A family of compact semitoric systems with two focus-focus singularities

About 6 years ago, semitoric systems were classified by Pelayo & Vu Ngoc by means of five invariants. Standard examples are the coupled spin oscillator on $\mathbb{S}^2 \times \mathbb{R}^2$ and coupled angular momenta on $\mathbb{S}^2 \times \mathbb{S}^2$, both having exactly one focus-focus singularity. But so far there were no explicit examples of systems with more than one focus-focus singularity which are semitoric in the sense of that classification. This paper introduces a 6-parameter family of integrable systems on $\mathbb{S}^2 \times \mathbb{S}^2$ and proves that, for certain ranges of the parameters, it is a compact semitoric system with precisely two focus-focus singularities. Since the twisting index (one of the semitoric invariants) is related to the relationship between different focus-focus points, this paper provides systems for the future study of the twisting index.Comment: Update to most recent version: some typos removed; minor inaccuracies corrected; better layou

Invariance of immersed Floer cohomology under Lagrangian surgery

We show that cellular Floer cohomology of an immersed Lagrangian brane is invariant under smoothing of a self-intersection point if the quantum valuation of the weakly bounding cochain vanishes and the Lagrangian has dimension at least two. The chain-level map replaces the two orderings of the self-intersection point with meridianal and longitudinal cells on the handle created by the surgery, and uses a bijection between holomorphic disks developed by Fukaya-Oh-Ohta-Ono. Our result generalizes invariance of potentials for certain Lagrangian surfaces in Dimitroglou-Rizell--Ekholm--Tonkonog, and implies the invariance of Floer cohomology under mean curvature flow with this type of surgery, as conjectured by Joyce.Comment: 100 pages. This version has minor corrections (one which was in the isomorphism of Floer cohomologies, but which did not affect the main result.

Edge-region grouping in figure-ground organization and depth perception.

Edge-region grouping (ERG) is proposed as a unifying and previously unrecognized class of relational information that influences figure-ground organization and perceived depth across an edge. ERG occurs when the edge between two regions is differentially grouped with one region based on classic principles of similarity grouping. The ERG hypothesis predicts that the grouped side will tend to be perceived as the closer, figural region. Six experiments are reported that test the predictions of the ERG hypothesis for 6 similarity-based factors: common fate, blur similarity, color similarity, orientation similarity, proximity, and flicker synchrony. All 6 factors produce the predicted effects, although to different degrees. In a 7th experiment, the strengths of these figural/depth effects were found to correlate highly with the strength of explicit grouping ratings of the same visual displays. The relations of ERG to prior results in the literature are discussed, and possible reasons for ERG-based figural/depth effects are considered. We argue that grouping processes mediate at least some of the effects we report here, although ecological explanations are also likely to be relevant in the majority of cases

Strengths and Silences: The Experiences of Lesbian, Gay, Bisexual and Transgender Students in Rural and Small Town Schools

For more than 20 years, GLSEN has worked to make schools safer for all students; it has sought specifically to reduce the bullying and harassment targeted at students' sexual orientation, gender identity, and gender expression. For lesbian, gay, bisexual, and transgender (LGBT) students across the country, violence and harassment experienced in school affect their ability to learn. Although schools in urban areas are typically regarded as more violent or dangerous than schools in other areas, findings from our National School Climate Surveys consistently show that it is most often rural schools that may pose the greatest threats for LGBT students. It may be that community characteristics, such as religious and cultural traditions, income, and educational levels, influence individual beliefs and attitudes toward LGBT people in these areas. It may also be that a lack of positive LGBT-related school resources negatively affects LGBT students' school engagement and academic performance, particularly if they also experience bullying and harassment. Although research on the educational experiences of LGBT youth has grown considerably over the past 25 years, less is known about rural students specifically. This research report examines the experiences of LGBT students in small town and rural areas on matters related to biased language in schools, school safety, harassment and victimization, educational outcomes, school engagement, and LGBT-related resources and support. It also examines the prevalence and utility of LGBT-related resources in rural schools. Finally, this report concludes by advocating for more intentional policies, measures, and programs that protect LGBT students

Discretion and the building of institutions: a critical examination of the administration of Indonesia’s overseas labour migration programme

This thesis examines the role of discretion in determining the evolving structures of Indonesia’s overseas labour migration programme. Focusing on the turbulent period following the establishment of the National Agency for the Placement and Protection of Overseas Indonesian Workers in 2007, the study examines the impact of intra-state conflict on the workings of the bureaucracy centrally, in five other locations in Indonesia and in three Asian host countries. Each of these case studies engages with the everyday strategies of bureaucrats as they seek to navigate the place-specific ways in which the legal framework of the programme collide with the objectives of the formal institutions competing for control over its implementation. In all of these cases, discretion emerges as a key resource for policymakers and administrators. At the highest level, it serves as a conduit for the ambitions of senior officials competing for influence in the brave new world of democratic Indonesia. For grassroots bureaucrats, it is a useful tool in the management of the complex – and sometimes conflicting – demands of managing the overseas labour migration programme during a period of prolonged inter-agency conflict. In effect, then, discretion serves as a kind of ‘institutional fix’ in situations where institutions begin to break down. In empirical terms, the thesis reveals the extent to which local context influences the level of discretion available to individual bureaucrats and the decisions they ultimately make. At a theoretical level, the study explains how that discretion draws on – and reinforces – misalignments between state institutions and the formal legal structures that govern them, while at the same time making it possible for those institutions to continue operating under difficult circumstances. In doing so, it confirms – in contradiction to the literature – that while discretion can indeed contribute to corruption and other forms of illegality, it can also play a positive role in the maintenance of state function