Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Avoidable hospitalizations in Switzerland: a small area analysis on regional variation, density of physicians, hospital supply and rurality.

BACKGROUND Avoidable hospitalizations (AH) are hospital admissions for diseases and conditions that could have been prevented by appropriate ambulatory care. We examine regional variation of AH in Switzerland and the factors that determine AH. METHODS We used hospital service areas, and data from 2008-2010 hospital discharges in Switzerland to examine regional variation in AH. Age and sex standardized AH were the outcome variable, and year of admission, primary care physician density, medical specialist density, rurality, hospital bed density and type of hospital reimbursement system were explanatory variables in our multilevel poisson regression. RESULTS Regional differences in AH were as high as 12-fold. Poisson regression showed significant increase of all AH over time. There was a significantly lower rate of all AH in areas with more primary care physicians. Rates increased in areas with more specialists. Rates of all AH also increased where the proportion of residences in rural communities increased. Regional hospital capacity and type of hospital reimbursement did not have significant associations. Inconsistent patterns of significant determinants were found for disease specific analyses. CONCLUSION The identification of regions with high and low AH rates is a starting point for future studies on unwarranted medical procedures, and may help to reduce their incidence. AH have complex multifactorial origins and this study demonstrates that rurality and physician density are relevant determinants. The results are helpful to improve the performance of the outpatient sector with emphasis on local context. Rural and urban differences in health care delivery remain a cause of concern in Switzerland.

Prediction of Benthic Impact for Salmon Net-Pens Based on the Balance of Benthic Oxygen Supply and Demand

The ratio between oxygen supply and oxygen demand was examined as a predictor of benthic response to organic enrichment caused by salmon net-pen aquaculture. Oxygen supply to the benthos was calculated based on Fickian diffusion and near-bottom flow velocities. A strong linear correlation was found between measured carbon sedimentation rates and rates of benthic metabolism. This relationship allowed an estimation of oxygen demand based on sedimentation rates. Comparison of several production sites in Maine (USA) coastal waters showed that for sites where oxygen demand exceeded supply benthic impacts were high and for sites where oxygen supply exceeded demand benthic impacts were low. These findings were summarized in the form of a predictive model that should be useful in siting salmon production facilities.