Moment-Based Multi-Resolution HWENO Scheme for Hyperbolic Conservation Laws

In this paper, a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory (HWENO) scheme is designed for hyperbolic conservation laws. The main idea of this scheme is derived from our previous work [J. Comput. Phys., 446 (2021) 110653], in which the integral averages of the function and its first order derivative are used to reconstruct both the function and its first order derivative values at the boundaries. However, in this paper, only the function values at the Gauss-Lobatto points in the one or two dimensional case need to be reconstructed by using the information of the zeroth and first order moments. In addition, an extra modification procedure is used to modify those first order moments in the troubled-cells, which leads to an improvement of stability and an enhancement of resolution near discontinuities. To obtain the same order of accuracy, the size of the stencil required by this moment-based multi-resolution HWENO scheme is still the same as the general HWENO scheme and is more compact than the general WENO scheme. Moreover, the linear weights are not unique and are independent of the node position, and the CFL number can still be 0.6 whether for the one or two dimensional case, which has to be 0.2 in the two dimensional case for other HWENO schemes. Extensive numerical examples are given to demonstrate the stability and resolution of such moment-based multi-resolution HWENO scheme.     

基于国家专利的中药复方治疗化学性肝损伤用药规律研究

目的分析国家专利治疗化学性肝损伤的组方用药规律,为新药研发及相关专利的申请提供参考。方法以国家知识产权局中国专利公布公告网站收录的授权专利为资料来源,使用Microsoft Excel 2018建立数据库,对中药频次与分类进行统计分析;采用SPSS Statistic 21.0和SPSS Modeler 15.0对高频中药(频次≥10)进行性味归经分析、系统聚类分析、关联度与网络分析。结果纳入专利100项,涉及中药186味,以葛根最为常见;高频中药15味,药味以甘为主,药性以温、平为主,多归脾、肝经;聚类分析得到7组中药组合;二项、三项和四项关联规则分别为6、24、2项,各项组合分别为6、16、2项;核心药物为葛根、五味子、丹参、甘草、山楂、枸杞子、黄芪、柴胡、姜黄和枳椇子。结论中药复方治疗化学性肝损伤常用补虚、解表、化瘀、活血、渗湿及利水药;临证多采用疏肝理气之剂,适当伍以柔润之品。     

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.     

以脾胃为中心的葛根相关配伍对糖尿病心肌病大鼠受损心肌线粒体的改善作用

目的:观察葛根及其配伍对糖尿病心肌病(DCM)大鼠心肌线粒体质量变化的影响,探寻治疗糖尿病心肌病的最优配伍及机制。方法:采用链脲佐菌素腹腔注射进行模型大鼠制备,并将60只成模大鼠随机分为模型组6.5 g/(kg·d)、达美康组16.7 mg/(kg·d)、葛根组1.04 g/(kg·d)、葛芪组2.6 g/(kg·d)、葛参组2.6 g/(kg·d)、葛蒌组4.48g/(kg·d)及葛芪参蒌组7.6 g/(kg·d)各8只,同时选取空白大鼠8只,为对照组6.5 g/(kg·d)。各组依据上述剂量,以相应药物持续灌胃9周后,对比各组心肌线粒体超微结构变化、心肌线粒体膜电位变化及心肌ATP变化情况。结果:电镜显示各药物干预组心肌线粒体超微结构较模型组均有不同程度的改善,其中葛芪参蒌组改善效果最为明显,与空白组无明显差异; 流式细胞仪检测显示:各干预组波峰均在模型组、空白组之间; 其中葛芪参蒌组、葛参组、葛根组波峰位于达美康组右侧; 葛芪组、葛蒌组则位于达美康组左侧; 以葛芪参蒌组波峰与空白组最为接近。心肌ATP浓度检测显示:各中药干预组心肌ATP浓度均较模型组有所提升(P<0.05),其中葛芪参蒌组ATP值较其余各干预组提升最为明显(P<0.05),但仍低于空白组(P>0.05)。结论:葛根相关配伍均能够对心肌线粒体结构、心肌线粒体膜电位进行正向调控,进而使因糖尿病心肌病导致的心肌线粒体受损得以恢复,其中以益气、化瘀、祛痰三法合用的组方原则进行配伍的葛芪参蒌方改善效果最优。可见其治疗机制可能是通过益气、化瘀、祛痰的协同作用,正向调控心肌线粒体质量而达到治疗目的。     

针灸治疗小儿脑瘫临床取穴配伍规律研究

目的:分析探讨近20年针灸治疗脑瘫取穴配伍特点及规律。方法:检索近20年CNKI、万方及维普数据库收录的针灸治疗脑瘫的相关文献,运用Excel及中医传承辅助平台软件分析数据。结果:研究共纳入文献311篇,取穴应用频次最多的为足三里、百会、四神聪、合谷、曲池、三阴交和阳陵泉,使用频次居前三位的经脉是督脉、足少阳胆经、手阳明大肠经,且取穴所在位置集中在下肢部、头颈部、上肢部,所选腧穴中特定穴以交会穴、五输穴、下合穴数量居多。穴位配伍百会和四神聪,合谷和足三里,曲池和合谷是针灸治疗脑瘫所取用的使用频次较高的腧穴配伍。结论:针灸治疗脑瘫具有注重四肢及头部选穴、侧重阳经取穴、注重特定穴的使用、重视上下配穴法的规律特点。     

The Legal Challenge of Abortion Stigma—and Government Restrictions on the Practice of Medicine

During the 2016 election, Donald Trump won conservative support by promising that he would, if elected, nominate “pro-life” justices to the U.S. Supreme Court. Whether President Trump makes good on his campaign promise to restrict abortion rights may come down to competing impulses of the chief justice, John Roberts. These dueling dispositions—from the man whom many see as the new “swing justice”—hold the key to a blockbuster new case that legal historians call “the most unpredictable the Supreme Court has been on abortion in decades.” The case, June Medical Services v. Russo, turns on arduous new requirements that Louisiana has imposed on facilities and clinicians that provide abortion. But the case is not just about abortion access. The Court will have to decide whether a clinic has a right to challenge the law in the first place.     

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.     

Relationship between retail food outlets near public schools and adolescent obesity in New York City

Using objectively-measured height and weight data from academic years 2009–2013 (n = 1,114,010 student-year observations), we estimated the association between the food outlet in closest proximity to schools and the likelihood of obesity among New York City public high school students. Obesity risk was higher for students with a corner store as the nearest option to schools, regardless of whether other food outlet types were located within a quarter mile or a half mile of schools (i.e., benchmarks for zoning policies). Policymakers may want to consider introducing healthier food options near schools, in conjunction with programs to support changes within corner stores.     

稀土氧化物着色钇稳定四方多晶氧化锆陶瓷与饰面瓷匹配性的研究

目的:探讨通过添加稀土氧化物着色剂而制备的钇稳定四方多晶氧化锆陶瓷与饰面瓷的匹配性。方法:以稀土氧化物(Pr6O11,CeO2,Er2O3)和过渡元素氧化物(MnO2)为着色剂,采用粉体掺杂方法,在四方多晶氧化锆陶瓷粉体中添加不同质量分数的着色剂,制备出6组钇稳定四方多晶氧化锆陶瓷,测定其与Vita VM9饰面瓷的抗热震性能及界面结合强度。采用SAS6.12软件包对数据进行单因素方差分析。结果:6组钇稳定四方多晶氧化锆陶瓷与Vita-VM9饰面瓷烧结后,各组在60℃～240℃测试过程未发现径向或层间开裂或裂纹现象,加热温度>240℃。6组钇稳定四方多晶氧化锆陶瓷与VitaVM9饰面瓷界面的抗剪切强度值为(36.03±3.82)～(37.98±4.89)MPa,均高于纯四方氧化锆陶瓷组的剪切强度值,但各组与纯四方氧化锆陶瓷的抗剪切强度值无显著差异(P>0.05)。结论:稀土氧化物着色钇稳定四方多晶氧化锆陶瓷与饰面瓷的匹配性达到临床应用水平。