pp-adic quotient sets

For $A \subseteq \mathbb{N}$, the question of when $R(A) = \{a/a' : a, a' \in A\}$ is dense in the positive real numbers $\mathbb{R}_+$ has been examined by many authors over the years. In contrast, the $p$-adic setting is largely unexplored. We investigate conditions under which $R(A)$ is dense in the $p$-adic numbers. Techniques from elementary, algebraic, and analytic number theory are employed in this endeavor. We also pose many open questions that should be of general interest.Comment: 24 page

Estimated Drug Overdose Deaths Averted by North America's First Medically-Supervised Safer Injection Facility

Illicit drug overdose remains a leading cause of premature mortality in urban settings worldwide. We sought to estimate the number of deaths potentially averted by the implementation of a medically supervised safer injection facility (SIF) in Vancouver, Canada.The number of potentially averted deaths was calculated using an estimate of the local ratio of non-fatal to fatal overdoses. Inputs were derived from counts of overdose deaths by the British Columbia Vital Statistics Agency and non-fatal overdose rates from published estimates. Potentially-fatal overdoses were defined as events within the SIF that required the provision of naloxone, a 911 call or an ambulance. Point estimates and 95% Confidence Intervals (95% CI) were calculated using a Monte Carlo simulation. Between March 1, 2004 and July 1, 2008 there were 1004 overdose events in the SIF of which 453 events matched our definition of potentially fatal. In 2004, 2005 and 2006 there were 32, 37 and 38 drug-induced deaths in the SIF's neighbourhood. Owing to the wide range of non-fatal overdose rates reported in the literature (between 5% and 30% per year) we performed sensitivity analyses using non-fatal overdose rates of 50, 200 and 300 per 1,000 person years. Using these model inputs, the number of averted deaths were, respectively: 50.9 (95% CI: 23.6–78.1); 12.6 (95% CI: 9.6–15.7); 8.4 (95% CI: 6.5–10.4) during the study period, equal to 1.9 to 11.7 averted deaths per annum.Based on a conservative estimate of the local ratio of non-fatal to fatal overdoses, the potentially fatal overdoses in the SIF during the study period could have resulted in between 8 and 51 deaths had they occurred outside the facility, or from 6% to 37% of the total overdose mortality burden in the neighborhood during the study period. These data should inform the ongoing debates over the future of the pilot project

Externalities and Spillovers from Sanitation and Waste Management in Urban and Rural Neighborhoods

Proper sanitation and waste management has important health benefits, both directly for the household making the decision and indirectly for its neighbors due to positive externalities. Nevertheless, construction and use of improved sanitation systems in much of the developing world continues to lag. Many recent interventions such as Community Led Total Sanitation (CLTS) have attempted to harness the power of social interactions to increase take-up of improved sanitation. Most evidence to date mobilizes social pressure in rural areas, yet evidence is more scarce in urban neighborhoods where high population density may lead to larger externalities from poor sanitation decisions. We review the recent literature on how sanitation decisions are inter-related within neighborhoods: the health externalities that sanitation decisions have on neighbors, and the social decision spillovers that drive take-up. We explore potential explanations for the low take-up and maintenance of sanitation systems, including the possibility of nonlinearities and thresholds in health externalities; the roles of social pressure, reciprocity, learning from others, and coordination in decision spillovers; and differences between urban and rural contexts

Social inequalities in male mortality amenable to medical intervention in British Columbia

The objective of this study is to examine the rates of mortality among different social classes and socioeconomic groups of British Columbian males from causes of death amenable to medical intervention. We examined the rates of avoidable mortality from the causes of death published by Charlton, excluding causes of death restricted to women as well as perinatal deaths. For the purposes of our study, we determined a population at risk using 20% samples of occupational data for men from the 1981, 1986 and 1991 censuses conducted by Statistics Canada. For the analysis of mortality by social class, individuals were divided into five social class levels based on occupation using an adaptation of the UK Registrar General's Social Class Scale. In addition, three levels of socioeconomic analysis were performed using the Blishen Index classification system. Once individuals were assigned to a social class in each classification system, the death rates from each amenable cause was calculated and standardized to the total population. For almost every cause of death examined, the rate of mortality was higher in individuals of lower social and socioeconomic classes than in individuals of the upper social and socioeconomic classes. These results were consistent regardless of the social class component, education, occupation, or income was being measured. The mortality gradient was most notable in deaths due to hypertensive heart disease, tuberculosis, asthma and pneumonia and bronchitis. Due to the fact that these causes of death were observed to be consistently higher in the lower social classes, we feel that specific measures aimed at improving survival from these conditions in lower social classes could help to amend the social class disparity.Avoidable mortality Socioeconomic status Social class British Columbia

Elevated rates of HIV infection among young Aboriginal injection drug users in a Canadian setting.

ObjectivesRecent reports have suggested that Aboriginal and American Indian people are at elevated risk of HIV infection. We undertook the present study to compare socio-demographic and risk variables between Aboriginal and non-Aboriginal young (aged 13 - 24 years) injection drug users (IDUs) and characterize the burden of HIV infection among young Aboriginal IDUs.MethodsWe compared socio-demographic and risk variables between Aboriginal and non-Aboriginal young IDUs. Data were collected through the Vancouver Injection Drug Users Study (VIDUS). Semi-annually, participants have completed an interviewer-administered questionnaire and have undergone serologic testing for HIV and Hepatitis C (HCV).ResultsTo date over 1500 Vancouver IDU have been enrolled and followed, among whom 291 were aged 24 years and younger. Of the 291 young injectors, 80 (27%) were Aboriginal. In comparison to non-Aboriginal youth, Aboriginal youth were more likely to test seropositive for either HIV (20% vs 7%, p=< 0.001) or Hepatitis C virus (HCV) (66% vs 38%, p =< 0.001), be involved in sex work and live in the city's IDU epi-centre at baseline. After 48 months of follow-up, Aboriginal youth experienced significantly higher HIV seroconversion rates than non-Aboriginal youth, 27.8 per ppy (95% CI: 13.4-42.2) vs. 7.0 per ppy (95% CI: 2.3-11.8) respectively (log-rank p = 0.005) and the incidence density over the entire follow-up period was 12.6 per 100 pyrs (CI: 6.49-21.96) and 3.9 per 100 pyrs (CI: 1.8-7.3) respectively.InterpretationThese findings demonstrate that culturally relevant, evidence based prevention programs are urgently required to prevent HIV infection among Aboriginal youth

Elevated rates of HIV infection among young Aboriginal injection drug users in a Canadian setting

Objectives: Recent reports have suggested that Aboriginal and American Indian people are at elevated risk of HIV infection. We undertook the present study to compare socio-demographic and risk variables between Aboriginal and non-Aboriginal young (aged 13 – 24 years) injection drug users (IDUs) and characterize the burden of HIV infection among young Aboriginal IDUs. Methods We compared socio-demographic and risk variables between Aboriginal and non-Aboriginal young IDUs. Data were collected through the Vancouver Injection Drug Users Study (VIDUS). Semi-annually, participants have completed an interviewer-administered questionnaire and have undergone serologic testing for HIV and Hepatitis C (HCV). Results To date over 1500 Vancouver IDU have been enrolled and followed, among whom 291 were aged 24 years and younger. Of the 291 young injectors, 80 (27%) were Aboriginal. In comparison to non-Aboriginal youth, Aboriginal youth were more likely to test seropositive for either HIV (20% vs 7%, p=< 0.001) or Hepatitis C virus (HCV) (66% vs 38%, p =< 0.001), be involved in sex work and live in the city's IDU epi-centre at baseline. After 48 months of follow-up, Aboriginal youth experienced significantly higher HIV seroconversion rates than non-Aboriginal youth, 27.8 per ppy (95% CI: 13.4–42.2) vs. 7.0 per ppy (95% CI: 2.3–11.8) respectively (log-rank p = 0.005) and the incidence density over the entire follow-up period was 12.6 per 100 pyrs (CI: 6.49–21.96) and 3.9 per 100 pyrs (CI: 1.8–7.3) respectively. Interpretation These findings demonstrate that culturally relevant, evidence based prevention programs are urgently required to prevent HIV infection among Aboriginal youth.Health Care and Epidemiology, Department ofMedicine, Faculty ofNon UBCReviewedFacult