Frobenius-Schur Indicators and Exponents of Spherical Categories

We obtain two formulae for the higher Frobenius-Schur indicators: one for a spherical fusion category in terms of the twist of its center and the other one for a modular tensor category in terms of its twist. The first one is a categorical generalization of an analogous result by Kashina, Sommerhauser, and Zhu for Hopf algebras, and the second one extends Bantay's 2nd indicator formula for a conformal field theory to higher degree. These formulae imply the sequence of higher indicators of an object in these categories is periodic. We define the notion of Frobenius-Schur (FS-)exponent of a pivotal category to be the global period of all these sequences of higher indicators, and we prove that the FS-exponent of a spherical fusion category is equal to the order of the twist of its center. Consequently, the FS-exponent of a spherical fusion category is a multiple of its exponent, in the sense of Etingof, by a factor not greater than 2. As applications of these results, we prove that the exponent and the dimension of a semisimple quasi-Hopf algebra H have the same prime divisors, which answers two questions of Etingof and Gelaki affirmatively for quasi-Hopf algebras. Moreover, we prove that the FS-exponent of H divides dim(H)^4. In addition, if H is a group-theoretic quasi-Hopf algebra, the FS-exponent of H divides dim(H)^2, and this upper bound is shown to be tight.Comment: 32p. LaTex file with macros and figures. Some typos and Thm 8.4 in v2 have been corrected. The current Thm 8.4 is a combined result of Thms 8.4 and 8.5 in version

Use of multicriteria decision analysis for assessing the benefit and risk of over-the-counter analgesics

Objectives To test the ability of a multicriteria decision analysis (MCDA) model to incorporate disparate data sources of varying quality along with clinical judgement in a benefit–risk assessment of six well-known pain-relief drugs. Methods Six over-the-counter (OTC) analgesics were evaluated against three favourable effects and eight unfavourable effects by seven experts who specialise in the relief of pain, two in a 2-day facilitated workshop whose input data and judgements were later peer-reviewed by five additional experts. Key findings Ibuprofen salts and solubilised emerged with the best benefit–risk profile, followed by naproxen, ibuprofen acid, diclofenac, paracetamol and aspirin. Conclusions Multicriteria decision analysis enabled participants to evaluate the OTC analgesics against a range of favourable and unfavourable effects in a group setting that enabled all issues to be openly aired and debated. The model was easily communicated and understood by the peer reviewers, so the model should be comprehensible to physicians, pharmacists and other health professionals

Drug therapies for reducing gastric acidity in people with cystic fibrosis.

BackgroundMalabsorption of fat and protein contributes to poor nutritional status in people with cystic fibrosis. Impaired pancreatic function may also result in increased gastric acidity, leading in turn to heartburn, peptic ulcers and the impairment of oral pancreatic enzyme replacement therapy. The administration of gastric acid-reducing agents has been used as an adjunct to pancreatic enzyme therapy to improve absorption of fat and gastro-intestinal symptoms in people with cystic fibrosis. It is important to establish the evidence regarding potential benefits of drugs that reduce gastric acidity in people with cystic fibrosis. This is an update of a previously published review.ObjectivesTo assess the effect of drug therapies for reducing gastric acidity for: nutritional status; symptoms associated with increased gastric acidity; fat absorption; lung function; quality of life and survival; and to determine if any adverse effects are associated with their use.Search methodsWe searched the Cochrane Cystic Fibrosis and Genetic Disorders Group Trials Register which comprises references identified from comprehensive electronic and non-electronic database searches, handsearches of relevant journals,  abstract books and conference proceedings. Both authors double checked the reference lists of the searches Most recent search of the Group's Trials Register: 26 April 2021. On the 26 April 2021 further searches were conducted on the clinicaltrials.gov register to identify any ongoing trials that may be of relevance. The WHO ICTRP database was last searched in 2020 and is not currently available for searching due to the Covid-19 pandemic.Selection criteriaAll randomised and quasi-randomised trials involving agents that reduce gastric acidity compared to placebo or a comparator treatment.Data collection and analysisBoth authors independently selected trials, assessed trial quality and extracted data.Main resultsThe searches identified 40 trials; 17 of these, with 273 participants, were suitable for inclusion, but the number of trials assessing each of the different agents was small. Seven trials were limited to children and four trials enrolled only adults. Meta-analysis was not performed, 14 trials were of a cross-over design and we did not have the appropriate information to conduct comprehensive meta-analyses. All the trials were run in single centres and duration ranged from five days to six months. The included trials were generally not reported adequately enough to allow judgements on risk of bias. However, one trial found that drug therapies that reduce gastric acidity improved gastro-intestinal symptoms such as abdominal pain; seven trials reported significant improvement in measures of fat malabsorption; and two trials reported no significant improvement in nutritional status. Only one trial reported measures of respiratory function and one trial reported an adverse effect with prostaglandin E2 analogue misoprostol. No trials have been identified assessing the effectiveness of these agents in improving quality of life, the complications of increased gastric acidity, or survival.Authors' conclusionsTrials have shown limited evidence that agents that reduce gastric acidity are associated with improvement in gastro-intestinal symptoms and fat absorption. Currently, there is insufficient evidence to indicate whether there is an improvement in nutritional status, lung function, quality of life, or survival. Furthermore, due to the unclear risks of bias in the included trials, we are unable to make firm conclusions based on the evidence reported therein. We therefore recommend that large, multicentre, randomised controlled clinical trials are undertaken to evaluate these interventions

First-Order Transition and Critical End-Point in Vortex Liquids in Layered Superconductors

We calculate various thermodynamic quantities of vortex liquids in a layered superconductor by using the nonperturbative parquet approximation method, which was previously used to study the effect of thermal fluctuations in two-dimensional vortex systems. We find there is a first-order transition between two vortex liquid phases which differ in the magnitude of their correlation lengths. As the coupling between the layers increases,the first-order transition line ends at a critical point. We discuss the possible relation between this critical end-point and the disappearance of the first-order transition which is observed in experiments on high temperature superconductors at low magnetic fields.Comment: 9 pages, 5 figure

Robert F. Furchgott, Nobel laureate (1916-2009) - a personal reflection

Robert F. Furchgott, pharmacologist and joint winner of the Nobel Prize for Medicine or Physiology (1998) died on the 12th of May 2009 aged 92. By unlocking the astonishingly diverse biological actions of nitric oxide, Furchgott leaves behind a rich legacy that has both revolutionized our understanding of human physiology and stimulated new and exciting opportunities for drug development in a wide range of pathological conditions. In this article, William Martin, who worked with Furchgott for 2 years (1983-1985), following the exciting discovery of endothelium-derived relaxing factor/nitric oxide, pays tribute to his close friend and colleague

Two strands of servitization: a thematic analysis of traditional and customer co-created servitization and future research directions

The servitization literature has diverged, some adopting a goods-dominant logic and some a service-dominant logic. While both literature streams deal with servitization, their conceptual underpinnings and use of key terms are fundamentally different and have become confused within literature. This lack of clarity and understanding presents a challenge to both research and practice. The paper asks what the points of convergence and divergence are between the two streams of literature. The extant literature is reviewed to identify and understand where and how the streams converge and diverge. A two-tiered thematic analysis with both semantic and latent theme analysis is employed. Our findings highlight five points of departure, as well as highlighting examples where both logics have been applied. The five points of departure are the differing conceptualisations of: Value-in-Use, Design of the Servitized Offering, Value Co-production and Value Co-creation, Contextual Variety and Complexity, and Business Model of Solutions and Outcomes. We also propose conditions under which one logic may be more appropriate, in particular we find that adoption of a goods-dominant logic and service-dominant logic are better suited to the pursuit of efficiency and effectiveness, respectively. Finally, we identify future research directions, particularly within the domain of the Internet-of-Things

Self-refraction, ready-made glasses and quality of life among rural myopic Chinese children: a non-inferiority randomized trial.

PURPOSE: To study, for the first time, the effect of wearing ready-made glasses and glasses with power determined by self-refraction on children's quality of life. METHODS: This is a randomized, double-masked non-inferiority trial. Children in grades 7 and 8 (age 12-15 years) in nine Chinese secondary schools, with presenting visual acuity (VA) ≤6/12 improved with refraction to ≥6/7.5 bilaterally, refractive error ≤-1.0 D and <2.0 D of anisometropia and astigmatism bilaterally, were randomized to receive ready-made spectacles (RM) or identical-appearing spectacles with power determined by: subjective cycloplegic retinoscopy by a university optometrist (U), a rural refractionist (R) or non-cycloplegic self-refraction (SR). Main study outcome was global score on the National Eye Institute Refractive Error Quality of Life-42 (NEI-RQL-42) after 2 months of wearing study glasses, comparing other groups with the U group, adjusting for baseline score. RESULTS: Only one child (0.18%) was excluded for anisometropia or astigmatism. A total of 426 eligible subjects (mean age 14.2 years, 84.5% without glasses at baseline) were allocated to U [103 (24.2%)], RM [113 (26.5%)], R [108 (25.4%)] and SR [102 (23.9%)] groups, respectively. Baseline and endline score data were available for 398 (93.4%) of subjects. In multiple regression models adjusting for baseline score, older age (p = 0.003) and baseline spectacle wear (p = 0.016), but not study group assignment, were significantly associated with lower final score. CONCLUSION: Quality of life wearing ready-mades or glasses based on self-refraction did not differ from that with cycloplegic refraction by an experienced optometrist in this non-inferiority trial