Lattice congruences of the weak order

We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group. Our starting point is a theorem from a previous paper which gives a geometric description of the poset of join-irreducibles of the congruence lattice of the poset of regions in terms of certain polyhedral decompositions of the hyperplanes. For a finite Coxeter system (W,S) and a subset K of S, let \eta_K:w \mapsto w_K be the projection onto the parabolic subgroup W_K. We show that the fibers of \eta_K constitute the smallest lattice congruence with 1\equiv s for every s\in(S-K). We give an algorithm for determining the congruence lattice of the weak order for any finite Coxeter group and for a finite Coxeter group of type A or B we define a directed graph on subsets or signed subsets such that the transitive closure of the directed graph is the poset of join-irreducibles of the congruence lattice of the weak order.Comment: 26 pages, 4 figure

Scanning optical pyrometer for measuring temperatures in hollow cathodes

Life-limiting processes in hollow cathodes are determined largely by the temperature of the electron emitter. To support cathode life assessment, a noncontact temperature measurement technique which employs a stepper motor-driven fiber optic probe was developed. The probe is driven inside the hollow cathode and collects light radiated by the hot interior surface of the emitter. Ratio pyrometry is used to determine the axial temperature profile. Thermocouples on the orifice plate provide measurements of the external temperature during cathode operation and are used to calibrate the pyrometer system in situ with a small oven enclosing the externally heated cathode. The diagnostic method and initial measurements of the temperature distribution in a hollow cathode are discussed

What are children's trusts? Early findings from a national survey

<i>Background:</i> The Children Act 2004 and National Service Framework for Children, Young People and Maternity Services require fuller integration of health, education and social services for children and young people in England and Wales. The UK government supported the establishment of 35 experimental children's trust pathfinders (henceforth called children's trusts) in England. <i>Methods:</i> A questionnaire was completed by managers in all 35 children's trusts a year after their start. Children's trust documents were examined. Census and performance indicators were compared between children's trust areas and the rest of England. <i>Results</i> Children's trust areas had demographic and social characteristics typical of England. All children's trusts aimed to improve health, education and social services by greater managerial and service integration. All had boards representing the three sectors; other agencies’ representation varied. Two-thirds of children's trusts had moved towards pooling budgets in at least some service areas. At this stage in their development, some had prioritized joint procurement or provision of services, with formal managerial structures, while others favoured an informal strategic planning, co-ordination and information sharing approach. The commonest priorities for services development were for disabled children (16 children's trusts), followed by early intervention (11) and mental health services (8). <i>Conclusions:</i> The diverse strategies adopted by these 35 children's trusts during their first year is due to their own characteristics and to the way government strategy developed during this period. Whilst some prioritized organizational development, joint financing and commissioning, and information sharing, others laid more emphasis on mechanisms for bringing front-line professionals closer together. Their experiences are of value to others deciding how best to integrate children's services

Effects of large-scale heathland management on thermal regimes and predation on adders Vipera berus

Management prescriptions for species of conservation concern often focus on creating appropriate habitat conditions, but the spatial scales over which these actions are applied can potentially impact their success. In Northwestern Europe, preventing further loss of lowland heathland through successional changes often involves the mechanical removal of vegetation, creating large blocks of open homogenous habitat. We investigate the influence of this broad-scale habitat management on a heathland specialist, the adder Vipera berus. By deploying temperature loggers and Plasticine adder models in heathland areas with and without complex vegetation cover, we show that (1) cleared areas lack both the temperature variation adders need to thermoregulate effectively and suitable refuges from dangerously high summer temperatures, and (2) attacks by dogs and trampling by grazing livestock are significantly more frequent in cleared areas and closer to footpaths. Habitat management strategies that retain some structural complexity of vegetation within cleared areas, and diverting footpaths away from cleared areas and/or strategic placement of barrier hedging around these areas could potentially reduce the exposure of adders to high predation risk and thermal extremes

Investigation of the Dimensional Variation of Microstructures Through the μMIM Process

The mass production of components with dimensions in the micron and sub-micron range is anticipated to be one of the leading technology areas for the present century and to be of high market potential. Micro metal injection molding (μMIM) has the potential to be an important contributor to this industry as it can produce precise metallic microstructures in large quantities at a relatively low production cost. The μMIM process is a miniaturization of metal injection molding (MIM) methods. The process comprises of four main steps: mixing, injection molding, debinding and sintering. A metallic powder is mixed with a binder system to form the feedstock. The feedstock is then injection molded into the required shape and the binder removed via thermal or other means. The final microstructures are obtained by sintering the remaining powder in a controlled environment. In this work, the dimensional variation of the microstructures, in particular the warpage, roughness and volume variation, at each stage of the μMIM process was quantified and compared. The results of a preliminary study of the sensitivity of warpage of the microstructures to the packing pressure are also reported.Singapore-MIT Alliance (SMA

Associahedra via spines

An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the associahedron with relevant properties related to the symmetric group and the classical permutahedron. We introduce the spine of a triangulation as its dual tree together with a labeling and an orientation. This notion extends the classical understanding of the associahedron via binary trees, introduces a new perspective on C. Hohlweg and C. Lange's construction closer to J.-L. Loday's original approach, and sheds light upon the combinatorial and geometric properties of the resulting realizations of the associahedron. It also leads to noteworthy proofs which shorten and simplify previous approaches.Comment: 27 pages, 11 figures. Version 5: minor correction

Investigating SSH Research and Publication Practices in Disciplinary and Institutional Contexts. A Survey-Based Comparative Approach in Two Universities

In this paper, we comparatively analyze, present and discuss the results from a survey on increasing the visibility of research achievements in the social sciences and humanities (SSH) that was carried out at the University of Vienna (Austria) and the University of Navarra (Spain) in 2016 and 2017. Covering four major topics—searching and finding literature, publishing, the visibility of research, and the assessment of research outputs—we ask the following questions: are there disciplinary differences to be identified, and how do they present themselves in the two institutional contexts? Discussing the results, we showcase how disciplinary and institutional traditions and contexts are important factors that influence research and publication practices in the SSH. Our results indicate that the practices of searching and finding literature as well as publication practices and behavior are shaped by disciplinary traditions and epistemic cultures. On the contrary, assessment and valuation of research outputs are influenced by institutional and national contexts in which SSH research is organized and carried out

Timing of surgical intervention for developmental dysplasia of the hip: a randomised controlled trial (Hip 'Op)

Background: Developmental dysplasia of the hip (DDH) is a very common congenital disorder, and late-presenting cases often require surgical treatment. Surgical reduction of the hip may be complicated by avascular necrosis (AVN), which occurs as a result of interruption to the femoral head blood supply during treatment and can result in long-term problems. Some surgeons delay surgical treatment until the ossific nucleus (ON) has developed, whereas others believe that the earlier the reduction is performed, the better the result. Currently there is no definitive evidence to support either strategy. Objectives: To determine, in children aged 12 weeks to 13 months, whether or not delayed surgical treatment of a congenitally dislocated hip reduces the incidence of AVN at 5 years of age. The main clinical outcome measures were incidence of AVN and the need for a secondary surgical procedure during 5 years’ follow-up. In addition, to perform (1) a qualitative evaluation of the adopted strategy and (2) a health economic analysis based on NHS and societal costs. Design: Phase III, unmasked, randomised controlled trial with qualitative and health economics analyses. Participants were randomised 1 : 1 to undergo either early or delayed surgery. Setting: Paediatric orthopaedic surgical centres in the UK. Participants: Children aged 12 weeks to 13 months with DDH, either newly diagnosed or following failed splintage, and who required surgery. We had a target recruitment of 636 children. Interventions: Surgical reduction of the hip performed as per the timing allocated at randomisation. Main outcome measures: Primary outcome – incidence of AVN at 5 years of age (according to the Kalamchi and MacEwen classification). Secondary outcomes – need for secondary surgery, presence or absence of the ON at the time of primary treatment, quality of life for the main carer and child, and a health economics and qualitative analysis. Results: The trial closed early after reaching < 5% of the recruitment target. Fourteen patients were randomised to early treatment and 15 to delayed treatment. Implementation of rescue strategies did not improve recruitment. No primary outcome data were collected, and no meaningful conclusions could be made from the small number of non-qualitative secondary outcome data. The qualitative work generated rich data around three key themes: (1) access to, and experiences of, primary and secondary care; (2) the impact of surgery on family life; and (3) participants’ experiences of being in the trial. Limitations: Overoptimistic estimates of numbers of eligible patients seen at recruiting centres during the planning of the trial, as well as an overestimation of the recruitment rate, may have also contributed to unrealistic expectations on achievable patient numbers. Future work: There may be scope for investigation using routinely available data. Conclusions: Hip ’Op has highlighted the importance of accurate advance information on numbers of available eligible patients, as well as support from all participating investigators when conducting surgical research. Despite substantial consultation with parents of children in the planning stage, the level of non-participation experienced during recruitment was much higher than anticipated. The qualitative work has emphasised the need for appropriate advice and robust support for parents regarding the ‘real-life’ aspects of managing children with DDH. Trial registration: Current Controlled Trials ISRCTN76958754. Funding: This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 21, No. 63. See the NIHR Journals Library website for further project information

Health economics and quality of life in a feasibility RCT of paediatric acute appendicitis: a protocol study

Background: Acute appendicitis is one of the most common acute surgical emergencies in children and accounts for an annual cost of approximately £50 million to the National Health Service. Investigating alternative treatment options offers the best prospect of enhancing the quality of care for patients and potential opportunities for cost savings through better allocative efficiency. A feasibility randomised controlled trial (RCT) comparing a non-operative treatment pathway with appendicectomy for children with acute uncomplicated appendicitis is underway (CONTRACT feasibility RCT). Aims: The prime objective of this economic substudy conducted alongside the CONTRACT feasibility RCT is to better understand and assess: (1) cost data collection tools and cost drivers by identifying patients’ pathways and (2) patient quality of life by assessing alternative paediatric health-related quality of life (HRQoL) instruments. Outcomes from this study will inform a future efficacy RCT assessing the effectiveness and cost-effectiveness of nonoperative treatment pathway for the treatment of acute uncomplicated appendicitis in children. Methods: The economic substudy will use individuallevel data and will be conducted from the health system perspective over the study’s 6-month follow-up period. Microcosting will include health resource and service use, while potential benefits acquired will be measured using the HRQoL measures, Child Health Utility 9D (CHU9D) and Euroqol-5 dimensions and 5 levels (EQ-5D-5L). We will assess the appropriateness of using the cost per quality-adjusted life year framework in the future RCT, as well as testing and identifying the most suitable HRQoL instrument. Conclusions: The outcomes of the investigational economic substudy will be used to inform the design of our future definitive RCT. However, the result from this economic study will also provide a detailed description and account of the issues inherent in paediatric Economic Evaluations Alongside Clinical Trials with an emphasis on costing methods of interventions taking place in secondary care settings. Trial registration number: ISRCTN1583043

Many non-equivalent realizations of the associahedron

Hohlweg and Lange (2007) and Santos (2004, unpublished) have found two different ways of constructing exponential families of realizations of the n-dimensional associahedron with normal vectors in {0,1,-1}^n, generalizing the constructions of Loday (2004) and Chapoton-Fomin-Zelevinsky (2002). We classify the associahedra obtained by these constructions modulo linear equivalence of their normal fans and show, in particular, that the only realization that can be obtained with both methods is the Chapoton-Fomin-Zelevinsky (2002) associahedron. For the Hohlweg-Lange associahedra our classification is a priori coarser than the classification up to isometry of normal fans, by Bergeron-Hohlweg-Lange-Thomas (2009). However, both yield the same classes. As a consequence, we get that two Hohlweg-Lange associahedra have linearly equivalent normal fans if and only if they are isometric. The Santos construction, which produces an even larger family of associahedra, appears here in print for the first time. Apart of describing it in detail we relate it with the c-cluster complexes and the denominator fans in cluster algebras of type A. A third classical construction of the associahedron, as the secondary polytope of a convex n-gon (Gelfand-Kapranov-Zelevinsky, 1990), is shown to never produce a normal fan linearly equivalent to any of the other two constructions.Comment: 30 pages, 13 figure