Moduli spaces of toric manifolds

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance is related to the Duistermaat-Heckman measure and the Hausdorff metric. While the moduli space, its topology and metric, may be constructed in any dimension, the tools we use in the proofs are four-dimensional, and hence so is our main result.Comment: To appear in Geometriae Dedicata, minor changes to previous version, 19 pages, 6 figure

Higher S-dualities and Shephard-Todd groups

Abstract: Seiberg and Witten have shown that in N=2$$\mathcal{N}=2$$ SQCD with Nf = 2Nc = 4 the S-duality group PSL2\u2124$$\mathrm{P}\mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right)$$ acts on the flavor charges, which are weights of Spin(8), by triality. There are other N=2$$\mathcal{N}=2$$ SCFTs in which SU(2) SYM is coupled to strongly-interacting non-Lagrangian matter: their matter charges are weights of E6, E7 and E8 instead of Spin(8). The S-duality group PSL2\u2124$$\mathrm{P}\mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right)$$ acts on these weights: what replaces Spin(8) triality for the E6, E7, E8root lattices? In this paper we answer the question. The action on the matter charges of (a finite central extension of) PSL2\u2124$$\mathrm{P}\mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right)$$ factorizes trough the action of the exceptional Shephard-Todd groups G4 and G8 which should be seen as complex analogs of the usual triality group S3 43WeylA2$${\mathfrak{S}}_3\simeq \mathrm{Weyl}\left({A}_2\right)$$. Our analysis is based on the identification of S-duality for SU(2) gauge SCFTs with the group of automorphisms of the cluster category of weighted projective lines of tubular type. \ua9 2015, The Author(s)

The Symbolic and cancellation-free formulae for Schur elements

In this paper we give a symbolical formula and a cancellation-free formula for the Schur elements associated to the simple modules of the degenerate cyclotomic Hecke algebras. As some direct applications, we show that the Schur elements are symmetric with respect to the natural symmetric group action and are integral coefficients polynomials and we give a different proof of Ariki-Mathas-Rui's criterion on the semi-simplicity of degenerate cyclotomic Hecke algebras.Comment: To appear in Monatshefte fur Mathemati

Regular Incidence Complexes, Polytopes, and C-Groups

Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of abstract regular polytopes has been well-studied. The paper describes the combinatorial structure of a regular incidence complex in terms of a system of distinguished generating subgroups of its automorphism group or a flag-transitive subgroup. Then the groups admitting a flag-transitive action on an incidence complex are characterized as generalized string C-groups. Further, extensions of regular incidence complexes are studied, and certain incidence complexes particularly close to abstract polytopes, called abstract polytope complexes, are investigated.Comment: 24 pages; to appear in "Discrete Geometry and Symmetry", M. Conder, A. Deza, and A. Ivic Weiss (eds), Springe

Assessment of Objectively Measured Physical Activity Levels in Individuals with Intellectual Disabilities with and without Down's Syndrome

Objective: To investigate, using accelerometers, the levels of physical activity being undertaken by individuals with intellectual disabilities with and without Down’s syndrome. Methods: One hundred and fifty two individuals with intellectual disabilities aged 12–70 years from East and South-East England. Physical activity levels in counts per minute (counts/min), steps per day (steps/day), and minutes of sedentary, light, moderate, vigorous, and moderate to vigorous physical activity (MVPA) measured with a uni-axial accelerometer (Actigraph GT1M) for seven days. Results: No individuals with intellectual disabilities met current physical activity recommendations. Males were more active than females. There was a trend for physical activity to decline and sedentary behaviour to increase with age, and for those with more severe levels of intellectual disability to be more sedentary and less physically active, however any relationship was not significant when adjusted for confounding variables. Participants with Down’s syndrome engaged in significantly less physical activity than those with intellectual disabilities without Down’s syndrome and levels of activity declined significantly with age. Conclusions: Individuals with intellectual disabilities, especially those with Down’s syndrome may be at risk of developing diseases associated with physical inactivity. There is a need for well-designed, accessible, preventive health promotio

Variational Analysis Down Under Open Problem Session

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We state the problems discussed in the open problem session at Variational Analysis Down Under conference held in honour of Prof. Asen Dontchev on 19–21 February 2018 at Federation University Australia

Survival benefits of statins for primary prevention: a cohort study

Objectives: Estimate the effect of statin prescription on mortality in the population of England and Wales with no previous history of cardiovascular disease.  Methods: Primary care records from The Health Improvement Network 1987-2011 were used.Four cohorts of participants aged 60, 65, 70, or 75 years at baseline included 118,700,199,574, 247,149, and 194,085 participants; and 1.4, 1.9, 1.8, and 1.1 million person-years of data, respectively. The exposure was any statin prescription at any time before the participant reached the baseline age (60, 65, 70 or 75) and the outcome was all-cause mortality at any age above the baseline age. The hazard of mortality associated with statin prescription was calculated by Cox's proportional hazard regressions, adjusted for sex, year of birth, socioeconomic status, diabetes,antihypertensive medication, hypercholesterolaemia, body mass index, smoking status, and general practice. Participants were grouped by QRISK2 baseline risk of afirst cardiovascular event in the next ten years of <10%, 10-19%, or ≥20%.  Results: There was no reduction in all-cause mortality for statin prescription initiated in participants with a QRISK2 score <10% at any baseline age, or in participants aged 60at baseline in any risk group. Mortality was lower in participants with a QRISK2 score≥20% if statin prescription had been initiated by age 65 (adjusted hazard ratio (HR)0.86 (0.79-0.94)), 70 (HR 0.83 (0.79-0.88)), or 75 (HR 0.82 (0.79-0.86)). Mortality reduction was uncertain with a QRISK2 score of 10-19%: the HR was 1.00 (0.91-1.11)for statin prescription by age 65, 0.89 (0.81-0.99) by age 70, or 0.79 (0.52-1.19) by age75.  Conclusions: The current internationally recommended thresholds for statin therapy for primary prevention of cardiovascular disease in routine practice may be too low and may lead to overtreatment of younger people and those at low risk

Human Skeletal Muscle Mitochondrial Uncoupling Is Associated with Cold Induced Adaptive Thermogenesis

Background: Mild cold exposure and overfeeding are known to elevate energy expenditure in mammals, including humans. This process is called adaptive thermogenesis. In small animals, adaptive thermogenesis is mainly caused by mitochondrial uncoupling in brown adipose tissue and regulated via the sympathetic nervous system. In humans, skeletal muscle is a candidate tissue, known to account for a large part of the epinephrine-induced increase in energy expenditure. However, mitochondrial uncoupling in skeletal muscle has not extensively been studied in relation to adaptive thermogenesis in humans. Therefore we hypothesized that cold-induced adaptive thermogenesis in humans is accompanied by an increase in mitochondrial uncoupling in skeletal muscle. Methodology/Principal Findings: The metabolic response to mild cold exposure in 11 lean, male subjects was measured in a respiration chamber at baseline and mild cold exposure. Skeletal muscle mitochondrial uncoupling (state 4) was measured in muscle biopsies taken at the end of the respiration chamber stays. Mild cold exposure caused a significant increase in 24h energy expenditure of 2.8 % (0.32 MJ/day, range of 20.21 to 1.66 MJ/day, p,0.05). The individual increases in energy expenditure correlated to state 4 respiration (p,0.02, R 2 = 0.50). Conclusions/Significance: This study for the first time shows that in humans, skeletal muscle has the intrinsic capacity for cold induced adaptive thermogenesis via mitochondrial uncoupling under physiological conditions. This opens possibilitie

Acute Pain and a Motivational Pathway in Adult Rats: Influence of Early Life Pain Experience

The importance of neonatal experience upon behaviour in later life is increasingly recognised. The overlap between pain and reward pathways led us to hypothesise that neonatal pain experience influences reward-related pathways and behaviours in adulthood