Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

Rôle des cellules souches épithéliales de la cornée et de leur micro-environnement dans le traitement des destructions de la surface oculaire [Darwin or Lamarck? Understanding the ocular surface and its normal or abnormal differentiation in order to cure ocular surface destruction with corneal opacification].

According to the World Health Organization, 5.1% of blindnesses or visual impairments are related to corneal opacification. Cornea is a transparent tissue placed in front of the color of the eye. Its transparency is mandatory for vision. The ocular surface is a functional unit including the cornea and all the elements involved in maintaining its transparency i.e., the eyelids, the conjunctiva, the lymphoid tissue of the conjunctiva, the limbus, the lacrymal glands and the tear film. The destruction of the ocular surface is a disease caused by : traumatisms, infections, chronic inflammations, cancers, toxics, unknown causes or congenital abnormalities. The treatment of the ocular surface destruction requires a global strategy including all the elements that are involved in its physiology. The microenvironnement of the ocular surface must first be restored, i.e., the lids, the conjunctiva, the limbus and the structures that secrete the different layers of the tear film. In a second step, the transparency of the cornea can be reconstructed. A corneal graft performed in a healthy ocular surface microenvironnement will have a better survival rate. To achieve these goals, a thorough understanding of the renewal of the epitheliums and the role of the epithelial stem cells are mandatory.

Normal weight obesity: relationship with lipids, glycaemic status, liver enzymes and inflammation

BACKGROUND AND AIMS: Normal weight obesity (NWO) is defined as an excessive body fat associated with a normal body mass index (BMI) and has been associated with early inflammation, but its relationship with cardiovascular risk factors await investigation. METHODS AND RESULTS: Cross-sectional study including 3213 women and 2912 men aged 35-75 years to assess the clinical characteristics of NWO in Lausanne, Switzerland. Body fat was assessed by bioimpedance. NWO was defined as a BMI<25 kg/m(2) and a % body fat ≥66(th) gender-specific percentiles. The prevalence of NWO was 5.4% in women and less than 3% in men, so the analysis was restricted to women. NWO women had a higher % of body fat than overweight women. After adjusting for age, smoking, educational level, physical activity and alcohol consumption, NWO women had higher blood pressure and lipid levels and a higher prevalence of dyslipidaemia (odds-ratio=1.90 [1.34-2.68]) and fasting hyperglycaemia (odds-ratio=1.63 [1.10-2.42]) than lean women, whereas no differences were found between NWO and overweight women. Conversely, no differences were found between NWO and lean women regarding levels of CRP, adiponectin and liver markers (alanine aminotransferase, aspartate aminotransferase and gamma glutamyl transferase). Using other definitions of NWO led to similar conclusions, albeit some differences were no longer significant. CONCLUSION: NWO is almost nonexistent in men. Women with NWO present with higher cardiovascular risk factors than lean women, while no differences were found for liver or inflammatory markers. Specific screening of NWO might be necessary in order to implement cardiovascular prevention.

Respiratory quotient evolution during normal pregnancy: what nutritional or clinical information can we get out of it?

Food intake increases to a varying extent during pregnancy to provide extra energy for the growing fetus. Measuring the respiratory quotient (RQ) during the course of pregnancy (by quantifying O2 consumption and CO2 production with indirect calorimetry) could be potentially useful since it gives an insight into the evolution of the proportion of carbohydrate vs. fat oxidized during pregnancy and thus allows recommendations on macronutrients for achieving a balanced (or slightly positive) substrate intake. A systematic search of the literature for papers reporting RQ changes during normal pregnancy identified 10 papers reporting original research. The existing evidence supports an increased RQ of varying magnitude in the third trimester of pregnancy, while the discrepant results reported for the first and second trimesters (i.e. no increase in RQ), explained by limited statistical power (small sample size) or fragmentary data, preclude safe conclusions about the evolution of RQ during early pregnancy. From a clinical point of view, measuring RQ during pregnancy requires not only sophisticated and costly indirect calorimeters but appears of limited value outside pure research projects, because of several confounding variables: (1) spontaneous changes in food intake and food composition during the course of pregnancy (which influence RQ); (2) inter-individual differences in weight gain and composition of tissue growth; (3) technical factors, notwithstanding the relatively small contribution of fetal metabolism per se (RQ close to 1.0) to overall metabolism of the pregnant mother.

On concentrators and related approximation constants

Pippenger [Pi77] showed the existence of (6m,4m,3m,6)-concentrator for each positive integer m using a probabilistic method. We generalize his approach and prove existence of (6m,4m,3m,5.05)-concentrator (which is no longer regular, but has fewer edges). We apply this result to improve the constant of approximation of almost additive set functions by additive set functions from 44.5 (established by Kalton and Roberts in [KaRo83] to 39. We show a more direct connection of the latter problem to the Whitney type estimate for approximation of continuous functions on a cube in &b&R&/b&&sup&d&/sup& by linear functions, and improve the estimate of this Whitney constant from 802 (proved by Brudnyi and Kalton in [BrKa00] to 73.

Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Differential control of Notch1 gene transcription by Klf4 and Sp3 transcription factors in normal versus cancer-derived keratinocytes.

In specific cell types like keratinocytes, Notch signaling plays an important pro-differentiation and tumor suppressing function, with down-modulation of the Notch1 gene being associated with cancer development. Besides being controlled by p53, little else is known on regulation of Notch1 gene expression in this context. We report here that transcription of this gene is driven by a TATA-less "sharp peak" promoter and that the minimal functional region of this promoter, which extends from the -342 bp position to the initiation codon, is differentially active in normal versus cancer cells. This GC rich region lacks p53 binding sites, but binds Klf4 and Sp3. This finding is likely to be of biological significance, as Klf4 and, to a lesser extent, Sp3 are up-regulated in a number of cancer cells where Notch1 expression is down-modulated, and Klf4 over-expression in normal cells is sufficient to down-modulate Notch1 gene transcription. The combined knock-down of Klf4 and Sp3 was necessary for the reverse effect of increasing Notch1 transcription, consistent with the two factors exerting an overlapping repressor function through their binding to the Notch1 promoter.

Genes for normal sleep and sleep disorders.

Sleep and wakefulness are complex behaviors that are influenced by many genetic and environmental factors, which are beginning to be discovered. The contribution of genetic components to sleep disorders is also increasingly recognized as important. Point mutations in the prion protein, period 2, and the prepro-hypocretin/orexin gene have been found as the cause of a few sleep disorders but the possibility that other gene defects may contribute to the pathophysiology of major sleep disorders is worth in-depth investigations. However, single gene disorders are rare and most common disorders are complex in terms of their genetic susceptibility, environmental effects, gene-gene, and gene-environment interactions. We review here the current progress in the genetics of normal and pathological sleep.

Hypoglycémie et traitement du diabète de type 2. Le retour à une normoglycémie n'est pas nécessairement la meilleure stratégie thérapeutique [Hypoglycemia and diabetes treatment: the return to normal glucose level is not always the best therapeutic strategy].

Recent clinical trials with type 2 diabetic patients and the quest of normal glyceamic values, have revealed difficulties and limitations. These too normal glyceamic targets corresponding to the physiological standards are associated with very high rate of hypoglycemia and an increase of mortality. A too simplistic view of treatment: "the lowest, the better is in the diabetes" is no longer defensible. The knowledge from complex systems behavior invites us to search targets adapted to a new state of equilibrium due to loss of self-regulation. These targets should not aim the physiological standards but to be adapted to patient's situation. Shared decision-making and consensus are the two pillars of this new strategy supported by the new ADA-EASD guidelines.

Hemodynamic, renal, and endocrine effects of 4-h infusions of human atrial natriuretic peptide in normal volunteers.

A synthetic human atrial natriuretic peptide of 26 aminoacids [human (3-28)ANP or hANP] was infused into normal male volunteers. Six subjects were infused for 4 h at 1-wk intervals with either hANP at the rate of 0.5 or 1.0 microgram/min or its vehicle in a single-blind randomized order. Human (3-28)ANP at the dose of 0.5 microgram/min raised immunoreactive plasma ANP levels from 104 +/- 17 to 221 +/- 24 pg/ml (mean +/- SEM), but it induced no significant change in blood pressure, heart rate, effective renal plasma flow, glomerular filtration rate, or renal electrolyte excretion. At the rate of 1.0 microgram/min, human (3-28)ANP increased immunoreactive plasma ANP levels from 89 +/- 12 to 454 +/- 30 pg/ml. It reduced effective renal plasma flow from 523 +/- 40 to 453 +/- 38 ml/min (P less than 0.05 vs. vehicle), but left glomerular filtration rate unchanged. Natriuresis rose from 207 +/- 52 to 501 +/- 69 mumol/min (P less than 0.05 vs. vehicle) and urinary magnesium excretion from 3.6 +/- 0.5 to 5.6 +/- 0.5 mumol/min (P less than 0.01 vs. vehicle). The excretion rate of the other electrolytes, blood pressure, and heart rate were not significantly modified. At both doses, human (3-28)ANP tended to suppress the activity of the renin-angiotensin-aldosterone system. In 3 additional volunteers, the skin blood flow response to human (3-28)ANP, infused for 4 h at the rate of 1.0 microgram/min, was studied by means of a laser-doppler flowmeter. The skin blood flow rose during the first 2 h of peptide administration, then fell progressively to values below baseline. After the infusion was discontinued, it remained depressed for more than 2 h. Thus, in normal volunteers, human (3-28)ANP at the dose of 1.0 microgram/min produced results similar to those obtained previously with rat (3-28)ANP. It enhanced natriuresis without changing the glomerular filtration rate while effective renal plasma flow fell. It also induced a transient vasodilation of the skin vascular bed.

Práticas assistenciais em reanimação do recém-nascido no contexto de um centro de parto normal

Aproximadamente 10 a 15% dos recém-nascidos (RNs) apresentam dificuldades de adaptação ao nascimento, o que requer habilidade e prontidão dos profis-sionais para intervir nessas situações. Este estudo observacional, transversal objetivou descrever as práticas assistenciais empregadas em reanimação neo-natal em um Centro de Parto Normal de um hospital público de São Paulo. Observou-se 100 atendimentos prestados pela equipe profissional e os dados foram registrados em um instrumento checklist. A presença de líquido meconial foi constatada em 24 (24,0%) partos e a aspiração das vias respiratórias foi realizada em 47 (47,0%) RNs. Desse total, 3 (6,4%) tiveram a traquéia aspirada e 26 (26,0%) RNs receberam oxigenação, sendo que 5 (19,2%) com máscara aberta e pressão positiva. Massagem cardíaca foi realizada em 1 (1,0%) RN. Após a reanimação neonatal inicial, 6 (6,0%)RNs foram transferidos à UTI neonatal devido desconforto respiratório.

Centro de parto normal e a assistência obstétrica centrada nas necessidades da parturiente

Levando em conta os vários estudos e reflexões a respeito do novo modelo de assistência ao parto e nascimento (assistência humanizada), e trabalhando como enfermeira obstétrica em um Centro de Parto Normal, surgiu o questionamento a respeito desse conceito, devido às diversas conotações dadas a esse termo. Este artigo foi produzido com a finalidade de divulgar nossa proposta de substituição da expressão "assistência humanizada ao parto", por "assistência obstétrica centrada nas necessidades da parturiente", e de discorrer como essa assistência é prestada no Centro de Parto Normal do Hospital Geral de Itapecerica da Serra (SP), que segue um protocolo de condutas obstétricas e normas preconizadas pelo Ministério da Saúde.

Fructose-rich diet-induced abdominal adipose tissue endocrine dysfunction in normal male rats.

We have currently studied the changes induced by administration of a fructose-rich diet (FRD) to normal rats in the mass and the endocrine function of abdominal (omental) adipose tissue (AAT). Rats were fed ad libitum a standard commercial chow and tap water, either alone (control diet, CD) or containing fructose (10%, w/vol) (FRD). Three weeks after treatment, circulating metabolic markers and leptin release from adipocytes of AAT were measured. Plasma free fatty acids (FFAs), leptin, adiponectin, and plasminogen activator inhibitor-1 (PAI-1) levels were significantly higher in FRD than in CD rats. AAT mass was greater in FRD than in CD rats and their adipocytes were larger, they secreted more leptin and showed impaired insulin sensitivity. While leptin mRNA expression increased in AAT from FRD rats, gene expression of insulin receptor substrate, IRS1 and IRS2 was significantly reduced. Our study demonstrates that administration of a FRD significantly affects insulin sensitivity and several AAT endocrine/metabolic functions. These alterations could be part of a network of interacting abnormalities triggered by FRD-induced oxidative stress at the AAT level. In view of the impaired glucose tolerance observed in FRD rats, these alterations could play a key role in both the development of metabolic syndrome (MS) and beta-cell failure.