An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’

Magnetic Miniband Structure and Quantum Oscillations in Lateral Semiconductor Superlattices

We present fully quantum-mechanical magnetotransport calculations for short-period lateral superlattices with one-dimensional electrostatic modulation. A non-perturbative treatment of both magnetic field and modulation potential proves to be necessary to reproduce novel quantum oscillations in the magnetoresistance found in recent experiments in the resistance component parallel to the modulation potential. In addition, we predict oscillations of opposite phase in the component perpendicular to the modulation not yet observed experimentally. We show that the new oscillations originate from the magnetic miniband structure in the regime of overlapping minibands.Comment: 6 pages with 4 figure

The hearing of fitness to practice cases by the General Medical Council: Current trends and future research agendas

Over the last three decades a risk-based model of medical regulation has emerged in the United Kingdom. To promote a risk-averse operational culture of transparency and professional accountability the regulatory state has intervened in medical governance and introduced best-evidenced practice frameworks, audit and performance appraisal, Against this background the paper analyses descriptive statistical data pertaining to the General Medical Council’s management of the process by which fitness to practice complaints against doctors are dealt with from initial receipt through to subsequent investigative and adjudication stages. Statistical trends are outlined regarding complaint data in relation to a doctor’s gender and race and ethnicity. The data shows that there has been an increase in rehabilitative and/or punitive action against doctors. In light of its findings the paper considers what the long-term consequences may be, for both patients and doctors, of the increasing use of risk-averse administrative systems to reform medical regulation and ensure professional accountability

Escape from an optoelectronic tweezer trap: experimental results and simulations

Optoelectronic tweezers (OET) are a microsystem actuation technology capable of moving microparticles at mm s−1 velocities with nN forces. In this work, we analyze the behavior of particles manipulated by negative dielectrophoresis (DEP) forces in an OET trap. A user-friendly computer interface was developed to generate a circular rotating light pattern to control the movement of the particles, allowing their force profiles to be conveniently measured. Three-dimensional simulations were carried out to clarify the experimental results, and the DEP forces acting on the particles were simulated by integrating the Maxwell stress tensor. The simulations matched the experimental results and enabled the determination of a new “hopping” mechanism for particle-escape from the trap. As indicated by the simulations, there exists a vertical DEP force at the edge of the light pattern that pushes up particles to a region with a smaller horizontal DEP force. We propose that this phenomenon will be important to consider for the design of OET micromanipulation experiments for a wide range of applications

Graph Neural Networks as Gradient Flows: understanding graph convolutions via energy

Gradient flows are differential equations that minimize an energy functional and constitute the main descriptors of physical systems. We apply this formalism to Graph Neural Networks (GNNs) to develop new frameworks for learning on graphs as well as provide a better theoretical understanding of existing ones. We derive GNNs as a gradient flow equation of a parametric energy that provides a physics-inspired interpretation of GNNs as learning particle dynamics in the feature space. In particular, we show that in graph convolutional models (GCN), the positive/negative eigenvalues of the channel mixing matrix correspond to attractive/repulsive forces between adjacent features. We rigorously prove how the channel-mixing can learn to steer the dynamics towards low or high frequencies, which allows to deal with heterophilic graphs. We show that the same class of energies is decreasing along a larger family of GNNs; albeit not gradient flows, they retain their inductive bias. We experimentally evaluate an instance of the gradient flow framework that is principled, more efficient than GCN, and achieves competitive performance on graph datasets of varying homophily often outperforming recent baselines specifically designed to target heterophily.Comment: First two authors equal contribution; 39 page

Sharing success - understanding barriers and enablers to secondary prophylaxis delivery for rheumatic fever and rheumatic heart disease

Background: Rheumatic fever (RF) and rheumatic heart disease (RHD) cause considerable morbidity and mortality amongst Australian Aboriginal and Torres Strait Islander populations. Secondary antibiotic prophylaxis in the form of 4-weekly benzathine penicillin injections is the mainstay of control programs. Evidence suggests, however, that delivery rates of such prophylaxis are poor. Methods: This qualitative study used semi-structured interviews with patients, parents/care givers and health professionals, to explore the enablers of and barriers to the uptake of secondary prophylaxis. Data from participant interviews (with 11 patients/carers and 11 health practitioners) conducted in four far north Queensland sites were analyzed using the method of constant comparative analysis. Results: Deficits in registration and recall systems and pain attributed to injections were identified as barriers to secondary prophylaxis uptake. There were also varying perceptions regarding responsibility for ensuring injection delivery. Enablers of secondary prophylaxis uptake included positive patient-healthcare provider relationships, supporting patient autonomy, education of patients, care givers and healthcare providers, and community-based service delivery. Conclusion: The study findings provide insights that may facilitate enhancement of secondary prophylaxis delivery systems and thereby improve uptake of secondary prophylaxis for RF/RHD