The asymptotic distribution function of the 4-dimensional shifted van der Corput sequence

Abstract Let γq(n) be the van der Corput sequence in the base q and g(x, y, z, u) be an asymptotic distribution function of the 4-dimensional sequence In this paper we find an explicit formula for g(x, x, x, x) and then as an example we find the limit for the base q = 4, 5, 6, . . . Also we find an explicit form of sth iteration T(s)(x) of the von Neumann-Kakutani transformation defined by T(γq(n)) = γq(n + 1)

Case report: Successful multimodal assessment and management of chemothorax

Dislocation or wrong placement of central venous catheters into the pleural cavity is rare, but if undiagnosed, may cause major, sometimes life-threatening, complications (pneumothorax, hemothorax, infection, and migration) and accidental pleural effusion due to intravenous injection of fluids containing drugs (i.e. chemotherapy, antibiotics, parenteral nutrition, other). We report a rare case of pleural effusion consisting of chemotherapy (chemothorax) directly injected into the pleural cavity due to the wrong placement of a central venous catheter (Porth-A-Cath) in a woman with breast cancer. A multidisciplinary management consisting of antidote administration, followed by removal of the venous device and washing of the pleural cavity through video-assisted thoracic surgery (VATS), avoided any major complication related to the adverse event

Real life experience on the use of Remdesivir in patients admitted to COVID-19 in two referral Italian hospital: a propensity score matched analysis

: Remdesivir (RDV) was the first Food and Drug Administration (FDA)-approved medication for COVID-19, with discordant data on efficacy in reducing mortality risk and disease progression. In the context of a dynamic and rapidly changing pandemic landscape, the utilization of real-world evidence is of utmost importance. The objective of this study is to evaluate the impact of RDV on patients who have been admitted to two university referral hospitals in Italy due to COVID-19. All patients older than 18 years and hospitalized at two different universities (Bari and Palermo) were enrolled in this study. To minimize the effect of potential confounders, we used propensity score matching with one case (Remdesivir) and one control that never experienced this kind of intervention during hospitalization. Mortality was the primary outcome of our investigation, and it was recorded using death certificates and/or medical records. Severe COVID-19 was defined as admission to the intensive care unit or a qSOFAscore ≥ 2 or CURB65scores ≥ 3. After using propensity score matching, 365 patients taking Remdesivir and 365 controls were included. No significant differences emerged between the two groups in terms of mean age and percentage of females, while patients taking Remdesivir were less frequently active smokers (p < 0.0001). Moreover, the patients taking Remdesivir were less frequently vaccinated against COVID-19. All the other clinical, radiological, and pharmacological parameters were balanced between the two groups. The use of Remdesivir in our cohort was associated with a significantly lower risk of mortality during the follow-up period (HR 0.56; 95% CI 0.37-0.86; p = 0.007). Moreover, RDV was associated with a significantly lower incidence of non-invasive ventilation (OR 0.27; 95% CI 0.20-0.36). Furthermore, in the 365 patients taking Remdesivir, we observed two cases of mild renal failure requiring a reduction in the dosage of Remdesivir and two cases in which the physicians decided to interrupt Remdesivir for bradycardia and for QT elongation. Our study suggests that the use of Remdesivir in hospitalized COVID-19 patients is a safe therapy associated with improved clinical outcomes, including halving of mortality and with a reduction of around 75% of the risk of invasive ventilation. In a constantly changing COVID-19 scenario, ongoing research is necessary to tailor treatment decisions based on the latest scientific evidence and optimize patient outcomes

SARS‐CoV‐2 infection and venous thromboembolism after surgery: an international prospective cohort study

SARS-CoV-2 has been associated with an increased rate of venous thromboembolism in critically ill patients. Since surgical patients are already at higher risk of venous thromboembolism than general populations, this study aimed to determine if patients with peri-operative or prior SARS-CoV-2 were at further increased risk of venous thromboembolism. We conducted a planned sub-study and analysis from an international, multicentre, prospective cohort study of elective and emergency patients undergoing surgery during October 2020. Patients from all surgical specialties were included. The primary outcome measure was venous thromboembolism (pulmonary embolism or deep vein thrombosis) within 30 days of surgery. SARS-CoV-2 diagnosis was defined as peri-operative (7 days before to 30 days after surgery); recent (1-6 weeks before surgery); previous (>= 7 weeks before surgery); or none. Information on prophylaxis regimens or pre-operative anti-coagulation for baseline comorbidities was not available. Postoperative venous thromboembolism rate was 0.5% (666/123,591) in patients without SARS-CoV-2; 2.2% (50/2317) in patients with peri-operative SARS-CoV-2; 1.6% (15/953) in patients with recent SARS-CoV-2; and 1.0% (11/1148) in patients with previous SARS-CoV-2. After adjustment for confounding factors, patients with peri-operative (adjusted odds ratio 1.5 (95%CI 1.1-2.0)) and recent SARS-CoV-2 (1.9 (95%CI 1.2-3.3)) remained at higher risk of venous thromboembolism, with a borderline finding in previous SARS-CoV-2 (1.7 (95%CI 0.9-3.0)). Overall, venous thromboembolism was independently associated with 30-day mortality (5.4 (95%CI 4.3-6.7)). In patients with SARS-CoV-2, mortality without venous thromboembolism was 7.4% (319/4342) and with venous thromboembolism was 40.8% (31/76). Patients undergoing surgery with peri-operative or recent SARS-CoV-2 appear to be at increased risk of postoperative venous thromboembolism compared with patients with no history of SARS-CoV-2 infection. Optimal venous thromboembolism prophylaxis and treatment are unknown in this cohort of patients, and these data should be interpreted accordingly