A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales

Algorithms based on deep neural networks (DNNs) have attracted increasing attention from the scientific computing community. DNN based algorithms are easy to implement, natural for nonlinear problems, and have shown great potential to overcome the curse of dimensionality. In this work, we utilize the multi-scale DNN-based algorithm (MscaleDNN) proposed by Liu, Cai and Xu (2020) to solve multi-scale elliptic problems with possible nonlinearity, for example, the p-Laplacian problem. We improve the MscaleDNN algorithm by a smooth and localized activation function. Several numerical examples of multi-scale elliptic problems with separable or non-separable scales in low-dimensional and high-dimensional Euclidean spaces are used to demonstrate the effectiveness and accuracy of the MscaleDNN numerical scheme.     

Impact of new technologies on diabetes care

Technologies for diabetes management, such as continuous subcutaneous insulin infusion (CSII) and continuous glucose monitoring (CGM) systems, have improved remarkably over the last decades. These developments are impacting the capacity to achieve recommended hemoglobin A1c levels and assisting in preventing the development and progression of micro- and macro vascular complications. While improvements in metabolic control and decreases in risk of severe and moderate hypoglycemia have been described with use of these technologies, large epidemiological international studies show that many patients are still unable to meet their glycemic goals, even when these technologies are used. This editorial will review the impact of technology on glycemic control, hypoglycemia and quality of life in children and youth with type 1 diabetes. Technologies reviewed include CSII, CGM systems and sensor-augmented insulin pumps. In addition, the usefulness of advanced functions such as bolus profiles, bolus calculators and threshold-suspend features will be also discussed. Moreover, the current editorial will explore the challenges of using these technologies. Indeed, despite the evidence currently available of the potential benefits of using advanced technologies in diabetes management, many patients still report barriers to using them. Finally this article will highlight the importance of future studies tailored toward overcome these barriers to optimizing glycemic control and avoiding severe hypoglycemia.     

m6A结合蛋白IGF2BP1在肝细胞癌中的基因调控网络分析

目的 分析m6A阅读器胰岛素样生长因子2-mRNA结合蛋白1（insulin-like growth factor 2 mRNA-binding protein 1，IGF2BP1）在肝细胞癌（hepatocellular carcinoma，HCC）中的表达水平及其对HCC患者预后的影响，并探讨IGF2BP1在HCC发生发展中的作用及其潜在机制。方法 基于5对HCC癌及相应癌旁组织mRNA-seq数据和TCGA数据库LIHC的mRNA-seq数据综合分析IGF2BP1在HCC中的表达情况，同时利用TCGA数据库中343例HCC患者的临床随访资料分析IGF2BP1表达水平对HCC患者总生存期的影响。基于TCGA数据库筛选IGF2BP1的共表达mRNA，并利用m6Avar在线网站预测mRNA的m6A位点及其RNA结合蛋白等信息，最终构建IGF2BP1的基因调控网络。结果 IGF2BP1基因在HCC中表达上调（log2FC HCC转录组数据=10.684，P<0.001；log2FC TCGA-LIHC数据集=7.032，P<0.001）。生存分析显示IGF2BP1低表达的HCC患者中位生存时间为5.84年，IGF2BP1高表达患者为4.44年，高表达患者总生存期缩短（P=0.011）。22个差异表达的mRNA与IGF2BP1存在靶向结合关系，并与其表达水平呈正相关。其中，HMGA2等15个高表达mRNA的HCC患者总生存期缩短。HMGA2、PEG10、CEP55、RHO、CDC6和KIF23基因中的潜在m6A甲基化位点位于mRNA 3'UTR端的miRNA结合区域。结论 IGF2BP1在HCC中高表达且导致患者总生存期缩短。IGF2BP1可能通过m6A甲基化及miRNA抑制作用的方式上调mRNA的表达，促进HCC发生并导致不良预后。     

生物安全柜的控制

生物安全柜是重要的一级屏障设备，适当的控制方式对生物安全柜的防护能力是很重要的。文中主要介绍了生物安全柜的控制要点和几种控制方式及其特点。     

Optimal control of a revenue management system with dynamic pricing facing linear demand

This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time‐varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two‐product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two‐product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd.     

Discrete time optimal control of linear time-delay systems

A discrete time optimal control for linear time-delay systems is developed to ensure that all closed-loop eigenvalues will lie inside a circular region centred at (β;, 0) with radius α. It is shown that by suitable manipulations the problem can be reduced to a standard discrete time quadratic regulator problem. An illustrative example is included to demonstrate the applicability of the proposed method.     

Dorsal and ventral dopaminergic innervation of the spinal cord: Functional implications

Several studies have demonstrated that a descending dopaminergic pathway innervates the dorsal and the intermediate gray matter of the spinal cord and have suggested that this pathway is involved in pain modulation and in the control of autonomie functions. Other studies have also demonstrated the presence of dopamine (DA) and DA metabolites as well as of DA receptors in the ventral cord. There is also evidence for the implication of DA in the control of motor functions at the spinal level. The occurrence of a dopaminergic innervation in the ventral horn has been, however, disputed until recently. But recent work has demonstrated that the motoneural cell groups in the ventral horn (lamina IX) are a target for descending dopaminergic fibers. In addition, the possibility that DA is a mediator of primary afferent fibers has also been postulated. Finally, the occurrence of dopaminergic cell bodies has been suggested in the spinal cord. This indicates that DA is probably implicated in a complex manner in spinal functions. In the present paper the possible involvement of DA in sensory and in motor functions at spinal level will be discussed in view of neurochemical observations made in polyarthritic rats, in which pain-related behavior and reduction of locomotor activity associated with a marked decrease in mobility, are observed.