A New Discontinuous Galerkin Finite Element Method for Directly Solving the Hamilton-Jacobi Equations

In this paper, we improve upon the discontinuous Galerkin (DG) method for Hamilton-Jacobi (HJ) equation with convex Hamiltonians in (Y. Cheng and C.-W. Shu, J. Comput. Phys. 223:398-415,2007) and develop a new DG method for directly solving the general HJ equations. The new method avoids the reconstruction of the solution across elements by utilizing the Roe speed at the cell interface. Besides, we propose an entropy fix by adding penalty terms proportional to the jump of the normal derivative of the numerical solution. The particular form of the entropy fix was inspired by the Harten and Hyman's entropy fix (A. Harten and J. M. Hyman. J. Comput. Phys. 50(2):235-269, 1983) for Roe scheme for the conservation laws. The resulting scheme is compact, simple to implement even on unstructured meshes, and is demonstrated to work for nonconvex Hamiltonians. Benchmark numerical experiments in one dimension and two dimensions are provided to validate the performance of the method

The Female Perspective on Self-Worth

How do we determine the value of ourselves? It is intuitive that our perception of self-worth has an implicit effect on our development as individuals. This thesis explores the process through which women determine their self-worth and why it is problematic

The safety of antipsychotic use during pregnancy

Aim: To investigate the patterns of gestational antipsychotics use and whether exposure to antipsychotic medications in pregnancy is associated with gestational diabetes mellitus (GDM) in mothers and seizure, attention deficit/hyperactivity disorder (ADHD), autism spectrum disorder (ASD), preterm birth (PTB) and small for gestational age (SFGA) in subsequent children. Methods: Firstly, a methodological review was conducted to review the methodological characteristics of existing observational studies that investigate the association between prenatal central nervous system (CNS) drugs use and CNS disorders. Secondly, a systematic review and meta-analysis was conducted to evaluate the evidence-based association between gestational antipsychotic use and GDM. Thirdly, a cross-sectional study was conducted to investigate the patterns and trends of antipsychotics use during pregnancy in the United Kingdom (UK) and Hong Kong (HK). Lastly, seven cohort studies were conducted to investigate the association between antipsychotics use in pregnancy and the risk of above-mentioned outcomes, respectively. Results: 4.64% and 0.34% of pregnancies were prescribed at least one prescription of antipsychotic during pregnancy in the UK and HK, respectively. When women who continued using antipsychotics during pregnancy were compared with those who had stopped, there was no evidence to demonstrate an increased risk of GDM. No evidence supported prenatal exposure to antipsychotics can increase the risk of ADHD/ASD/SFGA. Children with prenatal antipsychotics exposure was associated with an increased risk of seizure (HR 1.49, 95% CI 1.11-1.99) and PTB (OR 1.40, 95%CI 1.13-1.75), comparing to those without. However, further sibling-matched analyses and negative control analyses indicated no evidence supported the above-mentioned associations. Conclusion: This PhD project did not suggest an increased risk of GDM in mothers or seizure/ADHD/ASD/PTB/SFGA in children regarding antipsychotics use during pregnancy. Women are not recommended to stop their regular antipsychotic prescription during pregnancy due to the risk of developing GDM or delivering an offspring with seizure/ADHD/ASD/PTB/SFGA

Fork is All You Need in Heterogeneous Systems

We present a unified programming model for heterogeneous computing systems. Such systems integrate multiple computing accelerators and memory units to deliver higher performance than CPU-centric systems. Although heterogeneous systems have been adopted by modern workloads such as machine learning, programming remains a critical limiting factor. Conventional heterogeneous programming techniques either impose heavy modifications to the code base or require rewriting the program in a different language. Such programming complexity stems from the lack of a unified abstraction layer for computing and data exchange, which forces each programming model to define its abstractions. However, with the emerging cache-coherent interconnections such as Compute Express Link, we see an opportunity to standardize such architecture heterogeneity and provide a unified programming model. We present CodeFlow, a language runtime system for heterogeneous computing. CodeFlow abstracts architecture computation in programming language runtime and utilizes CXL as a unified data exchange protocol. Workloads written in high-level languages such as C++ and Rust can be compiled to CodeFlow, which schedules different parts of the workload to suitable accelerators without requiring the developer to implement code or call APIs for specific accelerators. CodeFlow reduces programmers' effort in utilizing heterogeneous systems and improves workload performance.Comment: Presented at the 3rd Workshop on Heterogeneous Composable and Disaggregated Systems (HCDS 2024