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

Simulation of Three Dimensional Electrostatic Field Configuration in Wire Chambers : A Novel Approach

Three dimensional field configuration has been simulated for a simple wire chamber consisting of one anode wire stretched along the axis of a grounded square cathode tube by solving numerically the boundary integral equation of the first kind. A closed form expression of potential due to charge distributed over flat rectangular surface has been invoked in the solver using Green's function formalism leading to a nearly exact computation of electrostatic field. The solver has been employed to study the effect of several geometrical attributes such as the aspect ratio ($\lambda = \frac{l}{d}$, defined as the ratio of the length $l$ of the tube to its width $d$) and the wire modeling on the field configuration. Detailed calculation has revealed that the field values deviate from the analytic estimates significantly when the $\lambda$ is reduced to 2 or below. The solver has demonstrated the effect of wire modeling on the accuracy of the estimated near-field values in the amplification region. The thin wire results can be reproduced by the polygon model incorporating a modest number of surfaces ($\geq 32$) in the calculation with an accuracy of more than 99%. The smoothness in the three dimensional field calculation in comparison to fluctuations produced by other methods has been observed.Comment: Revised version submitted to Elsevier Science including some more near-field calculation

Thaan Vuzha Nilam Tharisu: the land without a farmer becomes barren

This report forms a part of the international research project on policy and sustainable agriculture, Policies that Work for Sustainable Agriculture and Regenerated Rural Economies. The report details the findings of one of the constituent studies, undertaken by an Indian NGO, the Society for People's Education and Economic Change (SPEECH). The Importance of this project is that it concentrated on rainfed rather than irrigated agriculture - i.e. the sharp end of rural development in India, and that the focus was very much on the micro-level, looking at policy as seen from the ground. One of the recurring themes throughout the research was the importance of appreciating people as individuals, and in this spirit some of the personal qualities of the research team are shared. The research covers events in sites in the Virudhunagar district of Tamilnadu: Tiruchuli Panchayat Union and the Villur chain of tanks. This is an essentially rural area, where the need for sustainable forms of agriculture and rural livelihoods is clear. The political landscape is fractured and complex (§2.3), and the officials with the responsibility of implementing policy face significant obstacles and disincentives in doing so in response to the needs of local communities

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

Association of MMP3 but not TIMP2 gene variants with elite rugby player status and rugby code

Introduction: Achilles tendon pathology and anterior cruciate ligament rupture are multifactorial conditions for which genetic risk factors have been identified. Single nucleotide polymorphisms (SNPs) within the MMP3 (rs591058, rs679620, rs650108) and TIMP2 (rs4789932) genes have previously been associated with tendon and ligament pathologies. Although not entirely clear, prior literature indicates the risk alleles for Achilles tendon pathology as T (rs591058), G (rs679620) and A (rs650108) for MMP3. However, prior evidence regarding TIMP2 is equivocal. MMP3 is considered an essential regulator of matrix degradation and remodelling within diseased and normal musculoskeletal soft tissues. TIMP2 maintains homeostasis in the extracellular matrix in part by inhibiting MMP function. Given the high incidence and severity of tendon and ligament injuries in elite rugby athletes, we hypothesised that the aforementioned SNPs would be associated with career success. Methods: Participants from the RugbyGene project were elite Caucasian male rugby athletes (n = 566; 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 120 rugby league (RL) athletes. Non-athletes were 589 Caucasian men and women (n = 589, 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: As hypothesized, the MMP3 rs591058 risk genotype (TT) was less frequent in rugby athletes (28%) compared to non-athletes (33%) (Χ2 = 7.265, P = 0.026; OR = 1.18, 95% confidence intervals (CI) = 0.86-1.63). No differences were found for MMP3 rs679620, rs650108 or TIMP2 rs4789932 between rugby athletes and non-athletes. When RL athletes were compared to non-athletes, the risk genotype (TT) of MMP3 rs591058 was underrepresented in RL athletes (19%) compared to non-athletes (33%). The MMP3 rs679620 ‘protective’ allele (C) was more frequent in RL athletes (55%) compared to non-athletes (48%) (OR = 1.3, 95% CI = 0.98-1.74). However, for MMP3 rs650108 the ‘risk’ allele (A) was overrepresented in RL athletes (32%) compared to non-athletes (26%). There were no genotype differences for any gene variant between RU athletes and non-athletes. The ‘risk’ allele (T) of the MMP3 rs679629 polymorphism and the ‘protective’ allele (G) of the MMP3 rs650108 polymorphism were less common in RL (45%, 68%, respectively) than RU athletes (54%, 76%, respectively). Conclusion: We provide evidence for elite rugby athletes possessing a protective genetic profile regarding tendon and ligament injury risk. Notably, a less frequent rs591058 TT genotype in athletes suggests a lower risk of injury could therefore enhance career success in rugby. Furthermore, RL players appear to have differing genetic characteristics compared to their RU counterparts, which might reflect some differences in physiological demands between codes.Peer reviewedFinal Published versio

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