Billiards in Nearly Isosceles Triangles

We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some self-similarity phenomena in irrational triangular billiards. Our analysis illustrates the surprising fact that billiards on a triangle near a Veech triangle is extremely complicated even though Billiards on a Veech triangle is very well understood.Comment: Errors have been corrected in Section 9 from the prior and published versions of this paper. In particular, the formulas associated to homology classes of curves corresponding to stable periodic billiard paths in obtuse Veech triangles were corrected. See Remark 9.1 of the paper for more information. The main results and the results from other sections are unaffected. 82 pages, 43 figure

Medical Support for the Fleet

The attitude reflected above, that medical support is primarily for the provision of care to the wounded after the battle is over, is still widely held by naval officers. A few years ago, I interviewed a number of commanding officers regarding the medical support they were receiving. The general perception was that a medical officer’s primary function was to take care of casualties resulting from accidents or battle. This perception is understandable because the prevailing public view of medicine in general is that the doctor\u27s function is to treat illness or injury, and sailors as a group are generally healthy

Cascade diagrams for depicting complex interventions in randomised trials

Clarity about how trial interventions are delivered is important for researchers and those who might want to use their results. A new graphical representation aims to help make complex interventions clearer. Many medical interventions—particularly non-pharmacological ones—are complex, consisting of multiple interacting components targeted at different organisational levels. Published descriptions of complex interventions often do not contain enough detail to enable their replication. Reports of behaviour change interventions should include descriptions of setting, mode, intensity, and duration, and characteristics of the participants. Graphical methods, such as that showing the relative timing of assessments and intervention components, may improve clarity of reporting. However, these approaches do not reveal the connections between the different “actors” in a complex intervention.8 Different audiences may want different things from a description of an intervention, but visualising relationships between actors can clarify crucial features such as the fidelity with which the intervention is passed down a chain of actors and possible routes of contamination between treatment arms. Here we describe a new graphical approach—the cascade diagram—that highlights these potential problems

What is the evidence of the impact of microfinance on the well-being of poor people?

The concept of microcredit was first introduced in Bangladesh by Nobel Peace Prize winner Muhammad Yunus. Professor Yunus started Grameen Bank (GB) more than 30 years ago with the aim of reducing poverty by providing small loans to the country’s rural poor (Yunus 1999). Microcredit has evolved over the years and does not only provide credit to the poor, but also now spans a myriad of other services including savings, insurance, remittances and non-financial services such as financial literacy training and skills development programmes; microcredit is now referred to as microfinance (Armendáriz de Aghion and Morduch 2005, 2010). A key feature of microfinance has been the targeting of women on the grounds that, compared to men, they perform better as clients of microfinance institutions and that their participation has more desirable development outcomes (Pitt and Khandker 1998). Despite the apparent success and popularity of microfinance, no clear evidence yet exists that microfinance programmes have positive impacts (Armendáriz de Aghion and Morduch 2005, 2010; and many others). There have been four major reviews examining impacts of microfinance (Sebstad and Chen, 1996; Gaile and Foster 1996, Goldberg 2005, Odell 2010, see also Orso 2011). These reviews concluded that, while anecdotes and other inspiring stories (such as Todd 1996) purported to show that microfinance can make a real difference in the lives of those served, rigorous quantitative evidence on the nature, magnitude and balance of microfinance impact is still scarce and inconclusive (Armendáriz de Aghion and Morduch 2005, 2010). Overall, it is widely acknowledged that no well-known study robustly shows any strong impacts of microfinance (Armendáriz de Aghion and Morduch 2005, p199-230). Because of the growth of the microfinance industry and the attention the sector has received from policy makers, donors and private investors in recent years, existing microfinance impact evaluations need to be re-investigated; the robustness of claims that microfinance successfully alleviates poverty and empowers women must be scrutinised more carefully. Hence, this review revisits the evidence of microfinance evaluations focusing on the technical challenges of conducting rigorous microfinance impact evaluations

PIMS (Positioning In Macular hole Surgery) trial – a multicentre interventional comparative randomised controlled clinical trial comparing face-down positioning, with an inactive face-forward position on the outcome of surgery for large macular holes: study protocol for a randomised controlled trial

BACKGROUND: Idiopathic macular holes are an important cause of blindness. They have an annual incidence of 8 per 100,000 individuals, and prevalence of 0.2 to 3.3 per 1000 individuals with visual impairment. The condition occurs more frequently in adults aged 75 years or older. Macular holes can be repaired by surgery in which the causative tractional forces in the eye are released and a temporary bubble of gas is injected. To promote successful hole closure individuals may be advised to maintain a face-down position for up to 10 days following surgery. The aim of this study is to determine whether advice to position face-down improves the surgical success rate of closure of large (>400 μm) macular holes, and thereby reduces the need for further surgery. METHODS/DESIGN: This will be a multicentre interventional, comparative randomised controlled clinical trial comparing face-down positioning with face-forward positioning. At the conclusion of standardised surgery across all sites, participants still eligible for inclusion will be allocated randomly 1:1 to 1 of the 2 treatment arms stratified by site, using random permuted blocks of size 4 or 6 in equal proportions. We will recruit 192 participants having surgery for large macular holes (>400 μm); 96 in each of the 2 arms of the study. The primary objective is to determine the impact of face-down positioning on the likelihood of closure of large (≥400 μm) full-thickness macular holes following surgery. DISCUSSION: This will be the first multicentre randomised control trial to investigate the value of face-down positioning following macular hole standardised surgery. TRIAL REGISTRATION: UK CRN: 17966 (date of registration 26 November 2014)

The relationship between omega-3, omega-6 and total polyunsaturated fat and musculoskeletal health and functional status in adults: a systematic review and meta-analysis of RCTs

Purpose : We conducted a systematic review and meta-analysis to assess effects of increasing dietary omega-3, omega-6 and mixed polyunsaturated fatty acids (PUFA) on musculoskeletal health, functional status, sarcopenia and risk of fractures. Methods : We searched Medline, Embase, The Cochrane library, ClinicalTrials.gov, and the WHO International Clinical Trials Registry Platform (ICTRP) databases for Randomised Controlled Trials (RCTs) of adults evaluating effects of higher versus lower oral omega-3, omega-6 or mixed PUFA for ≥ 6 months on musculoskeletal and functional outcomes. Results : We included 28 RCTs (7288 participants, 31 comparisons), 23 reported effects of omega-3, one of omega-6 and four of mixed total PUFA. Participants and doses were heterogeneous. Six omega-3 trials were judged at low summary risk of bias.  We found low-quality evidence that increasing omega-3 increased lumbar spine BMD by 2.6% (0.03 g/cm2, 95% CI -0.02 to 0.07, 463 participants). There was also the suggestion of an increase in femoral neck BMD (of 4.1%), but the evidence was of very low-quality. There may be little or no effect of omega-3 on functional outcomes and bone mass, effects on other outcomes were unclear. Only one study reported on effects of omega-6 with very limited data. Increasing total PUFA had little or no effect on BMD or indices of fat free (skeletal) muscle mass (low-quality evidence); no data were available on fractures, BMD or functional status and data on bone turnover markers were limited. Conclusions : Trials assessing effects of increasing omega-3, omega-6 and total PUFA on functional status, bone and skeletal muscle strength are limited with data lacking or of low quality. While there is an indication that omega-3 may improve BMD, high quality RCTs are needed to confirm this and effects on other musculoskeletal outcomes