Statistical Analyses and Modelling of the Mixing Process of Euro Coins in Germany and Europe

This paper reports on the mixing of Euro coins from different countries of origin in Europe, which started on 1 January 2002. There is an interesting conclusion: that the mobility of small and large denominations is different. The long‐term behaviour of the mixing process is studied using a simple deterministic model and data from Germany, France and the Netherlands. The analysis leads to predictions about the future progress of the mixing process.     

A Unified Approach to the Approximation of Multivariate Densities

Approximation of a density by another density is considered in the case of different dimensionalities of the distributions. The results have been derived by inverting expansions of characteristic functions with the help of matrix techniques. The approximations obtained are all functions of cumulant differences and derivatives of the approximating density. The multivariate Edgeworth expansion follows from the results as a special case. Furthermore, the density functions of the trace and eigenvalues of the sample covariance matrix are approximated by the multivariate normal density and a numerical example is given     

Functional disability among chronic pain patients receiving long-term opioid treatment

This study of 2,163 adult chronic, non-cancer-pain, long-term opioid therapy patients examines the relationship of depression to functional disability by measuring average pain interference, activity limitation days, and employment status. Those with more depression symptoms compared to those with fewer were more likely to have worse disability on all 3 measures (average pain interference score >5, OR = 5.36, p < .0001; activity limitation days ≥ 30, OR = 4.05, p < .0001; unemployed due to health reasons, OR = 4.06, p < .0001). Depression might play a crucial role in the lives of these patients; identifying and treating depression symptoms in chronic pain patients should be a priority.     

Bisphenol A: How the Most Relevant Exposure Sources Contribute to Total Consumer Exposure

Bisphenol A (BPA) is an endocrine disrupting chemical that is found in human urine throughout industrial societies around the globe. Consumer exposure pathways to BPA include packaged food, household dust, air, and dental fillings. To date, information on the relative contribution of the different pathways to total consumer exposure is lacking, but is key for managing substance‐associated risks. We investigated the relative contributions of the pathways known to be most relevant for nine different consumer groups. Our results suggest that the most important pathways for infants and children are the use of polycarbonate (PC) baby bottles and for adults and teenagers the consumption of canned food. Dental surgery can also considerably contribute over a short time directly after the surgery. For infants fed with PC baby bottles with mean dose rates of 0.8 μg/kg_bw/d the highest exposure dose rate was calculated. This dose rate is far below the tolerable daily intake of 50 μg/kg_bw/d. However, it is of the same order of magnitude as recently reported concentrations that caused low‐dose health effects in rodents. We find a pattern of falling exposure levels with rising age that is supported by urinary concentrations of BPA available for selected consumer groups. Similarly, the exposure levels we predict are confirmed by the levels reported in these studies.