Background Patients hospitalised with COVID-19 are at risk for thrombotic events after discharge; the role of extended thromboprophylaxis in this population is unknown. Methods In this open-label, multicentre, randomised trial conducted at 14 centres in Brazil, patients hospitalised with COVID-19 at increased risk for venous thromboembolism (International Medical Prevention Registry on Venous Thromboembolism [IMPROVE] venous thromboembolism [VTE] score of ≥4 or 2–3 with a D-dimer >500 ng/mL) were randomly assigned (1:1) to receive, at hospital discharge, rivaroxaban 10 mg/day or no anticoagulation for 35 days. The primary efficacy outcome in an intention-to-treat analysis was a composite of symptomatic or fatal venous thromboembolism, asymptomatic venous thromboembolism on bilateral lower-limb venous ultrasound and CT pulmonary angiogram, symptomatic arterial thromboembolism, and cardiovascular death at day 35. Adjudication was blinded. The primary safety outcome was major bleeding. The primary and safety analyses were carried out in the intention-to-treat population. This trial is registered at ClinicalTrials.gov , NCT04662684 . Findings From Oct 8, 2020, to June 29, 2021, 997 patients were screened. Of these patients, 677 did not meet eligibility criteria; the remaining 320 patients were enrolled and randomly assigned to receive rivaroxaban (n=160 [50%]) or no anticoagulation (n=160 [50%]). All patients received thromboprophylaxis with standard doses of heparin during hospitalisation. 165 (52%) patients were in the intensive care unit while hospitalised. 197 (62%) patients had an IMPROVE score of 2–3 and elevated D-dimer levels and 121 (38%) had a score of 4 or more. Two patients (one in each group) were lost to follow-up due to withdrawal of consent and not included in the intention-to-treat primary analysis. The primary efficacy outcome occurred in five (3%) of 159 patients assigned to rivaroxaban and 15 (9%) of 159 patients assigned to no anticoagulation (relative risk 0·33, 95% CI 0·12–0·90; p=0·0293). No major bleeding occurred in either study group. Allergic reactions occurred in two (1%) patients in the rivaroxaban group. Interpretation In patients at high risk discharged after hospitalisation due to COVID-19, thromboprophylaxis with rivaroxaban 10 mg/day for 35 days improved clinical outcomes compared with no extended thromboprophylaxis. Funding Bayer.

A system of interacting vortices under overdamped motion, which has been commonly used in the literature to model flux-front penetration in disordered type-II superconductors, was recently related to a nonlinear Fokker-Planck equation, characteristic of nonextensive statistical mechanics, through an analysis of its stationary state. Herein, this connection is extended by means of a thorough analysis of the time evolution of this system. Numerical data from molecular-dynamics simulations are presented for both position and velocity probability distributions P(x,t) and P(v(x),t), respectively; both distributions are well fitted by similar q-Gaussian distributions, with the same index q=0, for all times considered. Particularly, the evolution of the system occurs in such a way that P(x,t) presents a time behavior for its width, normalization, and second moment, in full agreement with the analytic solution of the nonlinear Fokker-Planck equation. The present results provide further evidence that this system is deeply associated with nonextensive statistical mechanics.

Endovascular repair of pararenal aortic aneurysms and TAAAs, using manufactured F-BEVAR with supraceliac sealing zones, is safe and efficacious. Long-term follow-up is needed to assess the impact of four-vessel designs on device-related complications and progression of aortic disease.

Endovascular repair of thoracoabdominal aortic aneurysms can be performed with high technical success and low mortality and morbidity. However, the need for secondary reinterventions and continued graft surveillance represents major limitations compared with results of conventional open surgical repair. Long-term follow-up is needed before the widespread use of these techniques in younger or lower-risk patients.

Background Among asymptomatic patients with severe carotid artery stenosis but no recent stroke or transient cerebral ischaemia, either carotid artery stenting (CAS) or carotid endarterectomy (CEA) can restore patency and reduce long-term stroke risks. However, from recent national registry data, each option causes about 1% procedural risk of disabling stroke or death. Comparison of their long-term protective effects requires large-scale randomised evidence.Methods ACST-2 is an international multicentre randomised trial of CAS versus CEA among asymptomatic patients with severe stenosis thought to require intervention, interpreted with all other relevant trials. Patients were eligible if they had severe unilateral or bilateral carotid artery stenosis and both doctor and patient agreed that a carotid procedure should be undertaken, but they were substantially uncertain which one to choose. Patients were randomly allocated to CAS or CEA and followed up at 1 month and then annually, for a mean 5 years. Procedural events were those within 30 days of the intervention. Intention-to-treat analyses are provided. Analyses including procedural hazards use tabular methods. Analyses and meta-analyses of non-procedural strokes use Kaplan-Meier and log-rank methods. The trial is registered with the ISRCTN registry, ISRCTN21144362.

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Several previous results valid for one-dimensional nonlinear Fokker-Planck equations are generalized to N-dimensions. A general nonlinear N-dimensional FokkerPlanck equation is derived directly from a master equation, by considering nonlinearities in the transition rates. Using nonlinear Fokker-Planck equations, the H-theorem is proved; for that, an important relation involving these equations and general entropic forms is introduced. It is shown that due to this relation, classes of nonlinear N-dimensional Fokker-Planck equations are connected to a single entropic form. A particular emphasis is given to the class of equations associated to Tsallis entropy, in both cases of the standard, and generalized definitions for the internal energy.

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