On the analyticity of functions approximated by their q-Bernstein polynomials when q > 1

Since in the case q > 1 the q-Bernstein polynomials Bn,q are not positive linear operators on C[0, 1], the investigation of their convergence properties for q > 1 turns out to be much harder than the one for 0 < q < 1. What is more, the fast increase of the norms ∥Bn,q∥ as n → ∞, along with the sign oscillations of the q-Bernstein basic polynomials when q > 1, create a serious obstacle for the numerical experiments with the q-Bernstein polynomials. Despite the intensive research conducted in the area lately, the class of functions which are uniformly approximated by their q-Bernstein polynomials on [0, 1] is yet to be described. In this paper, we prove that if f:[0,1]→C is analytic at 0 and can be uniformly approximated by its q-Bernstein polynomials (q > 1) on [0, 1], then f admits an analytic continuation from [0, 1] into {z: z < 1}. © 2010 Elsevier Inc. All rights reserved

Maternal vaccination against COVID-19 and neonatal outcomes during Omicron: INTERCOVID-2022 study

Background: In early 2023, when Omicron was the variant of concern, we showed that vaccinating pregnant women decreased the risk for severe COVID-19-related complications and maternal morbidity and mortality. Objective: This study aimed to analyze the impact of COVID-19 during pregnancy on newborns and the effects of maternal COVID-19 vaccination on neonatal outcomes when Omicron was the variant of concern. Study design: INTERCOVID-2022 was a large, prospective, observational study, conducted in 40 hospitals across 18 countries, from November 27, 2021 (the day after the World Health Organization declared Omicron the variant of concern) to June 30, 2022, to assess the effect of COVID-19 in pregnancy on maternal and neonatal outcomes and to assess vaccine effectiveness. Women diagnosed with laboratory-confirmed COVID-19 during pregnancy were compared with 2 nondiagnosed, unmatched women recruited concomitantly and consecutively during pregnancy or at delivery. Mother-newborn dyads were followed until hospital discharge. The primary outcomes were a neonatal positive test for COVID-19, severe neonatal morbidity index, severe perinatal morbidity and mortality index, preterm birth, neonatal death, referral to neonatal intensive care unit, and diseases during the neonatal period. Vaccine effectiveness was estimated with adjustment for maternal risk profile. Results: We enrolled 4707 neonates born to 1577 (33.5%) mothers diagnosed with COVID-19 and 3130 (66.5%) nondiagnosed mothers. Among the diagnosed mothers, 642 (40.7%) were not vaccinated, 147 (9.3%) were partially vaccinated, 551 (34.9%) were completely vaccinated, and 237 (15.0%) also had a booster vaccine. Neonates of booster-vaccinated mothers had less than half (relative risk, 0.46; 95% confidence interval, 0.23-0.91) the risk of being diagnosed with COVID-19 when compared with those of unvaccinated mothers; they also had the lowest rates of preterm birth, medically indicated preterm birth, respiratory distress syndrome, and number of days in the neonatal intensive care unit. Newborns of unvaccinated mothers had double the risk for neonatal death (relative risk, 2.06; 95% confidence interval, 1.06-4.00) when compared with those of nondiagnosed mothers. Vaccination was not associated with any congenital malformations. Although all vaccines provided protection against neonatal test positivity, newborns of booster-vaccinated mothers had the highest vaccine effectiveness (64%; 95% confidence interval, 10%-86%). Vaccine effectiveness was not as high for messenger RNA vaccines only. Vaccine effectiveness against moderate or severe neonatal outcomes was much lower, namely 13% in the booster-vaccinated group (all vaccines) and 25% and 28% in the completely and booster-vaccinated groups, respectively (messenger RNA vaccines only). Vaccines were fairly effective in protecting neonates when given to pregnant women ≤100 days (14 weeks) before birth; thereafter, the risk increased and was much higher after 200 days (29 weeks). Finally, none of the neonatal practices studied, including skin-to-skin contact and direct breastfeeding, increased the risk for infecting newborns. Conclusion: When Omicron was the variant of concern, newborns of unvaccinated mothers had an increased risk for neonatal death. Neonates of vaccinated mothers had a decreased risk for preterm birth and adverse neonatal outcomes. Because the protective effect of COVID-19 vaccination decreases with time, to ensure that newborns are maximally protected against COVID-19, mothers should receive a vaccine or booster dose no more than 14 weeks before the expected date of delivery

A scale of degrees of independence of random variables

A scale of degrees of independence of two random variables is studied. The lowest point of the scale is the lack of correlation and the highest one being the usual independence. The "middle" point is so-called convolutional independence which is defined by the condition that the distribution function of the sum of random variables is the convolution of the distribution functions of the summands. The scale consists of two parts. The first one is a linearly ordered set, the second one is a partially ordered set

BIOLOGICAL ASPECTS OF ASSOCIATION BETWEEN CARDIOVASCULAR DISEASES AND PERIODONTITIS

Paradontitis is associated with the risk of developing cardiovascular diseases as a pathogenic factor. The onset and spread of periodontitis occurs as a result of dysbacteriosis of commensal oral microbiota, that is further interacts with the hosts immune system, being the cause of development of low rank systemic inflammation and the most frequent cause of cardiovascular diseases. An important virulence factor of gram-negative bacteria that dominate in the oral microbiota in periodontitis is lipopolysaccharides, which are part of their cell membranes and being endotoxins. In humans, lipopolysaccharides play a central role in host immune responses, which is characterized by cytokine synthesis, activation of the immune system and provokes the risk of atherosclerotic changes and thromboembolic processes. At the same time, serum lipopolysaccharide activity correlates with serum IgG levels against P. gingivalis, the main causative agent of periodontitis. Lipopolysaccharides are the molecular association between oral dysbacteriosis and cardiometabolic disorders. Saliva lipopolysaccharides correlate with serum lipopolysaccharide activity and this association is enhanced in the presence of periodontitis. The oral microbiota is stably associated with such cardiovascular diseases as acute coronary syndrome and atherosclerosis. Certain types of microflora associated with cardiovascular diseases are identified. Some types associated with periodontitis, such as Porphyromonas gingivalis, are able to invade epithelial cells and multiply in them. Inflammation associated with endotoxemia in periodontitis explains the association with the clinical manifestations of cardiovascular diseases. All bacterial structural components and virulence factors are recognized in the host organism as antigens. They lead to the formation of antibodies, however, the mechanisms of their participation in the pathogenesis of periodontitis and other chronic diseases associated with paradontium are not yet clear. The contribution of cross-reactive antibodies obtained against host antigens is investigated as a response to the similarity of their epitopes with the antigens of bacteria, which is called molecular mimicry and which promotes inflammation. One of the most frequently studied epitopes is present in heat shock proteins (HSP), therewith eight members of the HSP family are associated with the development of cardiovascular diseases and mortality from them. Proteins of the HSP60 family are identified as major antigens in a number of bacterial species associated with periodontitis. The levels of antibodies to A. actinomycetemcomitans and P. gingivalis, which dominate in the oral microbiota in periodontitis are being studied. Serum positivity of IgA to these species is a predictor of recurrent stroke, myocardial infarction and other cardiovascular diseases. The high combined IgG response to A. actinomycetemcomitans and P. gingivalis is combined with calcification of the coronary artery. The combined effect of some oral pathogens causes a more significant impact on the development of cardiovascular diseases than the effect of a single microbe. Thus, both direct and indirect mechanisms are involved in the development of cardiovascular diseases that are associated with periodontitis, while patients are constantly exposed to dysbiotic bacteria and their virulence, which causes and maintains systemic low rank inflammation. Endotoxemia and antibody response are mediators that connect oral dysbacteriosis with an increased risk of cardiovascular diseases