Improved bounds for cross-Sperner systems

A collection of families (F1,F2,⋯,Fk)∈P([n])k is cross-Sperner if there is no pair i≠j for which some Fi∈Fi is comparable to some Fj∈Fj. Two natural measures of the 'size' of such a family are the sum ∑ki=1|Fi| and the product ∏ki=1|Fi|. We prove new upper and lower bounds on both of these measures for general n and k≥2 which improve considerably on the previous best bounds. In particular, we construct a rich family of counterexamples to a conjecture of Gerbner, Lemons, Palmer, Patkós, and Szécsi from 2011

International Comparisons of Fetal and Neonatal Mortality Rates in High- Income Countries: Should Exclusion Thresholds Be Based on Birth Weight or Gestational Age?

Background: Fetal and neonatal mortality rates are essential indicators of population health, but variations in recording of births and deaths at the limits of viability compromises international comparisons. The World Health Organization recommends comparing rates after exclusion of births with a birth weight less than 1000 grams, but many analyses of perinatal outcomes are based on gestational age. We compared the effects of using a 1000-gram birth weight or a 28-week gestational age threshold on reported rates of fetal and neonatal mortality in Europe. Methods: Aggregated data from 2004 on births and deaths tabulated by birth weight and gestational age from 29 European countries/regions participating in the Euro-Peristat project were used to compute fetal and neonatal mortality rates using cut-offs of 1000-grams and 28-weeks (2.8 million total births). We measured differences in rates between and within countries using the Wilcoxon signed rank test and 95% confidence intervals, respectively. Principal Findings: For fetal mortality, rates based on gestational age were significantly higher than those based on birth weight (p,0.001), although these differences varied between countries. The use of a 1000-gram threshold included 8823 fetal deaths compared with 9535 using a 28-week threshold (difference of 712). In contrast, the choice of a cut-off made little difference for comparisons of neonatal deaths (difference of 16). Neonatal mortality rates differed minimally, by under 0.1 per 1000 in most countries (p = 0.370). Country rankings were comparable with both thresholds. Conclusions: Neonatal mortality rates were not affected by the choice of a threshold. However, the use of a 1000-gram threshold underestimated the health burden of fetal deaths. This may in part reflect the exclusion of growth restricted fetuses. In high-income countries with a good measure of gestational age, using a 28-week threshold may provide additional valuable information about fetal deaths occurring in the third trimester

Evolutionary success of prokaryotes

How can the evolutionary success of prokaryotes be explained ? How did they manage to survive conditions that have fluctuated, with drastic events over 3.5 billion years ? Which significant metabolisms and mechanisms have appeared over the course of evolution that have permitted them to survive the most inhospitable conditions from the physicochemical point of view ? In a 'Red Queen Race', prokaryotes have always run sufficiently fast to adapt to constraints imposed by the environment and the other living species with which they have established interactions. If the criterion retained to define the level of evolution of an organism is its capacity to survive and to yield the largest number of offsprings, prokaryotes must be considered highly evolved organisms