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

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

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 [11] 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 in [2], 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 2np where p is an odd prime. We use these results to determine all filled groups of order up to 2000

Physical Characteristics Explain Ball-Carrying Capability in Sub-Elite Rugby Union Players

Purpose: 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. Methods: 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. Results: 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. Conclusions: 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

The location of international practices: what is human rights practice?

This article opens up space to challenge state-centrism about human rights practice. To do so, it presents and critically assesses four methods that can be used to determine who and/or what counts as a part of any international practice: the agreement method, which locates a practice by referring to speech acts that define it; the contextual method, which locates a practice by referring to the actions, meanings, and intentions of practitioners; the value method, which locates a practice by identifying a value or principle that the practice reflects or instantiates; and the purpose method, which locates a practice by constructing an account of the sociopolitical reason(s) for a practice's existence. The purpose method, based on an interpretation of Rawls' constructivism, is developed, in a way that focuses on practitioners' judgement-based reasons to assign responsibility for human rights to any state or non-state actor

Relationship between alcohol-attributable disease and socioeconomic status, and the role of alcohol consumption in this relationship: a systematic review and meta-analysis

Background: Studies show that alcohol consumption appears to have a disproportionate impact on people of low socioeconomic status. Further exploration of the relationship between alcohol consumption, socioeconomic status and the development of chronic alcohol-attributable diseases is therefore important to inform the development of effective public health programmes. Methods: We used systematic review methodology to identify published studies of the association between socioeconomic factors and mortality and morbidity for alcohol-attributable conditions. To attempt to quantify differences in the impact of alcohol consumption for each condition, stratified by SES, we (i) investigated the relationship between SES and risk of mortality or morbidity for each alcohol-attributable condition, and (ii) where, feasible explored alcohol consumption as a mediating or interacting variable in this relationship. Results: We identified differing relationships between a range of alcohol-attributable conditions and socioeconomic indicators. Pooled analyses showed that low, relative to high socioeconomic status, was associated with an increased risk of head and neck cancer and stroke, and in individual studies, with hypertension and liver disease. Conversely, risk of female breast cancer tended to be associated with higher socioeconomic status. These findings were attenuated but held when adjusted for a number of known risk factors and other potential confounding factors. A key finding was the lack of studies that have explored the interaction between alcohol-attributable disease, socioeconomic status and alcohol use. Conclusions: Despite some limitations to our review, we have described relationships between socioeconomic status and a range of alcohol-attributable conditions, and explored the mediating and interacting effects of alcohol consumption where feasible. However, further research is needed to better characterise the relationship between socioeconomic status alcohol consumption and alcohol-attributable disease risk so as to gain a greater understanding of the mechanisms and pathways that influence the differential risk in harm between people of low and high socioeconomic status

Mother-infant interactions and regional brain volumes in infancy: an MRI study

Background: It is generally agreed that the human brain is responsive to environmental influences, and that the male brain may be particularly sensitive to early adversity. However, this is largely based on retrospective studies of older children and adolescents exposed to extreme environments in childhood. Less is understood about how normative variations in parent-child interactions are associated with the development of the infant brain in typical settings. Method: To address this, we used magnetic resonance imaging to investigate the relationship between observational measures of mother-infant interactions and regional brain volumes in a community sample of 3-6 month old infants (N=39). In addition, we examined whether this relationship differed in male and female infants. Results: We found that lower maternal sensitivity was correlated with smaller subcortical grey matter volumes in the whole sample, and that this was similar in both sexes. However, male infants who showed greater levels of positive communication and engagement during early interactions had smaller cerebellar volumes. Conclusion These preliminary findings suggest that variations in mother-infant interaction dimensions are associated with differences in infant brain development. Although the study is cross-sectional and causation cannot be inferred, the findings reveal a dynamic interaction between brain and environment that may be important when considering interventions to optimize infant outcomes

Stable Isotope Biogeochemistry of Seabird Guano Fertilization: Results from Growth Chamber Studies with Maize (Zea Mays)

Stable isotope analysis is being utilized with increasing regularity to examine a wide range of issues (diet, habitat use, migration) in ecology, geology, archaeology, and related disciplines. A crucial component to these studies is a thorough understanding of the range and causes of baseline isotopic variation, which is relatively poorly understood for nitrogen (δ(15)N). Animal excrement is known to impact plant δ(15)N values, but the effects of seabird guano have not been systematically studied from an agricultural or horticultural standpoint.This paper presents isotopic (δ(13)C and δ(15)N) and vital data for maize (Zea mays) fertilized with Peruvian seabird guano under controlled conditions. The level of (15)N enrichment in fertilized plants is very large, with δ(15)N values ranging between 25.5 and 44.7‰ depending on the tissue and amount of fertilizer applied; comparatively, control plant δ(15)N values ranged between -0.3 and 5.7‰. Intraplant and temporal variability in δ(15)N values were large, particularly for the guano-fertilized plants, which can be attributed to changes in the availability of guano-derived N over time, and the reliance of stored vs. absorbed N. Plant δ(13)C values were not significantly impacted by guano fertilization. High concentrations of seabird guano inhibited maize germination and maize growth. Moreover, high levels of seabird guano greatly impacted the N metabolism of the plants, resulting in significantly higher tissue N content, particularly in the stalk.The results presented in this study demonstrate the very large impact of seabird guano on maize δ(15)N values. The use of seabird guano as a fertilizer can thus be traced using stable isotope analysis in food chemistry applications (certification of organic inputs). Furthermore, the fertilization of maize with seabird guano creates an isotopic signature very similar to a high-trophic level marine resource, which must be considered when interpreting isotopic data from archaeological material

The Use of Physical Characteristics to Explain Variation in Ball-Carrying Capability in Elite Rugby Union: A Narrative Review

The effectiveness of offensive ball-carrying has been identified as a key determinant in elite rugby union try-scoring success and subsequent match outcome. Despite this, there is limited research evaluating the physical qualities believed to underpin ball-carrying capability amongst elite rugby union players. The aim of this review was to critically appraise the scientific literature that has investigated the use of physical characteristics to explain ball-carrying capability in elite rugby union. Measures of sprint performance, specifically acceleration, maximum sprinting speed, and sprint momentum have presented weak-to-strong correlations with the number of tries scored, line breaks, tackle breaks, defenders beaten, and dominant collisions recorded amongst international rugby union players. In addition, unilateral and bilateral vertical countermovement jump height, peak power output, and drop jump reactive strength index have each demonstrated meaningful associations with the number of tries scored, line breaks, tackle breaks, and dominant collisions. However, various measures of maximal lower-body strength have presented only trivial correlations with the game statistics associated with ball-carrying capability. These trivial correlations are likely a result of the inconsistent and inaccurate methods used to assess maximal lower-body strength, with methods ranging from a box-squat predicted one-repetition maximum to a maximal isometric mid-thigh pull. Further investigation is required to assess the contribution of maximal lower-body strength, agility, repeated sprint ability, and aerobic capacity to ball-carrying capability in elite rugby union. Such robust, objective data could be used to inform the specificity of physical preparation and maximise the transfer of these physical qualities to on-field performance