Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations

We give an expression for the {\L}ojasiewicz exponent of a wide class of n-tuples of ideals $(I_1,..., I_n)$ in \O_n using the information given by a fixed Newton filtration. In order to obtain this expression we consider a reformulation of {\L}ojasiewicz exponents in terms of Rees mixed multiplicities. As a consequence, we obtain a wide class of semi-weighted homogeneous functions $(\mathbb{C}^n,0)\to (\mathbb{C},0)$ for which the {\L}ojasiewicz of its gradient map $\nabla f$ attains the maximum possible value.Comment: 25 pages. Updated with minor change

Recurrent ischemic stroke and bleeding in patients with atrial fibrillation who suffered an acute stroke while on treatment with nonvitamin K antagonist oral anticoagulants: the RENO-EXTEND study

Background: In patients with atrial fibrillation who suffered an ischemic stroke while on treatment with nonvitamin K antagonist oral anticoagulants, rates and determinants of recurrent ischemic events and major bleedings remain uncertain. Methods: This prospective multicenter observational study aimed to estimate the rates of ischemic and bleeding events and their determinants in the follow-up of consecutive patients with atrial fibrillation who suffered an acute cerebrovascular ischemic event while on nonvitamin K antagonist oral anticoagulant treatment. Afterwards, we compared the estimated risks of ischemic and bleeding events between the patients in whom anticoagulant therapy was changed to those who continued the original treatment. Results: After a mean follow-up time of 15.0±10.9 months, 192 out of 1240 patients (15.5%) had 207 ischemic or bleeding events corresponding to an annual rate of 13.4%. Among the events, 111 were ischemic strokes, 15 systemic embolisms, 24 intracranial bleedings, and 57 major extracranial bleedings. Predictive factors of recurrent ischemic events (strokes and systemic embolisms) included CHA 2 DS 2 -VASc score after the index event (odds ratio [OR], 1.2 [95% CI, 1.0–1.3] for each point increase; P =0.05) and hypertension (OR, 2.3 [95% CI, 1.0–5.1]; P =0.04). Predictive factors of bleeding events (intracranial and major extracranial bleedings) included age (OR, 1.1 [95% CI, 1.0–1.2] for each year increase; P =0.002), history of major bleeding (OR, 6.9 [95% CI, 3.4–14.2]; P =0.0001) and the concomitant administration of an antiplatelet agent (OR, 2.8 [95% CI, 1.4–5.5]; P =0.003). Rates of ischemic and bleeding events were no different in patients who changed or not changed the original nonvitamin K antagonist oral anticoagulants treatment (OR, 1.2 [95% CI, 0.8–1.7]). Conclusions: Patients suffering a stroke despite being on nonvitamin K antagonist oral anticoagulant therapy are at high risk of recurrent ischemic stroke and bleeding. In these patients, further research is needed to improve secondary prevention by investigating the mechanisms of recurrent ischemic stroke and bleeding

Risk of recurrent stroke in patients with atrial fibrillation treated with oral anticoagulants alone or in combination with anti-platelet therapy

Introduction: Ischaemic stroke patients with atrial fibrillation (AF) are at high risk of stroke recurrence despite oral anticoagulation therapy. Patients with cardiovascular comorbidities may take both antiplatelet and oral anticoagulation therapy (OAC/AP). Our study aims to evaluate the safety and efficacy of OAC/AP therapy as secondary prevention in people with AF and ischaemic stroke. Patients and methods: We performed a post-hoc analysis of pooled individual data from multicenter prospective cohort studies and compared outcomes in the OAC/AP cohort and patients on DOAC/VKA anticoagulation alone (OAC cohort). Primary outcome was a composite of ischaemic stroke, systemic embolism, intracranial bleeding, and major extracranial bleeding, while secondary outcomes were ischaemic and haemorrhagic events considered separately. A multivariable logistic regression analysis was performed to identify independent predictors for outcome events. To compare the risk of outcome events between the two cohorts, the relation between the survival function and the set of explanatory variables were calculated by Cox proportional hazard models and the results were reported as adjusted hazard ratios (HR). Finally another analysis was performed to compare the overall risk of outcome events in both OAC/AP and OAC cohorts after propensity score matching (PSM). Results: During a mean follow-up time of 7.5 ± 9.1 months (median follow-up time 3.5 months, interquartile range ±3), 2284 stroke patients were on oral anticoagulants and 215 were on combined therapy. The multivariable model demonstrated that the composite outcome is associated with age (OR: 1.03, 95% CI: 1.01-1.04 for each year increase) and concomitant antiplatelet therapy (OR: 2.2, 95% CI: 1.48-3.27), the ischaemic outcome with congestive heart failure (OR: 1.55, 95% CI: 1.02-2.36) and concomitant antiplatelet therapy (OR: 1.93, 95% CI: 1.19-3.13) and the haemorrhagic outcome with age (OR: 1.03, 95% CI: 1.01-1.06 for each year increase), alcoholism (OR: 2.15, 95% CI: 1.06-4.39) and concomitant antiplatelet therapy (OR: 2.22, 95% CI: 1.23-4.02). Cox regression demonstrated a higher rate of the composite outcome (hazard ratio of 1.93 [95% CI, 1.35-2.76]), ischaemic events (HR: 2.05 [95% CI: 1.45-2.87]) and bleeding outcomes (HR: 1.90 [95% CI, 1.06-3.40]) in OAC/AP cohort. After PSM analysis, the composite outcome remained more frequent in people treated with OAC + AP (RR: 1.70 [95% CI, 1.05-2.74]). Discussion: Secondary prevention with combination of oral anticoagulant and antiplatelet therapy after ischaemic stroke was associated with worse outcomes in our cohort. Conclusion: Further research is needed to improve secondary prevention by investigating the mechanisms of recurrent ischaemic stroke in patients with atrial fibrillation

Human health risk assessment for aluminium, aluminium oxide, and aluminium hydroxide.

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