Multi-triangulations as complexes of star polygons

Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of looking at $k$-triangulations, namely as complexes of star polygons. With this tool we give new, direct, proofs of the fundamental properties of $k$-triangulations, as well as some new results. This interpretation also opens-up new avenues of research, that we briefly explore in the last section.Comment: 40 pages, 24 figures; added references, update Section

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

European Stroke Organisation - European Society for Minimally Invasive Neurological Therapy expedited recommendation on indication for intravenous thrombolysis before mechanical thrombectomy in patients with acute ischaemic stroke and anterior circulation large vessel occlusion

Six randomized controlled clinical trials have assessed whether mechanical thrombectomy (MT) alone is non-inferior to intravenous thrombolysis (IVT) plus MT within 4.5 hours of symptom onset in patients with anterior circulation large vessel occlusion (LVO) ischaemic stroke and no contraindication to IVT. An expedited recommendation process was initiated by the European Stroke Organisation (ESO) and conducted with the European Society of Minimally Invasive Neurological Therapy (ESMINT) according to ESO standard operating procedure based on the GRADE system. We identified two relevant Population, Intervention, Comparator, Outcome (PICO) questions, performed systematic reviews and meta-analyses of the literature, assessed the quality of the available evidence and wrote evidence-based recommendations. Expert opinion was provided if insufficient evidence was available to provide recommendations based on the GRADE approach. For stroke patients with anterior circulation LVO directly admitted to a MT-capable centre ('mothership') within 4.5 hours of symptom onset and eligible for both treatments, we recommend IVT plus MT over MT alone (moderate evidence, strong recommendation). MT should not prevent the initiation of IVT, nor should IVT delay MT. In stroke patients with anterior circulation LVO admitted to a centre without MT facilities and eligible for IVT <= 4.5 hrs and MT, we recommend IVT followed by rapid transfer to a MT capable-centre ('drip-and-ship') in preference to omitting IVT (low evidence, strong recommendation). Expert consensus statements on ischaemic stroke on awakening from sleep are also provided. Patients with anterior circulation LVO stroke should receive IVT in addition to MT if they have no contraindications to either treatment

European Stroke Organisation (ESO)-European Society for Minimally Invasive Neurological Therapy (ESMINT) expedited recommendation on indication for intravenous thrombolysis before mechanical thrombectomy in patients with acute ischemic stroke and anterior circulation large vessel occlusion

Six randomized controlled clinical trials have assessed whether mechanical thrombectomy (MT) alone is non-inferior to intravenous thrombolysis (IVT) plus MT within 4.5 hours of symptom onset in patients with anterior circulation large vessel occlusion (LVO) ischemic stroke and no contraindication to IVT. An expedited recommendation process was initiated by the European Stroke Organisation (ESO) and conducted with the European Society of Minimally Invasive Neurological Therapy (ESMINT) according to ESO standard operating procedure based on the GRADE system. We identified two relevant Population, Intervention, Comparator, Outcome (PICO) questions, performed systematic reviews and meta-analyses of the literature, assessed the quality of the available evidence, and wrote evidence-based recommendations. Expert opinion was provided if insufficient evidence was available to provide recommendations based on the GRADE approach.For stroke patients with anterior circulation LVO directly admitted to a MT-capable center ('mothership') within 4.5 hours of symptom onset and eligible for both treatments, we recommend IVT plus MT over MT alone (moderate evidence, strong recommendation). MT should not prevent the initiation of IVT, nor should IVT delay MT. In stroke patients with anterior circulation LVO admitted to a center without MT facilities and eligible for IVT ≤4.5 hours and MT, we recommend IVT followed by rapid transfer to a MT capable-center ('drip-and-ship') in preference to omitting IVT (low evidence, strong recommendation). Expert consensus statements on ischemic stroke on awakening from sleep are also provided. Patients with anterior circulation LVO stroke should receive IVT in addition to MT if they have no contraindications to either treatment