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.     

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.     

Fas/FasL在各阶段婴幼儿血管瘤中的表达及意义

目的 检测Fas／FasL在各阶段婴幼儿血管瘤组织中的表达，探讨Fas／FasL在婴幼儿血管瘤细胞凋亡中的作用。方法 应用EnVision法免疫组化染色和RT-PCR检测Fas／FasL蛋白及mRNA在各阶段血管瘤组织中的表达。结果 ①增生早期和增生中期，部分血管瘤细胞表达Fas；增生晚期，阳性细胞明显增多，Fas mRNA表达最强；消退早期，仍有少量微血管内皮细胞表达Fas，之后Fas表达迅速减弱。②最早期细胞团中没有FasL（＋）细胞；增生中期，血管瘤组织中出现少量FasL（＋）细胞；增生晚期FasL（＋）细胞显著增多，FasL mRNA表达最强；消退早期之后，FasL（＋）细胞迅速减少以至消失。结论 Fas／FasL与婴幼儿血管瘤演变过程有密切联系，Fas／FasL介导的血管瘤细胞凋亡可能是婴幼儿血管瘤自行消退的重要原因。     

A reaction route graph analysis of the electrochemical hydrogen oxidation and evolution reactions

The reaction route (RR) graph approach recently developed by us for complex, non-linear kinetic mechanisms is applied to the hydrogen oxidation and evolution reactions. A corresponding RR graph is constructed and translated into an equivalent electrical circuit network by associating each elementary step with a characteristic resistance for the steady-state case and considering the overall reaction as a power source. It is further shown that the steady-state kinetics of the reaction can be investigated employing the conventional methods of the electrical network theory. Using a set of rate constants for the hydrogen evolution reaction (her) in alkaline solutions from the literature, the dominant RRs are identified and simplified mechanisms and kinetics derived.     

Postembryonic development of tapeworms — source of novel phylogenetic characters for analysis of cestode evolution: comparative TEM studies

Summary Ultrastructural features of juvenile cestodes (metacestodes) can provide useful characters for phylogenetic and evolutionary analyses. Until now, however, they have been relatively little utilised (Beveridge 2001, Chervy 2002). The postembryonic development and structure of fully formed metacestodes were examined in two cyclophyllideans: Taenia parva Baer, 1926 (Taeniidae); and Sobolevitaenia verulamii (Mettrick, 1958) Korniushin, 1972 (Dilepididae). In T. parva, three developmental stages were recognized: (1) an early stage of exogenous budding at the surface of the central vesicle; (2) a stage of polycephalic cyst development accompanied by segmentation of the growing metacestode strobila and an obvious decrease in the size of the central vesicle; (3) a fully formed metacestode of the strobilocercus type with 14–24 invaginated scoleces. The tegument, scolex, subtegumental musculature of the strobilar segments, protonephridial system, calcareous corpuscles and medullary parenchyma of larvae exhibit general similarity to the same structures in adults at both LM and TEM levels. The morphogenesis of the metacestode of T. parva is compared with that of polycephalic metacestodes of other Taenia spp. (T. krepkogorski, T. twitchelli and T. endothoracica) and with other asexually multiplying metacestodes (Mesocestoides vogae, hymenolepidids and dilepidids). In S. verulamii, the body of the cysticercoid with invaginated scolex armed with a double crown of rostellar hooks was completely surrounded by the cercomer, which appears to be separated from the cyst and scolex. The surface of the suckers is covered with a thick layer of glycocalyx. Five cell types were distinguished in the sections: (1) perikarya of metacestode tegument; (2) glycolgen-storing parenchymal cells; (3) glandular-type cells with large, electron-dense secretory-like granules; (4) flame cells; and (5) calcareous corpuscle-forming cells. The surface of the cercomer is covered by elongated microvilli, which evidently differ from characteristic microtriches covering all other parts of the metacestode surface. The ultrastructure of S. verulamii evidently differs from that of the other dilepidid cestode examined to date, Lateriporus geographicus, the cyst wall of which more resembles cysticercoids of Hymenolepididae than those of Dilepididae. Concluding remarks: Ultrastructural studies on metacestodes have considerable promise for providing important new characters for phylogenetic analysis. New TEM data on a great variety of cestode species are urgently needed. Until now, this field has not been exploited in a systematic fashion. Until more comprehensive studies become available, the current data are not yet amenable to analysis.     

A study of the interrupted REM episode

Brief interruptions of REM sleep are considered to be part of the REM episode. The maximum allowable duration of such an interruption, which is used to define the end of the REM episode, is currently a matter of debate. Making measurements on individual REM cycles, inter-REM interval analysis was carried out to determine whether the generally adopted 15 minute empirical rule for this maximum needs to be extended to 25 minutes as suggested by several including Kobayashi et al. Our results show that there is no reason to alter the 15 minute rule and that measurements which do not take into account the time-of-night effect may be misleading. The proportion of interrupted REM episodes observed in our population of healthy adults is high. We have therefore also examined in some detail the phenomenology of the temporal evolution of the structure and content of the interrupted REM episodes. Both showed a definite change over the night: the interruptions in the earlier episodes tend to return the system to slow wave sleep while those in the later episodes tend to return it to wake. It is hypothesized that these interruptions reflect a measure of REM sleep pressure and its interaction with both slow wave sleep and wake pressures.     

Evolution and path models in human behavioral genetics

The evolutionary implications of the path-analysis model most often used in human behavior genetics are examined. With directional selection, a model of pure vertical environmental transmission does not respond in a fully adaptive fashion. Unless the coefficients of transmission are exactly 0.50, the population mean will not equilibrate at the selective optimum over time. If there is both genetic and vertical environmental transmission, then the population mean can equilibrate at the selective optimum. In the presence of genetic transmission, vertical environmental transmission increases population fitness and has a strong effect on the rapid movement of the mean toward the selective optimum. This raises the intriguing paradox of why empirical evidence suggests that vertical environmental transmission is usually small when it possesses such important fitness properties.This work was supported in part by Grant DA05131 from the National Institute on Drug Abuse.     

西方公共卫生评估的演化逻辑及其启示

公共卫生评估的历史发展大致经历了四个阶段：基本研究、状态评估、衡量效力以及责任和遵从标准。从公共卫生评估演变的轨迹我们可以得出下列启示：项目循环管理方法倾向、结果和过程评估的增加、强调方法上的精确、越来越多地使用定量的和混合的方法以及对公众的责任。