Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

Safety and Outcome of Revascularization Treatment in Patients With Acute Ischemic Stroke and COVID-19: The Global COVID-19 Stroke Registry.

BACKGROUND AND OBJECTIVES COVID-19 related inflammation, endothelial dysfunction and coagulopathy may increase the bleeding risk and lower efficacy of revascularization treatments in patients with acute ischemic stroke. We aimed to evaluate the safety and outcomes of revascularization treatments in patients with acute ischemic stroke and COVID-19. METHODS Retrospective multicenter cohort study of consecutive patients with acute ischemic stroke receiving intravenous thrombolysis (IVT) and/or endovascular treatment (EVT) between March 2020 and June 2021, tested for SARS-CoV-2 infection. With a doubly-robust model combining propensity score weighting and multivariate regression, we studied the association of COVID-19 with intracranial bleeding complications and clinical outcomes. Subgroup analyses were performed according to treatment groups (IVT-only and EVT). RESULTS Of a total of 15128 included patients from 105 centers, 853 (5.6%) were diagnosed with COVID-19. 5848 (38.7%) patients received IVT-only, and 9280 (61.3%) EVT (with or without IVT). Patients with COVID-19 had a higher rate of symptomatic intracerebral hemorrhage (SICH) (adjusted odds ratio [OR] 1.53; 95% CI 1.16-2.01), symptomatic subarachnoid hemorrhage (SSAH) (OR 1.80; 95% CI 1.20-2.69), SICH and/or SSAH combined (OR 1.56; 95% CI 1.23-1.99), 24-hour (OR 2.47; 95% CI 1.58-3.86) and 3-month mortality (OR 1.88; 95% CI 1.52-2.33).COVID-19 patients also had an unfavorable shift in the distribution of the modified Rankin score at 3 months (OR 1.42; 95% CI 1.26-1.60). DISCUSSION Patients with acute ischemic stroke and COVID-19 showed higher rates of intracranial bleeding complications and worse clinical outcomes after revascularization treatments than contemporaneous non-COVID-19 treated patients. Current available data does not allow direct conclusions to be drawn on the effectiveness of revascularization treatments in COVID-19 patients, or to establish different treatment recommendations in this subgroup of patients with ischemic stroke. Our findings can be taken into consideration for treatment decisions, patient monitoring and establishing prognosis

Safety and Outcome of Revascularization Treatment in Patients With Acute Ischemic Stroke and COVID-19: The Global COVID-19 Stroke Registry

BACKGROUND AND OBJECTIVES: COVID-19 related inflammation, endothelial dysfunction and coagulopathy may increase the bleeding risk and lower efficacy of revascularization treatments in patients with acute ischemic stroke. We aimed to evaluate the safety and outcomes of revascularization treatments in patients with acute ischemic stroke and COVID-19. METHODS: Retrospective multicenter cohort study of consecutive patients with acute ischemic stroke receiving intravenous thrombolysis (IVT) and/or endovascular treatment (EVT) between March 2020 and June 2021, tested for SARS-CoV-2 infection. With a doubly-robust model combining propensity score weighting and multivariate regression, we studied the association of COVID-19 with intracranial bleeding complications and clinical outcomes. Subgroup analyses were performed according to treatment groups (IVT-only and EVT). RESULTS: Of a total of 15128 included patients from 105 centers, 853 (5.6%) were diagnosed with COVID-19. 5848 (38.7%) patients received IVT-only, and 9280 (61.3%) EVT (with or without IVT). Patients with COVID-19 had a higher rate of symptomatic intracerebral hemorrhage (SICH) (adjusted odds ratio [OR] 1.53; 95% CI 1.16-2.01), symptomatic subarachnoid hemorrhage (SSAH) (OR 1.80; 95% CI 1.20-2.69), SICH and/or SSAH combined (OR 1.56; 95% CI 1.23-1.99), 24-hour (OR 2.47; 95% CI 1.58-3.86) and 3-month mortality (OR 1.88; 95% CI 1.52-2.33).COVID-19 patients also had an unfavorable shift in the distribution of the modified Rankin score at 3 months (OR 1.42; 95% CI 1.26-1.60). DISCUSSION: Patients with acute ischemic stroke and COVID-19 showed higher rates of intracranial bleeding complications and worse clinical outcomes after revascularization treatments than contemporaneous non-COVID-19 treated patients. Current available data does not allow direct conclusions to be drawn on the effectiveness of revascularization treatments in COVID-19 patients, or to establish different treatment recommendations in this subgroup of patients with ischemic stroke. Our findings can be taken into consideration for treatment decisions, patient monitoring and establishing prognosis