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

Budapesti Szemle

Here we report evidence of a mitochondrial–Wolbachia sweep in North American populations of the parasitoid wasp Nasonia vitripennis, a cosmopolitan species and emerging model organism for evolutionary and genetic studies. Analysis of the genetic variation of 89 N. vitripennis specimens from Europe and North America was performed using four types of genetic markers: a portion of the mitochondrial cytochrome oxidase I gene, nine polymorphic nuclear microsatellites, sequences from 11 single-copy nuclear markers and six Wolbachia genes. The results show that the European populations have a sevenfold higher mitochondrial sequence variation than North American populations, but similar levels of microsatellite and nuclear gene sequence variation. Variation in the North American mitochondria is extremely low (π=0.31%), despite a highly elevated mutation rate (~35–40 times higher than the nuclear genes) in the mitochondria of Nasonia. The data are indicative of a mitochondrial sweep in the North American population, possibly due to Wolbachia infections that are maternally co-inherited with the mitochondria. Owing to similar levels of nuclear variation, the data could not resolve whether N. vitripennis originated in the New or the Old World.

Chaotic behaviour of the map x ↦ ω(x, f)

"The research that lead to the present paper was partially supported by a grant of the group GNAMPA of INdAM