Partitioned likelihood support and the evaluation of data set conflict

In simultaneous analyses of multiple data partitions, the trees relevant when measuring support for a clade are the optimal tree, and the best tree lacking the clade (i.e., the most reasonable alternative). The parsimony-based method of partitioned branch support (PBS) forces each data set to arbitrate between the two relevant trees. This value is the amount each data set contributes to clade support in the combined analysis, and can be very different to support apparent in separate analyses. The approach used in PBS can also be employed in likelihood: a simultaneous analysis of all data retrieves the maximum likelihood tree, and the best tree without the clade of interest is also found. Each data set is fitted to the two trees and the log-likelihood difference calculated, giving partitioned likelihood support (PLS) for each data set. These calculations can be performed regardless of the complexity of the ML model adopted. The significance of PLS can be evaluated using a variety of resampling methods, such as the Kishino-Hasegawa test, the Shimodiara-Hasegawa test, or likelihood weights, although the appropriateness and assumptions of these tests remains debated.

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

Global and regional burden of disease and risk factors, 2001: systematic analysis of population health data

Background Our aim was to calculate the global burden of disease and risk factors for 2001, to examine regional trends from 1990 to 2001, and to provide a starting point for the analysis of the Disease Control Priorities Project (DCPP). Methods We calculated mortality, incidence, prevalence, and disability adjusted life years (DALYs) for 136 diseases and injuries, for seven income/geographic country groups. To assess trends, we re-estimated all-cause mortality for 1990 with the same methods as for 2001. We estimated mortality and disease burden attributable to 19 risk factors. Findings About 56 million people died in 2001. Of these, 10.6 million were children, 99% of whom lived in low-and-middle-income countries. More than half of child deaths in 2001 were attributable to acute respiratory infections, measles, diarrhoea, malaria, and HIV/AIDS. The ten leading diseases for global disease burden were perinatal conditions, lower respiratory infections, ischaemic heart disease, cerebrovascular disease, HIV/AIDS, diarrhoeal diseases, unipolar major depression, malaria, chronic obstructive pulmonary disease, and tuberculosis. There was a 20% reduction in global disease burden per head due to communicable, maternal, perinatal, and nutritional conditions between 1990 and 2001. Almost half the disease burden in low-and-middle-income countries is now from non-communicable diseases (disease burden per head in Sub-Saharan Africa and the low-and-middle-income countries of Europe and Central Asia increased between 1990 and 2001). Undernutrition remains the leading risk factor for health loss. An estimated 45% of global mortality and 36% of global disease burden are attributable to the joint hazardous effects of the 19 risk factors studied. Uncertainty in all-cause mortality estimates ranged from around 1% in high-income countries to 15-20% in Sub-Saharan Africa. Uncertainty was larger for mortality from specific diseases, and for incidence and prevalence of non-fatal outcomes. Interpretation Despite uncertainties about mortality and burden of disease estimates, our findings suggest that substantial gains in health have been achieved in most populations, countered by the HIV/AIDS epidemic in Sub-Saharan Africa and setbacks in adult mortality in countries of the former Soviet Union. our results on major disease, injury, and risk factor causes of loss of health, together with information on the cost-effectiveness of interventions, can assist in accelerating progress towards better health and reducing the persistent differentials in health between poor and rich countries.