Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Roflumilast in moderate-to-severe chronic obstructive pulmonary disease treated with longacting bronchodilators: two randomised clinical trials

Background Patients with chronic obstructive pulmonary disease (COPD) have few options for treatment. The efficacy and safety of the phosphodiesterase-4 inhibitor roflumilast have been investigated in studies of patients with moderate-to-severe COPD, but not in those concomitantly treated with longacting inhaled bronchodilators. The effect of roflumilast on lung function in patients with COPD that is moderate to severe who are already being treated with salmeterol or tiotropium was investigated. Methods In two double-blind, multicentre studies done in an outpatient setting, after a 4-week run-in, patients older than 40 years with moderate-to-severe COPD were randomly assigned to oral roflumilast 500 mu g or placebo once a day for 24 weeks, in addition to salmeterol (M2-127 study) or tiotropium (M2-128 study). The primary endpoint was change in prebronchodilator forced expiratory volume in 1s (FEV(1)). Analysis was by intention to treat. The studies are registered with ClinicalTrials.gov, number NCT00313209 for M2-127, and NCT00424268 for M2-128. Findings In the salmeterol plus roflumilast trial, 466 patients were assigned to and treated with roflumilast and 467 with placebo; in the tiotropium plus roflumilast trial, 371 patients were assigned to and treated with roflumilast and 372 with placebo. Compared with placebo, roflumilast consistently improved mean prebronchodilator FEV(1) by 49 mL (p<0.0001) in patients treated with salmeterol, and 80 mL (p<0.0001) in those treated with tiotropium. Similar improvement in postbronchodilator FEV(1) was noted in both groups. Furthermore, roflumilast had beneficial effects on other lung function measurements and on selected patient-reported outcomes in both groups. Nausea, diarrhoea, weight loss, and, to a lesser extent, headache were more frequent in patients in the roflumilast groups. These adverse events were associated with increased patient withdrawal. Interpretation Roflumilast improves lung function in patients with COPD treated with salmeterol or tiotropium, and could become an important treatment for these patients

Cross-sectional study of drivers of animal-source food consumption in low-income urban areas of Nairobi, Kenya

Background Malnutrition, including undernutrition and micronutrient deficiencies is a chronic problem in most developing countries. Animal-source foods (ASFs) provide essential sources of proteins and micronutrients, yet little is known about ASF consumption patterns or household preferences towards animal-source products among low-income populations. This is particularly critical for malnourished children for whom even small increases in consumption could help improve nutrition and health outcomes. This study analysed both the demand as well as the drivers and barriers for ASF consumption among households in two low-income areas in Nairobi, Kenya. Methods Data on ASF expenditures and quantities purchased in the previous week, and reasons for consuming or not consuming ASFs were collected in a cross-sectional study from 205 randomly selected households in Korogocho and Dagoretti settlements. Self-reported reasons for consuming or not-consuming ASFs were described. Demand for ASFs was estimated using the Almost Ideal Demand System to provide measures of demand elasticity for changes in food prices and expenditures. Results On average households purchased 48 grams of ASFs, including fresh milk, per week per household member. Expenditure on ASFs counted for 38% (520 Kenyan Schillings) of the overall food expenditure of which, on average, 48% was spent on fresh milk. Price was the most commonly self-reported barrier for consumption, while taste was reported as the main driver for consumption. The perceived nutritional value was an important driver for consuming more commonly purchased ASFs (beef, eggs, fish and milk). For less commonly purchased ASFs (pork, sausages, sheep and goat meat, offal) taste, access and tradition were given as main reasons for not consuming. Estimated demand elasticities indicated that increases in total food expenditure would lead to greatest increase in the demand for beef meat. Price reductions would increase the demand relatively more for fish, other meats and dairy. Conclusions For most ASFs better affordability would be a clear driver to increase the consumption. However, to increase the variety and quantity of ASFs eaten, other policies targeting improvements in physical access, food safety and consumer education on nutritional values and cooking methods should be considered

Food Supplements Have a Positive Impact on Weight Gain and the Addition of Animal Source Foods Increases Lean Body Mass of Kenyan Schoolchildren

Observational studies of dietary patterns and growth and studies with milk supplementation have shown that children consuming diets containing animal source foods grow better. This study evaluates the growth of 544 Kenyan schoolchildren (median age 7.1 y) after 23 mo of food supplementation with a meat, milk or energy supplement (similar to1255 W) compared to a control group without a supplement. Multivariate analyses controlled for covariates compared gain in weight, height, weight-for-height Z-score (WHZ), height-for-age Z-score (HAZ), mid-upper-arm circumference, triceps and subscapular skinfolds, mid-upper-arm muscle and mid-upper-arm fat area. Children in each of the supplementation groups gained similar to0.4 kg (10%) more weight than children in the Control group. Children in the Meat, Milk and Energy groups gained 0.33, 0.19 and 0.27 cm more, respectively, in mid-upper-arm circumference than children in the Control group. Children who received the Meat supplement gained 30-80% more mid-upper-arm muscle area than children in the other groups, and children who received the milk supplement gained 40% more mid-upper-arm muscle area than children who did not receive a supplement. No statistically significant overall effects of supplementation were found on height, HAZ, WHZ or measures of body fat. A positive effect of the milk supplement on height gain could be seen in the subgroup of children with a lower baseline HAZ (less than or equal to -1.4). The results indicate that food supplements had a positive impact on weight gain in the study children and that the addition of meat increased their lean body mass

Meat supplementation increases arm muscle area in Kenyan schoolchildren

The present study examines the effect of animal-source-food (ASF) intake on arm muscle area growth as part of a larger study examining causal links between ASF intake, growth rate, physical activity, cognitive function and micronutrient status in Kenyan schoolchildren. This randomised, controlled feeding intervention study was designed with three isoenergetic feeding interventions of meat, milk, and plain traditional vegetable stew (githeri), and a control group receiving no snack. A total of twelve elementary schools were randomly assigned to interventions, with three schools per group, and two cohorts of 518 and 392 schoolchildren were enrolled 1 year apart. Children in each cohort were given feedings at school and studied for three school terms per year over 2 years, a total of 9 months per year: cohort I from 1998 to 2000 and cohort II from 1999 to 2001. Food intake was assessed by 24 h recall every 1-2 months and biochemical analysis for micronutrient status conducted annually (in cohort I only). Anthropometric measurements included height, weight, triceps skinfold (TSF) and mid-upper-arm circumference (MUAC). Mid-upper-arm muscle area (MAMA) and mid-upper-arm fat area (MAFA) were calculated. The two cohorts were combined for analyses. The meat group showed the steepest rates of gain in MUAC and MAMA over time, and the milk group showed the next largest significant MUAC and MAMA gain compared with the plain githeri and control groups (P< 0.05). The meat group showed the least increase in TSF and MAFA of all groups. These findings have implications for increasing micronutrient intake and lean body mass in primary schoolchildren consuming vegetarian diets