The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics

By combining the join construction from Sasakian geometry with the Hamiltonian 2-form construction from K\"ahler geometry, we recover Sasaki-Einstein metrics discovered by physicists. Our geometrical approach allows us to give an algorithm for computing the topology of these Sasaki-Einstein manifolds. In particular, we explicitly compute the cohomology rings for several cases of interest and give a formula for homotopy equivalence in one particular 7-dimensional case. We also show that our construction gives at least a two dimensional cone of both Sasaki-Ricci solitons and extremal Sasaki metrics.Comment: 38 pages, paragraph added to introduction and Proposition 4.1 added, Proposition 4.15 corrected, Remark 5.5 added, and explanation for irregular Sasaki-Einstein structures expanded. Reference adde

The Sasaki Join, Hamiltonian 2-forms, and Constant Scalar Curvature

We describe a general procedure for constructing new Sasaki metrics of constant scalar curvature from old ones. Explicitly, we begin with a regular Sasaki metric of constant scalar curvature on a 2n+1-dimensional compact manifold M and construct a sequence, depending on four integer parameters, of rays of constant scalar curvature (CSC) Sasaki metrics on a compact Sasaki manifold of dimension $2n+3$. We also give examples which show that the CSC rays are often not unique on a fixed strictly pseudoconvex CR manifold or a fixed contact manifold. Moreover, it is shown that when the first Chern class of the contact bundle vanishes, there is a two dimensional subcone of Sasaki Ricci solitons in the Sasaki cone, and a unique Sasaki-Einstein metric in each of the two dimensional sub cones.Comment: 32 pages. A gap in the argument of applying the admissibility conditions to irregular Sasakian structures is filled. Some minor corrections and additions are also made. This is the final version which will appear in the Journal of Geometric Analysis. It also encorporates much from our paper arXiv:1309.706

Falling in Acute Mental Health Settings for Older People : Who falls, where, when and why?

Copyright: © 2014 Dickinson A et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Falls, slips and trips are a major patient safety concern in hospital settings accounting for 26 per cent of all reported patient safety incidents in England. Mental health conditions and their treatments add further to fall risk but we have little information regarding who falls, where and when within mental health settings. Methods: This paper presents an overview of the pattern of falls by older patients within an in-patient mental health setting in the South of England using routine records completed by staff when a fall occurs. 920 fall reports over three years were analysed, and 7 focus groups were undertaken with ward staff to explore how staff understood falls and their experiences of using the falls reporting system. Results: In terms of diagnosis 40% of fallers had a primary functional diagnosis, 46% an organic mental health diagnosis (14% non-specific diagnosis), average age was 81.7 years (range 59 to 99 years; SD 8.3) and 57% were female. Approximately one quarter, 27%, of falls were observed by staff. Falls were not evenly distributed across either day of week or time of day, with peak times for falls on Tuesday and Saturday and morning (7-8 and 9-10am) and subsidiary peaks between noon and 1pm and early evening (5-6pm). Almost half of falls occurred in private spaces in the ward such as bedrooms, and 42% in public spaces such as sitting rooms. However 60% of falls in public spaces were unseen. Reporting in these settings was problematic for staff and patients were sometimes described as placing themselves on the floor as a consequence of their mental health condition. The average time to first fall was 5 weeks. Conclusions: Routine mapping of falls could be undertaken at ward and organization level and contribute to better understanding of the local factors contributing to falls. Exploring incident report data in focus groups with staff helped us and them to interpret the data and to understand some of the decision making staff engage in everyday when reporting falls.Peer reviewedFinal Published versio

Diving Deep: Deepening the Intervention and Setting Strategic Vision for the Future

Richmond YPQI has provided a quality improvement process since 2012, growing from 12 sites to 50. Network leads will describe efforts to respond to network participant and funder/stakeholder needs to deepen the intervention and set strategic goals for the continuous quality improvement process. This includes creating a strategic plan, impact framework and rubric to assess the readiness of an organization to participate. Additional items include advanced Methods trainings and a professional learning community. A portion of the workshop will allow participants to reflect on their networks and consider opportunities to deepen the intervention and/or set strategic goals

Iterated S3S^3 Sasaki Joins and Bott Orbifolds

We present a categorical relationship between iterated $S^3$ Sasaki-joins and Bott orbifolds. Then we show how to construct smooth Sasaki-Einstein (SE) structures on the iterated joins. These become increasingly complicated as dimension grows. We give an explicit construction of (infinitely many) smooth SE structures up through dimension eleven, and conjecture the existence of smooth SE structures in all odd dimensions.Comment: 19 pages, Paper submitted to the upcoming conference {\it AMAZER: Analysis of Monge-Amp\`ere, a tribute to Ahmed Zeriahi} at the Institute of Mathematics of Toulouse (June 202