Groups whose locally maximal product-free sets are complete

Let G be a finite group and S a subset of G. Then S is product-free if S ∩ SS = ∅, and complete if G∗ ⊆ S ∪ SS. A product-free set is locally maximal if it is not contained in a strictly larger product-free set. If S is product-free and complete then S is locally maximal, but the converse does not necessarily hold. Street and Whitehead [J. Combin. Theory Ser. A 17 (1974), 219–226] defined a group G as filled if every locally maximal product-free set S in G is complete (the term comes from their use of the phrase ‘S fills G’ to mean S is complete). They classified all abelian filled groups, and conjectured that the finite dihedral group of order 2n is not filled when n = 6k +1 (k ≥ 1). The conjecture was disproved by two of the current authors [C.S. Anabanti and S.B. Hart, Australas. J. Combin. 63 (3) (2015), 385–398], where we also classified the filled groups of odd order. In this paper we classify filled dihedral groups, filled nilpotent groups and filled groups of order 2n p where p is an odd prime. We use these results to determine all filled groups of order up to 2000

Polarized light scattering by aerosols in the marine atmospheric boundary layer

The intensity and polarization of light scattered from marine aerosols affect visibility and contrast in the marine atmospheric boundary layer (MABL). The polarization properties of scattered light in the MABL vary with size, refractive index, number distributions, and environmental conditions. Laboratory measurements were used to determine the characteristics and variability of the polarization of light scattered by aerosols similar to those in the MABL. Scattering from laboratory-generated sea-salt-containing (SSC) [NaCl, (NH4)2SO4, and seawater] components of marine aerosols was measured with a scanning polarization-modulated nephelometer. Mie theory with Gaussian and log normal size distributions of spheres was used to calculate the polarized light scattering from various aerosol composition models and from experimentally determined distributions of aerosols in the marine boundary layer. The modeling was verified by comparison with scattering from distilled water aerosols. The study suggests that polarimetric techniques can be used to enhance techniques for improving visibility and remote imaging for various aerosol types, Sun angles, and viewing conditions

Association between MAPT polymorphism but not APOE promoter and elite rugby athlete status

INTRODUCTION: Incidence and outcomes of concussions have been hypothesised to be genetically influenced. The APOE Promoter G219T (rs405509) polymorphism has been associated with differential promoter activity and unfavourable outcomes after traumatic brain injury. The TT genotype is associated with a 3-fold greater risk of multiple concussions. The TT genotype of MAPT (rs10445337) has also been associated with poorer outcomes after concussion. Rugby has one of the highest incidences of concussion in sport, so it was hypothesised that APOE Promoter TT and MAPT TT genotypes would be less prevalent in elite rugby athletes because those genotypes, previously associated with increased risk, would be less compatible with achieving elite athlete status. METHODS: Participants were from the RugbyGene project, comprising elite Caucasian male rugby athletes (n = 528; mean (standard deviation) height 1.85 (0.07) m, mass 101 (14) kg, age 29 (7) yr), including 420 rugby union (RU) athletes that for some analyses were divided into forwards and backs and 108 rugby league (RL) athletes. Non-athletes were 592 Caucasian men and women (57% male, height 1.72 (0.10) m, mass 74 (14) kg, age 31 (7) yr). PCR of genomic DNA was used to determine genotypes using TaqMan probes, then groups were compared using χ2 and odds ratio (OR) statistics. RESULTS: All genotype data were in Hardy-Weinberg equilibrium. For MAPT (rs10445337), the risk genotype (TT) was underrepresented in rugby athletes (60%) compared to non-athletes (66%), CT more common in rugby athletes (34%) than non-athletes (29%) and little difference in CC genotype frequencies (χ2 = 7.092, P = 0.029; TT genotype frequency OR = 0.80, 95% confidence intervals (CI) = 0.62-1.02). There were no differences in MAPT (rs10445337) genotype frequencies between RU forwards and backs. For APOE Promoter G219T (rs405509), there were no differences in genotype frequencies between all athletes (RU and RL) and non-athletes (27% TT genotype in players and non-athletes), nor between RU forwards and backs. CONCLUSION: The MAPT (rs10445337) TT genotype is 6% less common in elite rugby athletes than non-athletes. Therefore, carrying at least one rs10445337 C allele appears to increase the probability of sustained career success in the high-risk concussion environment of elite rugby, perhaps via a greater ability to recover from concussions.Peer reviewe

High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: part 2, photon noise theory

High-resolution broadband spectroscopy at near-infrared (NIR) wavelengths (950 to 2450 nm) has been performed using externally dispersed interferometry (EDI) at the Hale telescope at Mt. Palomar, with the TEDI interferometer mounted within the central hole of the 200-in. primary mirror in series with the comounted TripleSpec NIR echelle spectrograph. These are the first multidelay EDI demonstrations on starlight. We demonstrated very high (10×) resolution boost and dramatic (20× or more) robustness to point spread function wavelength drifts in the native spectrograph. Data analysis, results, and instrument noise are described in a companion paper (part 1). This part 2 describes theoretical photon limited and readout noise limited behaviors, using simulated spectra and instrument model with noise added at the detector. We show that a single interferometer delay can be used to reduce the high frequency noise at the original resolution (1× boost case), and that except for delays much smaller than the native response peak half width, the fringing and nonfringing noises act uncorrelated and add in quadrature. This is due to the frequency shifting of the noise due to the heterodyning effect. We find a sum rule for the noise variance for multiple delays. The multiple delay EDI using a Gaussian distribution of exposure times has noise-to-signal ratio for photon-limited noise similar to a classical spectrograph with reduced slitwidth and reduced flux, proportional to the square root of resolution boost achieved, but without the focal spot limitation and pixel spacing Nyquist limitations. At low boost (∼1×) EDI has ∼1.4× smaller noise than conventional, and at >10× boost, EDI has ∼1.4× larger noise than conventional. Readout noise is minimized by the use of three or four steps instead of 10 of TEDI. Net noise grows as step phases change from symmetrical arrangement with wavenumber across the band. For three (or four) steps, we calculate a multiplicative bandwidth of 1.8:1 (2.3:1), sufficient to handle the visible band (400 to 700 nm, 1.8:1) and most of TripleSpec (2.6:1)

Dramatic robustness of a multiple delay dispersed interferometer to spectrograph errors: how mixing delays reduces or cancels wavelength drift

We describe demonstrations of remarkable robustness to instrumental noises by using a multiple delay externally dispersed interferometer (EDI) on stellar observations at the Hale telescope. Previous observatory EDI demonstrations used a single delay. The EDI (also called “TEDI”) boosted the 2,700 resolution of the native TripleSpec NIR spectrograph (950-2450 nm) by as much as 10x to 27,000, using 7 overlapping delays up to 3 cm. We observed superb rejection of fixed pattern noises due to bad pixels, since the fringing signal responds only to changes in multiple exposures synchronous to the applied delay dithering. Remarkably, we observed a ~20x reduction of reaction in the output spectrum to PSF shifts of the native spectrograph along the dispersion direction, using our standard processing. This allowed high resolution observations under conditions of severe and irregular PSF drift otherwise not possible without the interferometer. Furthermore, we recently discovered an improved method of weighting and mixing data between pairs of delays that can theoretically further reduce the net reaction to PSF drift to zero. We demonstrate a 350x reduction in reaction to a native PSF shift using a simple simulation. This technique could similarly reduce radial velocity noise for future EDI’s that use two delays overlapped in delay space (or a single delay overlapping the native peak). Finally, we show an extremely high dynamic range EDI measurement of our ThAr lamp compared to a literature ThAr spectrum, observing weak features (~0.001x height of nearest strong line) that occur between the major lines. Because of individuality of each reference lamp, accurate knowledge of its spectrum between the (unfortunately) sparse major lines is important for precision radial velocimetry

Physical characteristics explain ball-carrying capability in sub-elite rugby union players.

The aims of the present study were two-fold: (i) to investigate the relationship between physical characteristics and the game statistics associated with ball-carrying capability amongst sub-elite rugby union players; and (ii) to predict the level of change in these physical characteristics required to improve the associated game statistic via regression analysis. Thirty-eight senior professional players (forwards, n = 22; backs, n = 16) were assessed for body mass (BM), back squat (BS) single-repetition maximum (1RM) normalised to BM (1RM/BM), 10 m sprint velocity (S10), 10 m sprint momentum (SM10), and the game statistics from 22 games within the 2019/20 RFU Championship season. The relationship between these measures and the predicted level of change in a physical measure required to improve the total number of the associated game statistic by one were assessed by Pearson's correlation coefficient and simple regression analyses. In forwards, an ~ 11.5% reduction in BM, an ~ 11.8% improvement in BS 1RM/BM, or an ~ 11.5% increase in S10 was required to improve the game statistics associated with ball-carrying capability. In backs, a ~ 19.3% increase in BM or a ~ 15.6% improvement in SM10 was required. These findings demonstrate that improvements in lower-body relative strength, acceleration performance, and position-specific alterations in body mass are required to maximise the ball-carrying capability and therefore match outcome of sub-elite rugby union players

Sustaining dancer wellbeing through independent professional dance careers

Dancers dedicate their lives to their art. The lucky few dancers who reach professional careers, must navigate a casualised industry, balance financial pressures and maintain performance fitness. This research aimed to provide practical considerations for dancers to support their health and wellbeing through independent, professional dance careers. Dancers from Australian contemporary dance company Co3 participated in a training program involving psychological and physiotherapy assessments and fitness training in conjunction with a major performance season. Focus groups with company dancers and staff investigated the perceived efficacy of the training program within the company schedule and in supporting dancer wellbeing. Dancers were highly engaged with the training program. Dancers expressed various benefits and challenges in incorporating the training within the demands of their careers. Themes identified from the dancer responses included making time, program specificity, dance fitness, connecting as a company, dancer monitoring and scheduling. A need to maintain collegiality outside of contracted times through communities of practice was identified across many of the themes. It is posited that the human capital of dance is challenged through the casualisation of the dance sector and requires careful attention from aspiring dancers