Numerical Simulation of the Korteweg–de Vries Equation with Machine Learning

A machine learning procedure is proposed to create numerical schemes for solutions of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg–de Vries equation. It is observed to be more accurate than finite difference or spectral methods on coarse grids when the initial data is near enough to the training set

Hydraulic flow through a channel contraction: multiple steady states

We have investigated shallow water flows through a channel with a contraction by experimental and theoretical means. The horizontal channel consists of a sluice gate and an upstream channel of constant width $b_0$ ending in a linear contraction of minimum width $b_c$. Experimentally, we observe upstream steady and moving bores/shocks, and oblique waves in the contraction, as single and multiple steady states, as well as a steady reservoir with a complex hydraulic jump in the contraction occurring in a small section of the $b_c/b_0$ and Froude number parameter plane. One-dimensional hydraulic theory provides a comprehensive leading-order approximation, in which a turbulent frictional parametrization is used to achieve quantitative agreement. An analytical and numerical analysis is given for two-dimensional supercritical shallow water flows. It shows that the one-dimensional hydraulic analysis for inviscid flows away from hydraulic jumps holds surprisingly well, even though the two-dimensional oblique hydraulic jump patterns can show large variations across the contraction channel

A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on ℝ, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed

Atmospheric Propagation of High Energy Lasers: Thermal Blooming Simulation

High Energy Laser (HEL) propagation through turbulent atmosphere is examined via numerical simulation. The beam propagation is modeled with the paraxial equation, which in turn is written as a system of equations for a quantum fluid, via the Madelung transform. A finite volume solver is applied to the quantum fluid equations, which supports sharp gradients in beam intensity. The atmosphere is modeled via a coupled advection-diffusion equation whose initial data have Kolmogorov spectrum. In this model the combined effects of thermal blooming, beam slewing, and deep turbulence are simulated

Evolution of Coronal Magnetic Field Parameters during X5.4 Solar Flare

The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz|≥ 300 G, areas of flare brightening seen in SDO Atmospheric Imaging Assembly imagery, and areas with surface |B| ≥ 1000 G and high twist. Time series of the magnetic field parameters were analyzed to investigate the evolution of the coronal field during the solar flare event and discern pre-eruptive signatures. The data shows that areas with |B| ≥ 1000 G and |Tw|≥ 1.5 align well with areas of initial flare brightening during the pre-flare phase and at the beginning of the eruptive phase of the flare, suggesting that measurements of the photospheric magnetic field strength and twist can be used to predict the flare location within an active region if triggered. Additionally, the evolution of seven investigated magnetic field parameters indicated a destabilizing magnetic field structure that could likely erupt

Chlamydia trachomatis antigens in enteroendocrine cells and macrophages of the small bowel in patients with severe irritable bowel syndrome

<p>Abstract</p> <p>Background</p> <p>Inflammation and immune activation have repeatedly been suggested as pathogentic factors in irritable bowel syndrome (IBS). The driving force for immune activation in IBS remains unknown. The aim of our study was to find out if the obligate intracellular pathogen <it>Chlamydia </it>could be involved in the pathogenesis of IBS.</p> <p>Methods</p> <p>We studied 65 patients (61 females) with IBS and 42 (29 females) healthy controls in which IBS had been excluded. Full thickness biopsies from the jejunum and mucosa biopsies from the duodenum and the jejunum were stained with a monoclonal antibody to <it>Chlamydia </it>lipopolysaccharide (LPS) and species-specific monoclonal antibodies to <it>C. trachomatis </it>and <it>C. pneumoniae</it>. We used polyclonal antibodies to chromogranin A, CD68, CD11c, and CD117 to identify enteroendocrine cells, macrophages, dendritic, and mast cells, respectively.</p> <p>Results</p> <p><it>Chlamydia </it>LPS was present in 89% of patients with IBS, but in only 14% of healthy controls (p < 0.001) and 79% of LPS-positive biopsies were also positive for <it>C. trachomatis </it>major outer membrane protein (MOMP). Staining for <it>C. pneumoniae </it>was negative in both patients and controls. <it>Chlamydia </it>LPS was detected in enteroendocrine cells of the mucosa in 90% of positive biopsies and in subepithelial macrophages in 69% of biopsies. Biopsies taken at different time points in 19 patients revealed persistence of <it>Chlamydia </it>LPS up to 11 years. The odds ratio for the association of <it>Chlamydia </it>LPS with presence of IBS (43.1; 95% CI: 13.2-140.7) is much higher than any previously described pathogenetic marker in IBS.</p> <p>Conclusions</p> <p>We found <it>C. trachomatis </it>antigens in enteroendocrine cells and macrophages in the small bowel mucosa of patients with IBS. Further studies are required to clarify if the presence of such antigens has a role in the pathogenesis of IBS.</p

Measurement of the Top Quark Mass with the Collider Detector at Fermilab

This report describes a measurement of the top quark mass in \ppbar collisions at a center of mass energy of 1.8 TeV. The data sample was collected with the CDF detector during the 1992--95 collider run at the Fermilab Tevatron, and corresponds to an integrated luminosity of 106 \pb. Candidate $t\bar{t}$ events in the ``lepton+jets'' decay channel provide our most precise measurement of the top quark mass. For each event a top mass is determined by using energy and momentum constraints on the production of the \ttbar pair and its subsequent decay. A likelihood fit to the distribution of reconstructed masses in the data sample gives a top mass in the lepton+jets channel of 176.1\pm 5.1 (stat.)\pm 5.3 (syst.) \gevcc. Combining this result with measurements from the ``all-hadronic'' and ``dilepton'' decay topologies yields a top mass of 176.1\pm 6.6 \gevcc.Comment: 158 pages, 41 figure

A thin-slice of institutionalised police brutality: a tradition of excessive force in the Chicago Police Department

In the Chicago Police Department, a sustained tradition of tolerating violent conduct has contributed to the fostering of a police culture in which the use of force is celebrated. Evidence suggests that there has been a historical reluctance to take action to discipline officers accused of misconduct – many of whom are highly decorated veterans of the Chicago Police Department. It is the contention of this article that the long-standing endorsement of excessive force in Chicago policing has compromised officers’ ability to thin-slice, a psychological process in which people are able to draw on their experiences and socio-cultural context to make quick decisions under pressure. Instead, officers are instinctively drawn to engage in misconduct as a means to an end, with the confidence that their actions will not attract the sanction of their superiors

Albiglutide and cardiovascular outcomes in patients with type 2 diabetes and cardiovascular disease (Harmony Outcomes): a double-blind, randomised placebo-controlled trial

Background: Glucagon-like peptide 1 receptor agonists differ in chemical structure, duration of action, and in their effects on clinical outcomes. The cardiovascular effects of once-weekly albiglutide in type 2 diabetes are unknown. We aimed to determine the safety and efficacy of albiglutide in preventing cardiovascular death, myocardial infarction, or stroke. Methods: We did a double-blind, randomised, placebo-controlled trial in 610 sites across 28 countries. We randomly assigned patients aged 40 years and older with type 2 diabetes and cardiovascular disease (at a 1:1 ratio) to groups that either received a subcutaneous injection of albiglutide (30–50 mg, based on glycaemic response and tolerability) or of a matched volume of placebo once a week, in addition to their standard care. Investigators used an interactive voice or web response system to obtain treatment assignment, and patients and all study investigators were masked to their treatment allocation. We hypothesised that albiglutide would be non-inferior to placebo for the primary outcome of the first occurrence of cardiovascular death, myocardial infarction, or stroke, which was assessed in the intention-to-treat population. If non-inferiority was confirmed by an upper limit of the 95% CI for a hazard ratio of less than 1·30, closed testing for superiority was prespecified. This study is registered with ClinicalTrials.gov, number NCT02465515. Findings: Patients were screened between July 1, 2015, and Nov 24, 2016. 10 793 patients were screened and 9463 participants were enrolled and randomly assigned to groups: 4731 patients were assigned to receive albiglutide and 4732 patients to receive placebo. On Nov 8, 2017, it was determined that 611 primary endpoints and a median follow-up of at least 1·5 years had accrued, and participants returned for a final visit and discontinuation from study treatment; the last patient visit was on March 12, 2018. These 9463 patients, the intention-to-treat population, were evaluated for a median duration of 1·6 years and were assessed for the primary outcome. The primary composite outcome occurred in 338 (7%) of 4731 patients at an incidence rate of 4·6 events per 100 person-years in the albiglutide group and in 428 (9%) of 4732 patients at an incidence rate of 5·9 events per 100 person-years in the placebo group (hazard ratio 0·78, 95% CI 0·68–0·90), which indicated that albiglutide was superior to placebo (p&lt;0·0001 for non-inferiority; p=0·0006 for superiority). The incidence of acute pancreatitis (ten patients in the albiglutide group and seven patients in the placebo group), pancreatic cancer (six patients in the albiglutide group and five patients in the placebo group), medullary thyroid carcinoma (zero patients in both groups), and other serious adverse events did not differ between the two groups. There were three (&lt;1%) deaths in the placebo group that were assessed by investigators, who were masked to study drug assignment, to be treatment-related and two (&lt;1%) deaths in the albiglutide group. Interpretation: In patients with type 2 diabetes and cardiovascular disease, albiglutide was superior to placebo with respect to major adverse cardiovascular events. Evidence-based glucagon-like peptide 1 receptor agonists should therefore be considered as part of a comprehensive strategy to reduce the risk of cardiovascular events in patients with type 2 diabetes. Funding: GlaxoSmithKline