Sequences of Willmore surfaces

In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the twistor projection of a holomorphic curve into complex projective space or the inversion of a minimal surface with planar ends in 4-space. These results give a unified explanation of previous work on the characterization of Willmore spheres and Willmore tori with non-trivial normal bundles by various authors.Comment: 10 page

The Lamé Class of Lorenz Curves.

In this paper, the class of Lamé Lorenz curves is studied. This family has the advantage of modeling inequality with a single parameter. The family has a double motivation: it can be obtain from an economic model and from simple transformations of classical Lorenz curves. The underlying cumulative distribution functions have a simple closed form, and correspond to the Singh-Maddala and Dagum distributions, which are well known in the economic literature. The Lorenz order is studied and several inequality and polarization measures are obtained, including Gini, Donaldson-Weymark-Kakwani, Pietra and Wolfson indices. Some extensions of the Lamé family are obtained. Fitting and estimation methods under two different data configuration are proposed. Empirical applications with real data are given. Finally, some relationships with other curves are included.The authors thank to Ministerio de Econom a y Competitividad, project ECO2010-15455, for partial support. The second author thanks to the Ministerio de Educaci on (FPU AP-2010-4907) for partial support. We are grateful for the constructive suggestions provided by the reviewers, which improved the paper

The Origin, Early Evolution and Predictability of Solar Eruptions

Coronal mass ejections (CMEs) were discovered in the early 1970s when space-borne coronagraphs revealed that eruptions of plasma are ejected from the Sun. Today, it is known that the Sun produces eruptive flares, filament eruptions, coronal mass ejections and failed eruptions; all thought to be due to a release of energy stored in the coronal magnetic field during its drastic reconfiguration. This review discusses the observations and physical mechanisms behind this eruptive activity, with a view to making an assessment of the current capability of forecasting these events for space weather risk and impact mitigation. Whilst a wealth of observations exist, and detailed models have been developed, there still exists a need to draw these approaches together. In particular more realistic models are encouraged in order to asses the full range of complexity of the solar atmosphere and the criteria for which an eruption is formed. From the observational side, a more detailed understanding of the role of photospheric flows and reconnection is needed in order to identify the evolutionary path that ultimately means a magnetic structure will erupt

Gadoxetate-enhanced Abbreviated MRI for Hepatocellular Carcinoma Surveillance: Preliminary Experience.

To describe a single-center preliminary experience with gadoxetate disodium-enhanced abbreviated MRI for hepatocellular carcinoma (HCC) screening and surveillance in patients with cirrhosis or chronic hepatitis B virus (cHBV). This was a retrospective study of consecutive patients aged 18 years and older with cirrhosis or cHBV who underwent at least one gadoxetate-enhanced abbreviated MRI examination for HCC surveillance from 2014 through 2016. Examinations were interpreted prospectively by one of six abdominal radiologists for clinical care. Clinical, imaging, and other data were extracted from electronic medical records. Diagnostic adequacy was assessed in all patients. Diagnostic accuracy was assessed in the subset of patients who could be classified as having HCC or not having HCC on the basis of a composite reference standard. In this study, 330 patients (93% with cirrhosis; 45% women; mean age, 59 years) underwent gadoxetate-enhanced abbreviated MRI. In the 330 patients, 311 (94.2%) baseline gadoxetate-enhanced abbreviated MRI examinations were diagnostically adequate. Of 141 (43%) of the 330 patients, 91.4% (129 of 141) could be classified as not having HCC and 8.6% (12 of 141) could be classified as having HCC. Baseline gadoxetate-enhanced abbreviated MRI had 0.92 sensitivity (95% confidence interval [CI]: 0.62, 1.00) and 0.91 specificity (95% CI: 0.84, 0.95) for detection of HCC. Of the 330 patients who underwent baseline gadoxetate-enhanced abbreviated MRI, 187 (57%) were lost to follow-up. Gadoxetate-enhanced abbreviated MRI is feasible clinically, has a high diagnostic adequacy rate, and, on the basis of our preliminary experience, accurately depicts HCC in high-risk patients. Strategies to enhance follow-up compliance are needed.© RSNA, 2019Keywords: Abdomen/GI, Cirrhosis, Liver, MR-Imaging, Oncology, ScreeningSupplemental material is available for this article