Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?

We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. Within the class of Filippov solutions, if $\Sigma$ is attractive, one should expect solution trajectories to slide on $\Sigma$. It is well known, however, that the classical Filippov convexification methodology is ambiguous on $\Sigma$. The situation is further complicated by the possibility that, regardless of how sliding on $\Sigma$ is taking place, during sliding motion a trajectory encounters so-called generic first order exit points, where $\Sigma$ ceases to be attractive. In this work, we attempt to understand what behavior one should expect of a solution trajectory near $\Sigma$ when $\Sigma$ is attractive, what to expect when $\Sigma$ ceases to be attractive (at least, at generic exit points), and finally we also contrast and compare the behavior of some regularizations proposed in the literature. Through analysis and experiments we will confirm some known facts, and provide some important insight: (i) when $\Sigma$ is attractive, a solution trajectory indeed does remain near $\Sigma$, viz. sliding on $\Sigma$ is an appropriate idealization (of course, in general, one cannot predict which sliding vector field should be selected); (ii) when $\Sigma$ loses attractivity (at first order exit conditions), a typical solution trajectory leaves a neighborhood of $\Sigma$; (iii) there is no obvious way to regularize the system so that the regularized trajectory will remain near $\Sigma$ as long as $\Sigma$ is attractive, and so that it will be leaving (a neighborhood of) $\Sigma$ when $\Sigma$ looses attractivity. We reach the above conclusions by considering exclusively the given piecewise smooth system, without superimposing any assumption on what kind of dynamics near $\Sigma$ (or sliding motion on $\Sigma$) should have been taking place.Comment: 19 figure

k-core organization of complex networks

We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the structure of k-cores, their sizes, and their birth points -- the bootstrap percolation thresholds. We show that in networks with a finite mean number z_2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if z_2 diverges, the networks contain an infinite sequence of k-cores which are ultra-robust against random damage.Comment: 5 pages, 3 figure

ФОРМИРОВАНИЕ ТРЕХМЕРНЫХ СТРУКТУР В ПОДЛОЖКАХ КАРБИДА КРЕМНИЯ ПЛАЗМОХИМИЧЕСКИМ ТРАВЛЕНИЕМ

This article is a review of the technology for the formation of three−dimensional structures in silicon carbide substrates. The technological solution of these problems ion−stimulation plasmochemistry etching in its various modifications, the most successful being by ICP sources (sources of inductively coupled plasma).Silicon carbide consists of silicon and carbon which produce volatile fluorides in reaction with fluorine. Therefore for plasmochemistry etching of silicon carbide one uses fluorine−containing gases, most often sulfur hexafluoride (SF6), and sometimes with additions of oxygen and argon. During plasmochemistry etching of silicon carbide one  uses the  mask  the  material  of which does not interact with fluorine.  As a rule these are thin films of metals, e.g.  Cu, Al and Ni, and sometimes films of silicon oxides.The most  important technological trend of this process is making through holes  by etching of SiC substrates with GaN epitaxial layers, and their subsequent metallization.In this review we will present examples of ICP source applications for the formation of micro− and nano−sized three−dimensional structures in silicon carbide substrates, including  making  through holes  in SiC substrates with GaN epitaxial layers.Представлен обзор, посвященный технологии формирования трехмерных структур в подложках  карбида кремния. Технологически эта задача решается ионно−стимулированным плазмо-химическим травлением в различных его вариациях, и наиболее успешно — с помощью источника с индуктивно связанной плазмой (ICP).Карбид  кремния состоит из кремния и углерода, которые в реакции со фтором образуют летучие фториды. Реакция травления идет при взаимодействии кремния и углерода с активными радикалами и ионами фтора. Поэтому для плазмохимического травления карбида кремния используют фторсодержащий газ, в большинстве случаев — шестифтористую серу SF6 (часто с добавкой кислорода и иногда  аргона). В качестве масок при плазмохимическом травлении карбида кремния применяют  материалы, не взаимодействующие с фтором. Преимущественно это пленки металлов Cu, Al и Ni, реже — пленки оксида кремния.Особо  важное технологическое направление, связанное с плазмохимическим травлением подложек SiC с нанесенными на них эпитаксиальными слоями GaN, — это получение в них сквозных  отверстий и их последующая металлизация.Приведены примеры использования источников ICP для формирования трехмерных структур с микро− и наноразмерами в карбиде кремния.В том числе рассмотрено формирование сквозных  отверстий в подложках карбида кремния с эпитаксиальными слоями нитрида галлия

Turning points: the personal and professional circumstances that lead academics to become middle managers

In the current higher education climate, there is a growing perception that the pressures associated with being an academic middle manager outweigh the perceived rewards of the position. This article investigates the personal and professional circumstances that lead academics to become middle managers by drawing on data from life history interviews undertaken with 17 male and female department heads from a range of disciplines, in a post-1992 UK university. The data suggests that experiencing conflict between personal and professional identities, manifested through different socialization experiences over time, can lead to a ‘turning point’ and a decision that affects a person’s career trajectory. Although the results of this study cannot be generalized, the findings may help other individuals and institutions move towards a firmer understanding of the academic who becomes head of department—in relation to theory, practice and research

Professional learning for Islamic education teachers in the UAE

© 2020 Christian Education. Islamic education (IE) is currently receiving increased attention and undergoing major changes at the international level. A few studies have investigated the structured professional development programmes provided to IE teachers. However, the area of autonomous IE teacher professional learning continues to be under-researched. Based on Al-Zarnuji\u27s framework of lifelong learning, the authors interviewed IE teachers to investigate the practices, attitudes, and influencing factors regarding IE teacher professional learning in the United Arab Emirates (UAE). This study shows that IE teachers are eager to engage in teacher-driven learning experiences. The directions for the IE teachers’ intended growth are mainly influenced by contemporary advancements in the field of education. The findings of this study highlight how IE teachers’ professional learning capitalises on the Islamic concept of lifelong learning and thereby opens a promising route for their effective growth to meet the high demand for skilled IE teachers in the UAE

Titin mutations in iPS cells define sarcomere insufficiency as a cause of dilated cardiomyopathy

Human mutations that truncate the massive sarcomere protein titin [TTN-truncating variants (TTNtvs)] are the most common genetic cause for dilated cardiomyopathy (DCM), a major cause of heart failure and premature death. Here we show that cardiac microtissues engineered from human induced pluripotent stem (iPS) cells are a powerful system for evaluating the pathogenicity of titin gene variants. We found that certain missense mutations, like TTNtvs, diminish contractile performance and are pathogenic. By combining functional analyses with RNA sequencing, we explain why truncations in the A-band domain of TTN cause DCM, whereas truncations in the I band are better tolerated. Finally, we demonstrate that mutant titin protein in iPS cell-derived cardiomyocytes results in sarcomere insufficiency, impaired responses to mechanical and {beta}-adrenergic stress, and attenuated growth factor and cell signaling activation. Our findings indicate that titin mutations cause DCM by disrupting critical linkages between sarcomerogenesis and adaptive remodeling

Nebuliser therapy in the intensive care unit

The relationship between identity, lived experience, sexual practices and the language through which these are conveyed has been widely debated in sexuality literature. For example, ‘coming out’ has famously been conceptualised as a ‘speech act’ (Sedgwick 1990) and as a collective narrative (Plummer 1995), while a growing concern for individuals’ diverse identifications in relations to their sexual and gender practices has produced interesting research focusing on linguistic practices among LGBT-identified individuals (Leap 1995; Kulick 2000; Cameron and Kulick 2006; Farqhar 2000). While an explicit focus on language remains marginal to literature on sexualities (Kulick 2000), issue of language use and translation are seldom explicitly addressed in the growing literature on intersectionality. Yet intersectional perspectives ‘reject the separability of analytical and identity categories’ (McCall 2005:1771), and therefore have an implicit stake in the ‘vernacular’ language of the researched, in the ‘scientific’ language of the researcher and in the relationship of continuity between the two. Drawing on literature within gay and lesbian/queer studies and cross-cultural studies, this chapter revisits debates on sexuality, language and intersectionality. I argue for the importance of giving careful consideration to the language we choose to use as researchers to collectively define the people whose experiences we try to capture. I also propose that language itself can be investigated as a productive way to foreground how individual and collective identifications are discursively constructed, and to unpack the diversity of lived experience. I address intersectional complexity as a methodological issue, where methodology is understood not only as the methods and practicalities of doing research, but more broadly as ‘a coherent set of ideas about the philosophy, methods and data that underlie the research process and the production of knowledge’ (McCall 2005:1774). My points are illustrated with examples drawn from my ethnographic study on ‘lesbian’ identity in urban Russia, interspersed with insights from existing literature. In particular, I aim to show that an explicit focus on language can be a productive way to explore the intersections between the global, the national and the local in cross-cultural research on sexuality, while also addressing issues of positionality and accountability to the communities researched

How should we measure psychological resilience in sport performers?

Psychological resilience is important in sport because athletes must constantly withstand a wide range of pressures to attain and sustain high performance. To advance psychologists’ understanding of this area, there exists an urgent need to develop a sport-specific measure of resilience. The purpose of this paper is to review psychometric issues in resilience research and to discuss the implications for sport psychology. Drawing on the wider general psychology literature to inform the discussion, the narrative is divided into three main sections relating to resilience and its assessment: adversity, positive adaptation, and protective factors. The first section reviews the different ways that adversity has been measured and considers the potential problems of using items with varying degrees of controllability and risk. The second section discusses the different approaches to assessing positive adaptation and examines the issue of circularity pervasive in resilience research. The final section explores the various issues related to the assessment of protective factors drawing directly from current measures of resilience in other psychology sub-disciplines. The commentary concludes with key recommendations for sport psychology researchers seeking to develop a measure of psychological resilience in athletes