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.     

Gendered dimensions of population mobility associated with HIV across three epidemics in rural Eastern Africa

Mobility in sub-Saharan Africa links geographically-separate HIV epidemics, intensifies transmission by enabling higher-risk sexual behavior, and disrupts care. This population-based observational cohort study measured complex dimensions of mobility in rural Uganda and Kenya. Survey data were collected every 6 months beginning in 2016 from a random sample of 2308 adults in 12 communities across three regions, stratified by intervention arm, baseline residential stability and HIV status. Analyses were survey-weighted and stratified by sex, region, and HIV status. In this study, there were large differences in the forms and magnitude of mobility across regions, between men and women, and by HIV status.We found that adult migration varied widely by region, higher proportions of men than women migrated within the past one and five years, and men predominated across all but the most localized scales of migration: a higher proportion of women than men migrated within county of origin. Labor-related mobility was more common among men than women, while women were more likely to travel for non-labor reasons. Labor-related mobility was associated with HIV positive status for both men and women, adjusting for age and region, but the association was especially pronounced in women. The forms, drivers, and correlates of mobility in eastern Africa are complex and highly gendered. An in-depth understanding of mobility may help improve implementation and address gaps in the HIV prevention and care continua.     

Development and validation of a food frequency questionnaire for assessing dietary calcium intake in the general population

The aim of this study was to develop and evaluate a food frequency questionnaire (FFQ) for assessing dietary calcium intake in the general population, since all available questionnaires at present are age- and/or gender-specific. A total of 1001 individuals (including children, adults, and elderly people of both genders) were randomly recruited throughout Greece. Estimates of calcium intake from the 30-item FFQ were compared with those from a multi-pass 24-h recall. The FFQ underestimated mean calcium intake compared to the 24-h recall by (mean±SD) –133±333 mg/day or –5.4±47.6% (P<0.001). The two methods were strongly correlated (r=0.639, P<0.001), but the 95% limits of agreement for individual assessment were rather wide, as the FFQ could provide estimates of calcium intake from 533 mg/day above to 799 mg/day below the 24-h recall. Actual values for surrogate FFQ quartiles manifested a progressive increase, with significant differences between mean calcium intakes (P<0.001). The FFQ could identify individuals who consumed less calcium than 800 mg/day or less than the age-specific adequate intake with a relatively high sensitivity (82.8 and 95.5%, respectively), but low specificity (54.9 and 34.1%, respectively). Cross-classification analysis indicated that only 17 subjects (1.7%) were grossly misclassified (lowest quartile for one method and highest quartile for the other), while 827 subjects (82.6%) were correctly classified (into the same or adjacent quartiles). The FFQ could be used in population-based epidemiological studies or screening programs involving individuals of all ages and both genders, where the discrimination of subjects with relatively low (<500 mg/day) and relatively high (>1000 mg/day) calcium intakes is of primary interest. Results, however, do not support its use for the quantitative assessment of individual calcium intakes.     

Gender ratio of migraine without aura: observations over time

Abstract Migraine without aura is typically considered a female condition. The purpose of this study was to determine if there have been any changes in the female-to-male ratio of the disease over time. We included in the study all patients with migraine without aura (n=3457) referred to the Parma University Headache Centre between 1976 and 1995. They were divided into subgroups with respect to gender and year-range of onset of migraine (before 1960, in the 1960s, in the 1970s, in the 1980s, and between 1990 and 1995). Gender ratio ranged from 3.6:1 (in patients with onset before 1960) to 2.8:1 (in patients with onset in the 1980s), with no statistically significant changes during the observation period.     

Cardiovascular responses to various autonomic tests in males and females

The results of cardiovascular autonomic reflex tests on 224 healthy, randomly selected subjects were analysed to study possible sex differences in the autonomic responses. The heart rate response to the Valsalva manoeuvre (Valsalva ratio) was greater in females over 50 years than in males of the same age (1.58 ± 0.34 vs. 1.44 ± 0.30,p < 0.05). The heart rate response to deep breathing (E/I ratio) was higher in females under 50 years than in males under 50 years (1.37 ± 0.17 vs. 1.34 ± 0.18,p < 0.001). The diastolic blood pressure response to isometric handgrip was higher in males under 50 years than in females of the same age (p < 0.05). Although there were sex differences in the magnitude of the responses, the effect of age was similar in males and females and accelerated attenuation of the autonomic responses could not be demonstrated with increasing age. It can be concluded that significant sex differences exist in cardiovascular autonomic responses. The implication of such differences need consideration.     

颈椎病与中医辨证关系的探讨(附100例分析)

目的:探讨颈椎病与中医分型的辨证关系。方法:对100例该病的影像表现与中医分型进行系统分析。结果:主要临床表现颈部活动受限,颈、肩、背部疼痛,常伴头痛、头晕、视物模糊、耳鸣等症状。风寒型以软组织所致颈曲改变为主。肝肾亏虚型、痰湿交阻型以骨质增生、椎间隙及椎间孔狭窄为主。结论:X线、CT是本病首选检查方法,能与中医辨证有机结合,对中西医治疗有重要意义。     

肥胖与胆石病的多因素条件Logistic回归分析

目的探讨肥胖与结石病发病的关系。方法采用调查表的方式对1997年住院手术确诊为结石病的病人进行回顾性调查，内容包括：年龄、性别、体重、身高、是否吃早餐。对调查表进行多因素logstic统计分析。结果分析结果表明我们调查了我院102例结石病患者和101名正常人发现肥胖、女性、不经常吃早餐、饮用高硬度的水均是结石病的危险因紊，对那些长时间不吃早餐的人更容易患结石病，（相对危险度OR〉40．139）。结论我们建议今后应注意膳食营养的均衡，保持标准体重，饮用卫生水。     

Adolescent alcohol initiation: A review of psychosocial risk factors

Longitudinal research studies focused on alcohol use initiation in adolescence were reviewed to determine which variables function as antecedent predictors or risk factors. Only studies that focused on time-1 abstainers were included. Classes of risk factors examined include sociodemographic, family, peer, personality, and behavioral variables. The most consistent antecedent risk factors for starting to drink in adolescence were parental and peer approval and models for drinking and drug use as well as adolescents’ own prior involvement in delinquent behavior. There was little evidence for gender differences in risk factors for alcohol use initiation. Secondary analyses of existing longitudinal data sets are encouraged to examine whether there are ethnic/racial differences in the risk factors for starting to drink and to establish those factors that serve a protective or buffering function, delaying onset of alcohol use in adolescence.