The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Memory Th1 Cells Are Protective in Invasive Staphylococcus aureus Infection

Mechanisms of protective immunity to Staphylococcus aureus infection in humans remain elusive. While the importance of cellular immunity has been shown in mice, T cell responses in humans have not been characterised. Using a murine model of recurrent S. aureus peritonitis, we demonstrated that prior exposure to S. aureus enhanced IFNγ responses upon subsequent infection, while adoptive transfer of S. aureus antigen-specific Th1 cells was protective in naïve mice. Translating these findings, we found that S. aureus antigen-specific Th1 cells were also significantly expanded during human S. aureus bloodstream infection (BSI). These Th1 cells were CD45RO+, indicative of a memory phenotype. Thus, exposure to S. aureus induces memory Th1 cells in mice and humans, identifying Th1 cells as potential S. aureus vaccine targets. Consequently, we developed a model vaccine comprising staphylococcal clumping factor A, which we demonstrate to be an effective human T cell antigen, combined with the Th1-driving adjuvant CpG. This novel Th1-inducing vaccine conferred significant protection during S. aureus infection in mice. This study notably advances our understanding of S. aureus cellular immunity, and demonstrates for the first time that a correlate of S. aureus protective immunity identified in mice may be relevant in humans

Online Stakeholder Interactions in the Early Stage of a Megaproject

The purpose of this paper is to examine the network structure of online stakeholder discussions in the planning stage of a UK public mega project, High Speed Rail. By providing new rail connections between London, Birmingham and Manchester, this project is highly complex as it is embedded in a network of stakeholder relationships that may support or oppose the project. Data drawn from Twitter was analyzed using Social Network Analysis and inductive analysis of user profiles and content. Findings indicate that the majority of online stakeholders oppose the project and form stable clusters. Larger clusters within this network may attempt to deploy power directly in the form of a manipulation strategy while smaller clusters may seek to ally themselves with more powerful groups, a pathway strategy. Overall, the methodology is a useful complement to existing methods and may provide real time insights into the complex, evolving discussions around mega projects

Clustering of diet, physical activity and sedentary behaviour among Australian children: cross-sectional and longitudinal associations with overweight and obesity

BACKGROUND/OBJECTIVES: Evidence suggests diet, physical activity (PA) and sedentary behaviour cluster together in children, but research supporting an association with overweight/obesity is equivocal. Furthermore, the stability of clusters over time is unknown. The aim of this study was to examine the clustering of diet, PA and sedentary behaviour in Australian children and cross-sectional and longitudinal associations with overweight/obesity. Stability of obesity-related clusters over 3-years was also examined. SUBJECTS/METHODS: Data were drawn from the baseline (T1: 2002/03) and follow-up waves (T2: 2005/06) of the Health Eating and Play Study. Parents of Australian children aged 5-6 (n=87) and 10-12 years (n=123) completed questionnaires. Children wore accelerometers and height and weight were measured. Obesity-related clusters were determined using K-medians cluster analysis. Multivariate regression models assessed cross-sectional and longitudinal associations between cluster membership, and BMI z-score and weight status. Kappa statistics assessed cluster stability over time. RESULTS: Three clusters, labelled \u27most Healthy\u27, \u27Energy-dense (ED) consumers who watch TV\u27 and \u27high sedentary behaviour/low moderate-to-vigorous physical activity\u27 were identified at baseline and at follow-up. No cross-sectional associations were found between cluster membership, and BMI z-score or weight status at baseline. Longitudinally, children in the \u27ED consumers who watch TV\u27 cluster had a higher odds of being overweight/obese at follow-up (OR=2.8; 95% CI: 1.1, 6.9; P<0.05). Tracking of cluster membership was fair to moderate in younger (K=0.24; P=0.0001) and older children (K=0.46; P<0.0001). CONCLUSIONS: This study identified an unhealthy cluster of TV viewing with ED food/drink consumption which predicted overweight/obesity in a small longitudinal sample of Australian children. Cluster stability was fair to moderate over three years and is a novel finding. Prospective research in larger samples is needed to examine how obesity-related clusters track over time and influence the development of overweight and obesity.International Journal of Obesity accepted article preview online, 24 April 2015. doi:10.1038/ijo.2015.66