Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings

The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider several aspects of these groups: First, their systematic construction from associative algebras, secondly, their suitability for the characterization of wavefront sets, and finally, the question of constructing embeddings into the symplectic group in a way that intertwines the quasi-regular representation with the metaplectic one. For all questions, it is possible to treat the full class of generalized shearlet groups in a comprehensive and unified way, thus generalizing known results to an infinity of new cases. Our presentation emphasizes the interplay between the algebraic structure underlying the construction of the shearlet dilation groups, the geometric properties of the dual action, and the analytic properties of the associated shearlet transforms.Comment: 28 page

Parental decisional satisfaction after hypospadias repair in the United Kingdom

Background: in hypospadias, the aim of surgical treatment is to achieve both desirable functional and cosmetic outcomes; however, complications following surgery are common and 18% of boys require re-operation. In mild degrees of hypospadias, repair may be offered entirely to improve cosmesis, meaning parents should be fully informed of this and the potential for complications, during the consent process. Parents’ decision-making may be aided by making them aware of how others in a similar position have felt about the decision that they made for their child. One method of measuring parental satisfaction is decisional regret (DR). Objectives: to assess parental satisfaction following hypospadias surgery in the United Kingdom by assessing DR and to determine the feasibility of obtaining meaningful data via a mobile phone survey. Study design: the National Outcomes Audit in Hypospadias database was commissioned by the British Association of Paediatric Surgeons to capture clinical information from hypospadias repairs. Following ethical approval (16/NW/0819), a text message was sent to mobile numbers in the database inviting participation in a questionnaire incorporating the validated DR scale (DRS). The primary outcome measure was mean DRS score, which was correlated with clinical information, a score of zero indicated no regret and 100 indicated maximum regret. Results: there were 340 (37%) responses. The median age at the primary procedure was 16 (interquartile range 13–20) months. No DR (score = 0) was detected in 186 (55% [95%CI 49–60]) respondents; however, moderate-to-severe DR (score = 26–100) was seen in 21 (6.2% [95%CI 3.6–8.7]) respondents. On multivariate analysis, a distal meatus, a small glans and developing complications requiring repeat surgery were all associated with increased levels of regret (Table). There was no association between DR and cases performed per surgeon. Discussion: around half of respondents demonstrated no DR and postoperative complications requiring surgery were associated with the highest levels of DR, which is similar to a Canadian study. Lorenzo et al. however found that DR was associated with circumcision, which was undertaken in all boys; however, in this UK study, around a third of boys were circumcised and regret levels between those circumcised and those not circumcised were similar. The limitations of this work include the following: surgeons submitting their own data on complications and there is potential of selection bias between respondents and non-respondents as with any survey. Conclusions: data from this study can be used to improve pre-operative counselling during the consent process. Smart mobile phone technology can be used successfully to distribute and collect parent-reported outcomes. [Table presented]</p

Morfologia de sementes e do desenvolvimento pós-seminal de espécies de Bromeliaceae Seed and post-seminal development morphology on Bromeliaceae species

O estudo teve como objetivos caracterizar as sementes, fornecendo informações sobre o tipo e o tempo médio de germinação e de formação de plântulas, além de descrever a morfologia do desenvolvimento pós-seminal de seis espécies de Bromeliaceae. Os resultados mostram germinação do tipo epígea e plântulas criptocotiledonares para todas as espécies. As porcentagens máximas de germinação obtidas, acima de 80%, indicam alta qualidade fisiológica das sementes. O tempo médio de germinação e de formação de plântulas foi de 4-15 e 8-18 dias, respectivamente. As sementes são filiformes a elípticas, lisas ou com apêndices plumosos. Os caracteres morfológicos mais relevantes para a diferenciação entre gêneros e subfamílias de Bromeliaceae referem-se à forma e ao tipo de apêndices das sementes, e na forma e tamanho da bainha cotiledonar, hipocótilo e raiz primária das plântulas, subsidiando estudos taxonômicos, ecológicos e na área de tecnologia de sementes.<br>The aim of this study was to characterize the seeds, providing information about germination type and seedling rate, in addition to describe the post-seminal development morphology of the six species of Bromeliaceae. The results showed that the germination is epigeal with cryptocotylar seedlings. Maximum germination percentage was over 80%, for all species, indicating high physiological quality of the seeds. Germination and seedling rate was 4-15 and 8-18 days, respectively. Seeds are filiform to elliptical, smooth or with flight apparatus. The most relevant morphological characters for distinguishing among genera and subfamilies are shape and appendices of the seeds, form and size of the cotyledonal sheath, hypocotyl and primary root, providing information on taxonomic, ecological and seed technology studies