The graphic nature of the symmetric group

We investigate a remarkable class of exponential sums which are derived from the symmetric groups and which display a diverse array of visually appealing features. Our interest in these expressions stems not only from their astounding visual properties, but also from the fact that they represent a novel and intriguing class of supercharacters.Comment: 23 pages, many figures. To appear in Experimental Mathematic

On-plot drinking water supplies and health: a systematic review

Many studies have found that household access to water supplies near to or on the household plot can reduce the probability of diarrhea, trachoma, and other water-related diseases, and it is generally accepted that on-plot water supplies produce health benefits for households. However, the collective body of research literature has not been analyzed to weigh the evidence supporting this. A systematic literature review was conducted to investigate the impacts of on-plot water supplies on diarrhea, trachoma, child growth, and water-related diseases, to further examine the relationship between household health and distance to water source and to assess whether on-plot water supplies generate health gains for households. Studies provide evidence that households with on-plot water supplies experience fewer diarrheal and helminth infections and greater child height. Findings suggest that water-washed diseases are more strongly impacted by on-plot water access than waterborne diseases. Few studies analyzed the effects of on-plot water access on quantity of domestic water used, hygiene behavior, and use of multiple water sources, and the lack of evidence for these relationships reveals an important gap in current literature. The review findings indicate that on-plot water access is a useful health indicator and benchmark for the progressive realization of the Sustainable Development Goal target of universal safe water access as well as the human right to safe water

The Graphic Nature of the Symmetric Group

We investigate a remarkable class of exponential sums which are derived from the symmetric groups and which display a diverse array of visually appealing features. Our interest in these expressions stems not only from their astounding visual properties, but also from the fact that they represent a novel and intriguing class of supercharacters

Helicobacter pylori

BACKGROUND: Alaska Native persons experience gastric cancer incidence and mortality rates that are three to four times higher than in the general United States population

Supercharacters, Exponential Sums, and the Uncertainty Principle

The theory of supercharacters, which generalizes classical character theory, was recently introduced by P. Diaconis and I.M. Isaacs, building upon earlier work of C. Andre. We study supercharacter theories on $(Z/nZ)^d$ induced by the actions of certain matrix groups, demonstrating that a variety of exponential sums of interest in number theory (e.g., Gauss, Ramanujan, and Kloosterman sums) arise in this manner. We develop a generalization of the discrete Fourier transform, in which supercharacters play the role of the Fourier exponential basis. We provide a corresponding uncertainty principle and compute the associated constants in several cases

International Circumpolar Surveillance, An Arctic Network for the Surveillance of Infectious Diseases

Hospitals, public health agencies, and reference laboratories work together to detect and control infectious disease in Arctic regions

The relative invasive disease potential of Streptococcus pneumoniae among children after PCV introduction: A systematic review and meta-analysis

Objectives Burden of pneumococcal disease depends on the prevalence and invasive disease potential of serotypes. We aimed to estimate the invasive disease potential of serotypes in children under 5 years of age by combining data from different settings with routine immunisation with pneumococcal conjugate vaccines (PCV). Methods We conducted a systematic review, supplemented by unpublished data, to identify data on the frequency of pneumococcal serotypes in carriage and invasive pneumococcal disease (IPD). We estimated the invasive disease potential of serotypes as the ratio of IPD in relation to carriage (odds ratio and 95%CI) compared with 19A (reference serotype) by meta-analysis. We report results based on a random effects model for children aged 0–23, 24–29, and 0–59 months and by invasive clinical syndromes. Results In comparison with 19A, serotypes 1, 7F, and 12F had a significantly higher invasive disease potential in children aged 0–23 and 0–59 months for all IPD and clinical syndromes (OR > 5). Several non-vaccine types (NVTs) (6C, 15A, 15BC, 16F, 23B, in these two age groups) had a lower invasive disease potential than 19A (OR 0.1–0.3). NVTs 8, 12F, 24F, and 33F were at the upper end of the invasiveness spectrum. Conclusions There is substantial variation among pneumococcal serotypes in their potential to cause IPD and disease presentation, which is influenced by age and time after PCV introduction. Surveillance of IPD and carriage is critical to understand the expected effectiveness of current PCVs (in the longer term) and guide the development of future vaccines