Troubled-Cell Indicator Based on Mean Value Property for Hybrid WENO Schemes

In this paper, we introduce a new type of troubled-cell indicator to improve hybrid weighted essentially non-oscillatory (WENO) schemes for solving the hyperbolic conservation laws. The hybrid WENO schemes selectively adopt the high-order linear upwind scheme or the WENO scheme to avoid the local characteristic decompositions and calculations of the nonlinear weights in smooth regions. Therefore, they can reduce computational cost while maintaining non-oscillatory properties in non-smooth regions. Reliable troubled-cell indicators are essential for efficient hybrid WENO methods. Most of troubled-cell indicators require proper parameters to detect discontinuities precisely, but it is very difficult to determine the parameters automatically. We develop a new troubled-cell indicator derived from the mean value theorem that does not require any variable parameters. Additionally, we investigate the characteristics of indicator variable; one of the conserved properties or the entropy is considered as indicator variable. Detailed numerical tests for 1D and 2D Euler equations are conducted to demonstrate the performance of the proposed indicator. The results with the proposed troubled-cell indicator are in good agreement with pure WENO schemes. Also the new indicator has advantages in the computational cost compared with the other indicators.     

线性法测量皮质下缺血性血管病患者脑萎缩及其与认知损害的相关性分析

目的通过线性法测量皮质下缺血性血管病(SIVD)患者脑萎缩,分析其与认知功能损害的相关性。方法共纳入SIVD组50例,健康对照组50例。所有入组对象均完成一般情况评定、Mo CA量表评估认知功能、头颅MRI检查,线性法进行脑萎缩测量。结果 SIVD组代表脑室系统横径的测量值及脑沟测量值,除桥池宽度外,均较对照组显著增大(P 0. 05)。SIVD组的脑萎缩测量相对值除脑干指数外,均显著高于对照组(P 0. 05)。SIVD组双侧侧脑室两额角间最宽距离、双侧侧脑室额角两侧尾状核头间最小距离、第三脑室宽度、双侧侧脑室腰部外侧壁最小距离与Mo CA评分呈显著负相关(P 0. 05)。SIVD组脑萎缩测量相对值中的额角指数、尾状核指数、哈氏值、第三脑室宽度与视空间能力、计算力、延迟记忆和定向力均呈负相关(P 0. 05)。结论 SIVD患者存在明显的皮质和皮质下萎缩,并与认知功能损害相关。哈氏值、额角指数、尾状核指数、第三脑室宽度可作为SIVD患者脑萎缩的预测指标,提示执行功能/视空间及计算力、记忆力的损害。     

Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning

Conservation laws are considered to be fundamental laws of nature. It has broad applications in many fields, including physics, chemistry, biology, geology, and engineering. Solving the differential equations associated with conservation laws is a major branch in computational mathematics. The recent success of machine learning, especially deep learning in areas such as computer vision and natural language processing, has attracted a lot of attention from the community of computational mathematics and inspired many intriguing works in combining machine learning with traditional methods. In this paper, we are the first to view numerical PDE solvers as an MDP and to use (deep) RL to learn new solvers. As proof of concept, we focus on 1-dimensional scalar conservation laws. We deploy the machinery of deep reinforcement learning to train a policy network that can decide on how the numerical solutions should be approximated in a sequential and spatial-temporal adaptive manner. We will show that the problem of solving conservation laws can be naturally viewed as a sequential decision-making process, and the numerical schemes learned in such a way can easily enforce long-term accuracy. Furthermore, the learned policy network is carefully designed to determine a good local discrete approximation based on the current state of the solution, which essentially makes the proposed method a meta-learning approach. In other words, the proposed method is capable of learning how to discretize for a given situation mimicking human experts. Finally, we will provide details on how the policy network is trained, how well it performs compared with some state-of-the-art numerical solvers such as WENO schemes, and supervised learning based approach L3D and PINN, and how well it generalizes.     

电子直线加速器照射对NIH 3T3细胞的细胞周期及凋亡的影响

目的 探讨电子直线加速器照射对细胞周期及细胞凋亡的影响。方法 采用直线加速器对NIH 3T3细胞进行照射，观察细胞周期及细胞凋亡的改变情况；同时测定损伤前后p53蛋白的表达情况。结果 照射后细胞凋亡数增加，p53蛋白表达量上升。结论 电子直线加速器照射损伤可诱导细胞凋亡。     

State and output feedback design for robust tracking of linear systems with rate limited actuators

A design technique (Control of Uncertain Systems with Bounded Inputs, Tarbouriech S, Garcia G, (Eds), Lecture Notes in Control and Information Sciences, vol. 227 , Springer: Berlin, 1997; 173–186) recently proposed for stabilization of a linear system with rate‐limited actuators is utilized to design feedback laws that cause the system output to track a desired command signal. This design technique combines two design techniques recently developed for linear systems with position limited actuators, piecewise‐linear LQ control (Automatica, 1994; 30 : 403–416) and low‐and‐high gain feedback (IEEE Trans. Automat. Control, 1996; 41 : 368–378), and hence takes advantage of both design techniques, while avoiding their disadvantages. In the case that only the output is available for feedback, the performance of the state feedback law is preserved by the use of a fast observer. An open‐loop exponentially unstable fighter aircraft is used to demonstrate the effectiveness of the proposed control design method. Copyright © 2002 John Wiley & Sons, Ltd.     

Fisher information matrix for nonlinear mixed effects multiple response models: Evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

We focus on the Fisher information matrix used for design evaluation and optimization in nonlinear mixed effects multiple response models. We evaluate the appropriateness of its expression computed by linearization as proposed for a single response model. Using a pharmacokinetic–pharmacodynamic (PKPD) example, we first compare the computation of the Fisher information matrix with approximation to one derived from the observed matrix on a large simulation using the stochastic approximation expectation–maximization algorithm (SAEM). The expression of the Fisher information matrix for multiple responses is also evaluated by comparison with the empirical information obtained through a replicated simulation study using the first‐order linearization estimation methods implemented in the NONMEM software (first‐order (FO), first‐order conditional estimate (FOCE)) and the SAEM algorithm in the MONOLIX software. The predicted errors given by the approximated information matrix are close to those given by the information matrix obtained without linearization using SAEM and to the empirical ones obtained with FOCE and SAEM. The simulation study also illustrates the accuracy of both FOCE and SAEM estimation algorithms when jointly modelling multiple responses and the major limitations of the FO method. This study highlights the appropriateness of the approximated Fisher information matrix for multiple responses, which is implemented in PFIM 3.0, an extension of the R function PFIM dedicated to design evaluation and optimization. It also emphasizes the use of this computing tool for designing population multiple response studies, as for instance in PKPD studies or in PK studies including the modelling of the PK of a drug and its active metabolite. Copyright © 2009 John Wiley & Sons, Ltd.     

ITERATIVE DYNAMIC PROGRAMMING FOR MINIMUM ENERGY CONTROL PROBLEMS WITH TIME DELAY

This paper presents the use of iterative dynamic programming employing exact penalty functions for minimum energy control problems. We show that exact continuously non-differentiable penalty functions are superior to continuously differentiable penalty functions in terms of satisfying final state constraints. We also demonstrate that the choice of an appropriate penalty function factor depends on the relative size of the time delay with respect to the final time and on the expected value of the energy consumption. A quadratic approximation (QA) of the delayed variables is much better than a linear approximation (LA) of the same for relatively large time delays. The QA improves the rate of convergence and avoids the formation of ‘kinks‘. A more general way of selecting appropriate penalty function factors is given and the results obtained using four illustrative examples of varying complexity corroborate the efficacy of the method.     

瓦里安2300C/D直线加速器COLL联锁故障检修

介绍和讨论瓦里安 2300C/D直线加速器 COLL联锁故障的发生原因和检修.