Fundamental matrices and green matrices for non-homogeneous elliptic systems

In this paper, we establish existence, uniqueness, and scale-invariant estimates for fundamental solutions of non-homogeneous second order elliptic systems with bounded measurable coefficients in Rn and for the corresponding Green functions in arbitrary open sets. We impose certain non-homogeneous versions of de Giorgi– Nash–Moser bounds on the weak solutions and investigate in detail the assumptions on the lower order terms sufficient to guarantee such conditions. Our results, in particular, establish the existence and fundamental estimates for the Green functions associated to the Schr¨odinger (−∆ + V ) and generalized Schrödinger (− div A∇ + V ) operators with real and complex coefficients, on arbitrary domains.In this paper, we establish existence, uniqueness, and scale-invariant estimates for fundamental solutions of non-homogeneous second order elliptic systems with bounded measurable coefficients in Rn and for the corresponding Green functions in arbitrary open sets. We impose certain non-homogeneous versions of de Giorgi– Nash–Moser bounds on the weak solutions and investigate in detail the assumptions on the lower order terms sufficient to guarantee such conditions. Our results, in particular, establish the existence and fundamental estimates for the Green functions associated to the Schr¨odinger (−∆ + V ) and generalized Schrödinger (− div A∇ + V ) operators with real and complex coefficients, on arbitrary domains

Method for Using Rubric Ratings on Fishbone Diagrams to Compare Case Studies

Background: In multi-case study program evaluations, the large amount of qualitative data that are generated from interviews can be difficult to utilize. This is particularly so when inference must be made as to why some cases succeed and some fail. Purpose: This paper shows a method for comparing multiple evaluation sites by using a rubric to define ratings for relevant factors, and an Ishikawa fishbone diagram as a model to show relationships among those factors. We show how this technique identified reasons for differences in outcomes among the sites. Setting: The evaluation setting was a large-scale safety innovation in the U.S. railroad industry. Four cases were considered—two passenger railroads and two freight railroads. Intervention: The Confidential Close Call Reporting System (C3RS) program allowed railroad workers to confidentially submit “close calls” which were reviewed by a team made up of labor, management, and the Federal Railroad administration to determine ways to improve safety. Research design: Multiple comparative case study, Ishikawa root and contributing cause modeling, evaluative rubric scoring, and data visualization techniques. Data collection & analysis: Interview data were collected from four pilot railroad sites, each of which participated in a five-year test of C3RS. Testing periods overlapped, with the entire evaluation lasting about 12 years. Findings: The method of using Ishikawa fishbone diagrams with ratings from an evaluative rubric was an effective method to summarize, analyze, and present large quantities of qualitative data. The approach succeeded in explaining degrees of success and failure across the sites. The sponsor and industry stakeholders were able to understand the analysis and the findings, and to develop deep insight into how to promote successful implementation. Keywords: Multiple comparative case studies; qualitative methodology; qualitative coding; data visualization; fishbone diagrams; Ishikawa diagrams; evaluative rubrics; close calls; near miss; data visualization

Validating Virtual Reality as an effective Training Medium in the Security Domain

Virtual Reality (VR) training simulations are an idea which is being explored in numerous industries and professions. However, evidence purporting to the effectiveness of VR technology in relation to standard real-world exercises is still relatively thin. In this paper, we discuss our approach for validating the effectiveness of a VR training for law enforcement professionals in the context of the AUGGMED project, and present results of the validation study. Our study indicates that realistic VR-based trainings, either by themselves or in combination with the traditional hands-on training, can be as effective as highly resource-intensive practical training sessions

Introduction: Serious Games for Law Enforcement Agencies

This chapter is an introduction to the field of serious games, with emphasis on law enforcement agencies. It outlines their use focusing on four concrete application cases: crime scene investigations, investigative interviews, communication skills and terrorism training. It further outlines the general benefits of serious games compared to traditional training methods

Breaking the shackles: the continuing fight against censorship and spin 2008

This is the 2008 edition of the Alliance\u27s annual report into the state of press freedom in Australia, and reports some promising developments over the past twelve months

Using Mendelian randomization to investigate a possible causal relationship between adiposity and increased bone mineral density at different skeletal sites in children

Lean mass is positively associated with bone mineral density (BMD). However, the relationship between adiposity and BMD is more controversial. In particular, it is unclear if the observational association between the two reflects a causal effect of fat mass on BMD. Previous Mendelian randomization (MR) studies using variants in the FTO and MC4R genes as genetic instruments for adiposity have suggested that fat mass does indeed causally influence BMD. However, it is possible that these genetic variants pleiotropically influence lean mass and affect BMD through pathways independent of adiposity, invalidating one of the core assumptions of MR and complicating interpretation of the analysis.To investigate whether adiposity causally affects BMD, we investigated the relationship between fat mass and BMD at the skull (SK), upper limbs (UL) and lower limbs (LL), spine (SP) and pelvis (PE), using 32 body mass index (BMI)-associated SNPs, including a variant near ADCY3 that was strongly associated with fat but not lean mass in our sample. Dual-energy X-ray absorptiometry (DXA) scans and genetic data were available for 5221 subjects (mean age 9.9 years) from the Avon Longitudinal Study of Parents and Children. We performed a series of MR analyses involving single BMI-associated SNPs and allelic scores of these SNPs. We used new extensions of the MR method including MR Egger regression and multivariable MR, which are more robust to possible confounding effects due to horizontal pleiotropy and, in the case of multivariable MR, specifically account for the effect of lean mass in the analysis. Bidirectional Mendelian randomization analysis was also performed to examine whether BMD causally affected BMI and adiposity.Observationally, fat mass was strongly positively related to BMD at all sites, but more weakly at the skull. Instrumental variables (IV) analyses using an allelic score of BMI SNPs suggested that fat mass was causally related to LL-BMD, UL-BMD, SP-BMD and PE-BMD but not SK-BMD. Multivariable MR, Egger regression and IV analyses involving the ADCY3 variant suggested a positive causal effect of adiposity on all sites except the skull, and that an effect was present even after taking lean mass into account. Finally, IV analyses using BMD allelic scores showed no evidence of reverse causality between BMD and fat mass.Our results suggest that adiposity is causally related to increased BMD at all sites except the skull, perhaps reflecting positive effects of loading on bone formation at weighted but not unweighted sites. In contrast, we found no evidence for BMD causally affecting BMI or measures of adiposity. Our results illustrate how MR can be used profitably to investigate clinical questions relevant to osteoporosis

High impact activity is related to lean but not fat mass:findings from a population-based study in adolescents

Background Objective measures of physical activity calibrated against energy expenditure may have limited utility in studying relationships with musculoskeletal phenotypes. We wished to assess an alternative approach using an accelerometer calibrated according to impact loading. Methods Of the 17-year olds from the Avon Longitudinal Study of Parents and Children (ALSPAC), 732 wore Newtest accelerometers while performing day-to-day activities for a mean of 5.8 days. Outputs were categorized as light, moderate, high and very high impact, based on the thresholds identified in 22 adolescents during graded activities. In subsequent regression analyses, activity data and fat mass were normalized by log transformation. Results The number of counts relating to high impact activity was ∼2% that of light impact activity, and 33% greater in boys when compared with girls. High impact activity was more strongly related to lean mass [light: 0.033 (95% CI −0.023 to 0.089), moderate: 0.035 (95% CI −0.010 to 0.080) and high: 0.044 (95% CI 0.010 to 0.078)] (β = SD change in outcome per doubling in activity, height adjusted, boys and girls combined). In contrast, lower impact activity was more strongly related to fat mass [light: −0.069 (95% CI −0.127 to −0.011), moderate: −0.060 (95% CI −0.107 to −0.014) and high: −0.033 (95% CI −0.069 to 0.003)]. In a more fully adjusted model including other activity types and fat/lean mass, lean mass was related to only high activity (boys and girls combined), whereas fat mass was related to only moderate activity (girls only). Conclusions Using an accelerometer calibrated according to impact loading revealed that high impact activity is related to lean but not fat mass