Nonlocal and multipoint boundary value problems for linear evolution equations

We derive the solution representation for a large class of nonlocal boundary value problems for linear evolution PDEs with constant coefficients in one space variable. The prototypical such PDE is the heat equation, for which problems of this form model physical phenomena in chemistry and for which we formulate and prove a full result. We also consider the third order case, which is much less studied and has been shown by the authors to have very different structural properties in general. The nonlocal conditions we consider can be reformulated as \emph{multipoint conditions}, and then an explicit representation for the solution of the problem is obtained by an application of the Fokas transform method. The analysis is carried out under the assumption that the problem being solved is well posed, i.e.\ that it admits a unique solution. For the second order case, we also give criteria that guarantee well-posedness.Comment: 28 pages, 4 figure

Unbound Universe

Astronom

Bleeding changes after levonorgestrel 52-mg intrauterine system insertion for contraception in women with self-reported heavy menstrual bleeding.

BackgroundThe levonorgestrel 52-mg intrauterine system has proven efficacy for heavy menstrual bleeding treatment in clinical trials, but few data exist to demonstrate how rapidly the effects occur and the effects in women with self-reported heavy bleeding, as seen commonly in clinical practice.ObjectiveEvaluate changes in bleeding patterns in women with self-reported heavy menstrual bleeding before levonorgestrel 52-mg intrauterine system insertion.Study designA total of 1714 women aged 16-45 years old received a levonorgestrel 52-mg intrauterine system in a multicenter trial evaluating contraceptive efficacy and safety for up to 10 years. At screening, participants described their baseline menstrual bleeding patterns for the previous 3 months. Participants completed daily diaries with subjective evaluation of bleeding information for the first 2 years. For this analysis, we included women with at least 1 complete 28-day cycle of intrauterine system use and excluded women using a hormonal or copper intrauterine contraception in the month prior to study enrollment. We evaluated changes in menstrual bleeding and discontinuation for bleeding complaints per 28-day cycle over 26 cycles (2 years) in women who self-reported their baseline pattern as heavy. We also compared rates of amenorrhea, defined as no bleeding or spotting, within the entire study population in women with subjective heavy menstrual bleeding at baseline compared with those who did not complain of heavy menstrual bleeding.ResultsOf the 1513 women in this analysis, 150 (9.9%) reported baseline heavy menstrual bleeding. The majority of women reported no longer experiencing heavy menstrual bleeding by the end of cycle 1 (112/150, 74.7%) with even greater rates by cycle 2 (124/148, 83.8%). At the end of cycles 6, 13, and 26, 129 of 140 (92.1%; 95% confidence interval, 87.7%-96.6%), 114 of 123 (92.7%; 95% confidence interval, 88.1%-97.3%), and 100 of 103 (97.1%; 95% confidence interval, 93.8%-100%) women reported no heavy menstrual bleeding, respectively. After cycles 13 and 26, 63 of 123 (51.2%; 95% confidence interval, 42.4%-60.1%) and 66 of 103 (64.1%; 95% confidence interval, 54.8%-73.3%), respectively, reported their bleeding as amenorrhea or spotting only. A lower proportion of women with baseline self-reported heavy menstrual bleeding reported amenorrhea as compared with women in the overall study cohort without heavy menstrual bleeding at the end of 6 cycles (319 [25.5%] vs 21 [15.0%], P=.005) and 13 cycles (382 [34.4%] vs 26 [21.1%], P=.003); differences were not significant after 19 cycles (367 [37.2%] vs 36 [31.0%], P=.022) and 26 cycles (383 [43.5%] vs 38 [36.9%], P=.21). Only 4 (2.7%) women with baseline heavy menstrual bleeding discontinued for bleeding complaints (2 for heavy menstrual bleeding and 2 for irregular bleeding), all within the first year.ConclusionMost women who self-report heavy menstrual bleeding experience significant improvement quickly after levonorgestrel 52-mg intrauterine system insertion. Discontinuation for bleeding complaints among women with baseline heavy menstrual bleeding is very low

UN Human Rights Violations Here at Home? The Plight of Undocumented and DACA Students in South Carolina, USA

South Carolina is arguably the most restrictive state in the nation as it pertains to access to higher education for immigrant students, particularly undocumented and DACA (Deferred Action for Childhood Arrivals) students. As we show through personal interviews, this has had a detrimental effect on the lives of many immigrant students throughout the state. It also conflicts with the ideals of human rights in regard to access to higher education and equality which are laid out in the UNESCO Convention Against Discrimination in Education. Our analysis of South Carolina’s policies helps shed a light on the greater issues related to immigrant education rights across the nation and how they compare to the immigration policies of more welcoming developed nations. As the United States seeks to be a champion for human rights around the world, we need to confront our own problematic educational policies, which often leave many students behind

Developing a panarchy model of landscape conservation and management of alpine-mountain grassland in Northern Italy.

This paper explores methods of applying resilience theory to a case study of natural resource management and the cultural landscape of upland and alpine pasture in northern Italy. We identify that the close interaction between alpine pastures and its managers offers a strong fit with the concept of a social-ecological system that maintains the cultural landscape. We first considered a descriptive approach looking historically at socio-economic development in the study area. We explored whether this can be related to resilience phenomena such as regime shifts, thresholds and/or regime stability through adaptive processes. However, we found it difficult at this overarching level to conceptually combine natural and social capital of alpine pastures and their managers in any quantitative way. We also interpreted our data through considering economic, social and ecological information as acting within separate but interacting domains. This led us to construct conceptual models of adaptive cycles to describe the alpine mountain grassland ecosystem of our study site and to conclude that a panarchy model can offer a powerful metaphor for its ecological dynamics. This has practical implications both for the management of Natura 2000 interest and the maintenance of the cultural landscape in which this Alpine interest occurs. We suggest that Resilience theory through its dynamic approach of interacting scales of adaptive cycles offers useful insights into the resource management (of valued cultural and natural attributes) but that care is needed in distinguishing between descriptive metaphor and predictive model or "real" system.natural resource management, natural and social capital

FMG-Net and W-Net: Multigrid Inspired Deep Learning Architectures For Medical Imaging Segmentation

Accurate medical imaging segmentation is critical for precise and effective medical interventions. However, despite the success of convolutional neural networks (CNNs) in medical image segmentation, they still face challenges in handling fine-scale features and variations in image scales. These challenges are particularly evident in complex and challenging segmentation tasks, such as the BraTS multi-label brain tumor segmentation challenge. In this task, accurately segmenting the various tumor sub-components, which vary significantly in size and shape, remains a significant challenge, with even state-of-the-art methods producing substantial errors. Therefore, we propose two architectures, FMG-Net and W-Net, that incorporate the principles of geometric multigrid methods for solving linear systems of equations into CNNs to address these challenges. Our experiments on the BraTS 2020 dataset demonstrate that both FMG-Net and W-Net outperform the widely used U-Net architecture regarding tumor subcomponent segmentation accuracy and training efficiency. These findings highlight the potential of incorporating the principles of multigrid methods into CNNs to improve the accuracy and efficiency of medical imaging segmentation.Comment: Submitted to LatinX in AI (LXAI) Research Workshop @ NeurIPS 202