Motion by Curvature of Planar Networks

We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional multiphase system where the energy is simply the sum of the lengths of the interfaces, in particular it is a possible model for the growth of grain boundaries. Moreover, the motion of these networks of curves is the simplest example of curvature flow for sets which are ``essentially'' non regular. As a first step, in this paper we study in detail the case of three curves in the plane concurring at a single triple junction and with the other ends fixed. We show some results about the existence, uniqueness and, in particular, the global regularity of the flow, following the line of analysis carried on in the last years for the evolution by mean curvature of smooth curves and hypersurfaces

African Caribbean Pupils and Art Education

This work looks at the implications for teaching art and design to children of African Caribbean heritage in the British educational system. It is organised in three sections. The first provides the broad rationale for the thesis and includes an analysis of viewpoints on the diasporic state, this instead of a literature review. It asserts that children of African Caribbean and wider diasporic backgrounds are disadvantaged by not being made familiar with material from their cultural heritages. This has come about, I argue, by the enduring effects of the rupture that was the slave trade and the lack of acknowledgement of the significance of the black presence in the West. Consequently, the study contends, diasporic peoples are rendered invisible. The thesis asserts that culture as a context for teaching is fundamental to art and design education. Therefore African Caribbean learners, whose cultural heritages are not seen, are disadvantaged and appear culturally impoverished relative to· others. To substantiate this critical viewpoint, key texts by theorists on diasporic studies are referenced and analysed. These include David Dabydeen, CLR James, Stuart Hall and Kamau Brathwaite. My intention in this first section, therefore, is to throw light on the tensions surrounding the black subject, their lack of a positive presence in the critical and contextual material that children are exposed to and how this tension impacts on the teaching of art. The values disseminated in such pedagogies are central to the enquiry. Section two is dedicated to the presentation of the research findings. Six London-based art and design educationalists that work in environments with high numbers of African Caribbean students are interviewed about the undergirding rationale that drives their work. Four of the educationalists are black. This number of black teachers was selected in the expectation that they would have a particularly high commitment to black children's learning, and as such would have experimented with pedagogies that take account of their learning needs. The outcomes are, however, at times very different from what I had anticipated. This element of surprise is fundamental to the research and the analysis of the meanings embedded in such unexpected material is critical to it. One group of six African Caribbean young people from south London was also interviewed. This interview provided an opportunity to garner information from African Caribbean learners on their experience of state education. The short interview with them furnished critical viewpoints that throw light on young people's perceptions of teaching and learning in London schools. The third section presents a theoretical analysis of key points emerging from the data that could have a bearing on African Caribbean student learning in art and design. Finally, the concluding chapter reflects on the findings in the thesis and provides a pointer to their significance for teachers and school pupils

Post-intervention Status in Patients With Refractory Myasthenia Gravis Treated With Eculizumab During REGAIN and Its Open-Label Extension

OBJECTIVE: To evaluate whether eculizumab helps patients with anti-acetylcholine receptor-positive (AChR+) refractory generalized myasthenia gravis (gMG) achieve the Myasthenia Gravis Foundation of America (MGFA) post-intervention status of minimal manifestations (MM), we assessed patients' status throughout REGAIN (Safety and Efficacy of Eculizumab in AChR+ Refractory Generalized Myasthenia Gravis) and its open-label extension. METHODS: Patients who completed the REGAIN randomized controlled trial and continued into the open-label extension were included in this tertiary endpoint analysis. Patients were assessed for the MGFA post-intervention status of improved, unchanged, worse, MM, and pharmacologic remission at defined time points during REGAIN and through week 130 of the open-label study. RESULTS: A total of 117 patients completed REGAIN and continued into the open-label study (eculizumab/eculizumab: 56; placebo/eculizumab: 61). At week 26 of REGAIN, more eculizumab-treated patients than placebo-treated patients achieved a status of improved (60.7% vs 41.7%) or MM (25.0% vs 13.3%; common OR: 2.3; 95% CI: 1.1-4.5). After 130 weeks of eculizumab treatment, 88.0% of patients achieved improved status and 57.3% of patients achieved MM status. The safety profile of eculizumab was consistent with its known profile and no new safety signals were detected. CONCLUSION: Eculizumab led to rapid and sustained achievement of MM in patients with AChR+ refractory gMG. These findings support the use of eculizumab in this previously difficult-to-treat patient population. CLINICALTRIALSGOV IDENTIFIER: REGAIN, NCT01997229; REGAIN open-label extension, NCT02301624. CLASSIFICATION OF EVIDENCE: This study provides Class II evidence that, after 26 weeks of eculizumab treatment, 25.0% of adults with AChR+ refractory gMG achieved MM, compared with 13.3% who received placebo

Minimal Symptom Expression' in Patients With Acetylcholine Receptor Antibody-Positive Refractory Generalized Myasthenia Gravis Treated With Eculizumab

The efficacy and tolerability of eculizumab were assessed in REGAIN, a 26-week, phase 3, randomized, double-blind, placebo-controlled study in anti-acetylcholine receptor antibody-positive (AChR+) refractory generalized myasthenia gravis (gMG), and its open-label extension