-order HG modes. However, the traditional data-driven deep learning method necessitates a substantial amount of labeled data for training, entails a lengthy data acquisition process, and imposes stringent requirements on system stability. In practical applications, these methods are confronted with challenges such as the high cost of data labeling. This paper proposes a method that integrates a physical model with deep learning. By utilizing only a single intensity distribution of the target optical field and incorporating the physical model, the training of the neural network can be accomplished, thereby eliminating the dependency of traditional data-driven deep learning methods on large datasets. Experimental results demonstrate that, compared with the traditional data-driven deep learning method, the method proposed in this paper yields a smaller root mean squared error between the generated higher-order HG modes. The quality of the generated modes is higher, while the training time of the neural network is shorter, indicating greater efficiency. By incorporating the physical model into deep learning, this approach overcomes the limitations of traditional deep learning methods, offering a novel solution for applying deep learning in light field manipulation, quantum physics, and other related fields.

In this paper, based on a three-dimensional Bao system, a memristor-based hyper-chaotic Bao-like system is successfully constructed, and a simulated equivalent circuit is designed, which is used to verify the chaotic behaviors of the system. Meanwhile, a control method called periodically intermittent control with variable control width is proposed. The control width sequence in the proposed method is not only variable, but also monotonically decreasing, and the method can effectively stabilize most existing nonlinear systems. Moreover, the memristor-based hyper-chaotic Bao-like system is controlled by combining the proposed method with the Lyapunov stability principle. Finally, we should that the proposed method can effectively control and stabilize not only the proposed hyper-chaotic system, but also the Chua’s oscillator.

So many real life problems ranging from medicine, agriculture, biology and finance are modelled by nonlinear systems. In this case, a chaotic nonlinear system is considered and, as opposed to solving Linear Matrix Inequality (LMI), which is the usual approach but cumbersome, a completely different approach was used. In some other cases, the computation of singular value of matrix was used but the method in this study needs not such. In addition, most models, if not all, concentrate on finding a control matrix J under some sufficient conditions. The problem is that only one such matrix J is provided. In reality, the actual control quantity may have a little deviation from the theoretical J. Hence, the study in this paper provides a set of infinite uncertain matrices Jα which are able to adapt to control the system under uncertain conditions. It turns out that this new method controls the system in shorter time with less computational complexities.

In this paper, we investigate cooperative and noncooperative three transboundary pollution problems in Three Gorges Reservoir Area where emission permits trading and abatement costs under learning by doing are considered. The abatement cost depends on two key factors: the level of pollution abatement and the experience of using pollution abatement technology. We use the optimal control theory to study the optimal emission paths and the optimal pollution abatement strategies under cooperative and noncooperative three transboundary pollution problems, respectively. By using the actual economic data of Wanzhou District, Kaizhou District and Yunyang County, we obtain the abatement level and the pollution stock of cooperative and noncooperative three transboundary pollution problems based on the four order Runge-Kutta method. We also discuss the influence of the change of parameter for the abatement level and the pollution stock.

In this paper, we investigate residual-based a posteriori error estimates for the hp version of the finite element approximation of nonlinear parabolic optimal control problems. By using the hp finite element approximation for both the state and the co-state variables and the hp discontinuous Galerkin finite element approximation for the control variable, we derive hp residual-based a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, can be used to construct a reliable hp adaptive finite element approximation for the nonlinear parabolic optimal control problems.

This paper investigates a differential game modeling transboundary pollution management in the Upper Yangtze River Basin under noncooperative and cooperative scenarios, incorporating emissions trading, learning-by-doing effects, and abatement investment costs. The maximum principle of optimal control theory was employed to derive equilibrium solutions for both models. Numerical simulations identified optimal emission levels and abatement investments for the Chongqing Municipality and Sichuan Province under each scenario, with the pollution stock trajectories computed using the fourth-order Runge-Kutta method. Numerical validation demonstrated that ecological compensation mechanisms enhance mitigation effectiveness. Furthermore, the study revealed that learning-by-doing efficiency gains and reductions in regional abatement investment costs synergistically enhance both pollution mitigation and economic returns within this framework.

In this paper, we discuss a cooperative stochastic differential game for the transboundary industrial pollution problems of Three Gorges Reservoir Area. Base on the stochastic optimal control theory, we derive the Hamilton–Jacobi–Bellman equations for the cooperative games. Furthermore we solve the Hamilton–Jacobi–Bellman equations by using a fitted finite volume method. Finally, an empirical study base on the datum of Three Gorges Reservoir Area is given to demonstrate the efficiency and usefulness of the numerical method.

Objective To explore the expression of matrix metalloproteinase-2 (MMP-2) and its inhibitor tissue inhibitor of metalloproteinase-2 (TIMP-2) and their relation with glioma of different malignancy degree. Methods Immunohistochemical SP method was employed to examine the level of MMP-2 and TIMP-2 in surgical samples from 67 patients suffering from gliomas and 10 patients with cerebral trauma. Results As the tumor’s malignancy degree increased, the expression of MMP-2 increased but the expression of TIMP-2 decreased as the tumor malignancy degree increased. Conclusion MMP-2 and TIMP-2 have a great significance in evaluating the malignancy degree of human gliomas. 目的 探讨基质金属蛋白酶-2(MMP-2)及其抑制因子TIMP-2的表达及其与脑胶质瘤恶性程度之间的关系。方法 采用免疫组化SP法检测并比较了67例不同级别胶质瘤组织和10例正常脑组织中MMP-2和TIMP-2蛋白的表达情况。结果 随着肿瘤恶性程度的增加，MMP-2蛋白表达增高而TIMP-2蛋白表达降低。结论 MMP-2及TIMP-2对胶质瘤恶性程度的评估有重要的意义。