Operator splitting for the Benjamin-Ono equation

In this paper we analyze operator splitting for the Benjamin-Ono equation, u_t = uu_x + Hu_xx, where H denotes the Hilbert transform. If the initial data are sufficiently regular, we show the convergence of both Godunov and Strang splitting.Comment: 18 Page

Multilevel Monte Carlo for Random Degenerate Scalar Convection Diffusion Equation

We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous dependence of weak solutions on data in the deterministic case, we develop a definition of random entropy solution. We establish existence, uniqueness, measurability and integrability results for these random entropy solutions, generalizing \cite{Mishr478,MishSch10a} to possibly degenerate hyperbolic-parabolic problems with random data. We next address the numerical approximation of random entropy solutions, specifically the approximation of the deterministic first and second order statistics. To this end, we consider explicit and implicit time discretization and Finite Difference methods in space, and single as well as Multi-Level Monte-Carlo methods to sample the statistics. We establish convergence rate estimates with respect to the discretization parameters, as well as with respect to the overall work, indicating substantial gains in efficiency are afforded under realistic regularity assumptions by the use of the Multi-Level Monte-Carlo method. Numerical experiments are presented which confirm the theoretical convergence estimates.Comment: 24 Page

The effectiveness of public health interventions to reduce the health impact of climate change:a systematic review of systematic reviews

Climate change is likely to be one of the most important threats to public health in the coming years. Yet despite the large number of papers considering the health impact of climate change, few have considered what public health interventions may be of most value in reducing the disease burden. We aimed to evaluate the effectiveness of public health interventions to reduce the disease burden of high priority climate sensitive diseases

Prox1 Regulates the Notch1-Mediated Inhibition of Neurogenesis

During development of the spinal cord, Prox1 controls the balance between proliferation and differentiation of neural progenitor cells via suppression of Notch1 gene expression

Cardiac lymphatics in health and disease

The lymphatic vasculature, which accompanies the blood vasculature in most organs, is indispensable in the maintenance of tissue fluid homeostasis, immune cell trafficking, and nutritional lipid uptake and transport, as well as in reverse cholesterol transport. In this Review, we discuss the physiological role of the lymphatic system in the heart in the maintenance of cardiac health and describe alterations in lymphatic structure and function that occur in cardiovascular pathology, including atherosclerosis and myocardial infarction. We also briefly discuss the role that immune cells might have in the regulation of lymphatic growth (lymphangiogenesis) and function. Finally, we provide examples of how the cardiac lymphatics can be targeted therapeutically to restore lymphatic drainage in the heart to limit myocardial oedema and chronic inflammation.Peer reviewe