Thurston equivalence of topological polynomials

We answer Hubbard's question on determining the Thurston equivalence class of ``twisted rabbits'', i.e. images of the ``rabbit'' polynomial under n-th powers of the Dehn twists about its ears. The answer is expressed in terms of the 4-adic expansion of n. We also answer the equivalent question for the other two families of degree-2 topological polynomials with three post-critical points. In the process, we rephrase the questions in group-theoretical language, in terms of wreath recursions.Comment: 40 pages, lots of figure

Association between dispatch of mobile stroke units and functional outcomes among patients with acute ischemic stroke in Berlin

Importance Effects of thrombolysis in acute ischemic stroke are time-dependent. Ambulances that can administer thrombolysis (mobile stroke units [MSUs]) before arriving at the hospital have been shown to reduce time to treatment. Objective To determine whether dispatch of MSUs is associated with better clinical outcomes for patients with acute ischemic stroke. Design, Setting, and Participants This prospective, nonrandomized, controlled intervention study was conducted in Berlin, Germany, from February 1, 2017, to October 30, 2019. If an emergency call prompted suspicion of stroke, both a conventional ambulance and an MSU, when available, were dispatched. Functional outcomes of patients with final diagnosis of acute cerebral ischemia who were eligible for thrombolysis or thrombectomy were compared based on the initial dispatch (both MSU and conventional ambulance or conventional ambulance only). Exposure Simultaneous dispatch of an MSU (computed tomographic scanning with or without angiography, point-of-care laboratory testing, and thrombolysis capabilities on board) and a conventional ambulance (n = 749) vs conventional ambulance alone (n = 794). Main Outcomes and Measures The primary outcome was the distribution of modified Rankin Scale (mRS) scores (a disability score ranging from 0, no neurological deficits, to 6, death) at 3 months. The coprimary outcome was a 3-tier disability scale at 3 months (none to moderate disability; severe disability; death) with tier assignment based on mRS scores if available or place of residence if mRS scores were not available. Common odds ratios (ORs) were used to quantify the association between exposure and outcome; values less than 1.00 indicated a favorable shift in the mRS distribution and lower odds of higher levels of disability. Results Of the 1543 patients (mean age, 74 years; 723 women [47%]) included in the adjusted primary analysis, 1337 (87%) had available mRS scores (primary outcome) and 1506 patients (98%) had available the 3-tier disability scale assessment (coprimary outcome). Patients with an MSU dispatched had lower median mRS scores at month 3 (1; interquartile range [IQR], 0-3) than did patients without an MSU dispatched (2; IQR, 0-3; common OR for worse mRS, 0.71; 95% CI, 0.58-0.86; P < .001). Similarly, patients with an MSU dispatched had lower 3-month coprimary disability scores: 586 patients (80.3%) had none to moderate disability; 92 (12.6%) had severe disability; and 52 (7.1%) had died vs patients without an MSU dispatched: 605 (78.0%) had none to moderate disability; 103 (13.3%) had severe disability; and 68 (8.8%) had died (common OR for worse functional outcome, 0.73, 95% CI, 0.54-0.99; P = .04). Conclusions and Relevance In this prospective, nonrandomized, controlled intervention study of patients with acute ischemic stroke in Berlin, Germany, the dispatch of mobile stroke units, compared with conventional ambulances alone, was significantly associated with lower global disability at 3 months. Clinical trials in other regions are warranted.This cohort study compares global disability at 3 months among Berlin patients with out-of-hospital ischemic stroke brought to care via a mobile stroke unit ambulance (with prehospital CT scanning with or without angiography, point-of-care laboratory testing, prehospital thrombolysis) vs conventional ambulance alone.Question Is the dispatch of mobile stroke units in the out-of-hospital setting before arriving at the hospital associated with better functional outcomes among patients with acute ischemic stroke eligible for thrombolysis or thrombectomy? Findings In this prospective nonrandomized controlled intervention study involving 1543 patients in Berlin, Germany, the dispatch of mobile stroke units in addition to conventional ambulances vs conventional ambulances alone was significantly associated with lower levels of global disability at 3 months (common odds ratio for higher modified Rankin Scale scores [ie, worse outcome], 0.71). Meaning Among patients with acute ischemic stroke in Berlin, Germany, dispatch of a mobile stroke unit was associated with lower global disability at 3 months; further research in diverse settings is needed.Clinical epidemiolog

A randomised controlled trial comparing the effectiveness of Tai Chi alongside usual care with usual care alone on the postural balance of community-dwelling people with dementia: Protocol for The TACIT Trial (TAi ChI for people with dementia).

Background: Falls are a public health issue for the older adult population and more so for people with dementia (PWD). Compared with their cognitively intact peers, PWD are at higher risk of falls and injurious falls. This randomised controlled trial aims to test the clinical and cost effectiveness of Tai Chi to improve postural balance among community-dwelling PWD and to assess the feasibility of conducting a larger definitive trial to reduce the incidence of falls among PWD. Methods: A 3-centre parallel group randomised controlled trial with embedded process evaluation. One hundred and fifty community-dwelling dyads of a person with dementia and their informal carer will be recruited and assessed at baseline and at six-month follow-up. Dyads will be randomised in a 1:1 ratio to either usual care or usual care plus a Tai Chi intervention for 20 weeks. The Tai Chi intervention will consist of weekly classes (45 minutes’ Tai Chi plus up to 45 minutes for informal discussion, with up to 10 dyads per class) and home-based exercises (20 minutes per day to be facilitated by the carer). Home practice of Tai Chi will be supported by the use of behaviour change techniques with the Tai Chi instructor at a home visit in week 3-4 of the intervention (action planning, coping planning, self-monitoring, and alarm clock reminder) and at the end of each class (feedback on home practice). The primary outcome is dynamic balance measured using the Timed Up and Go test, coinciding with the end of the 20-week intervention phase for participants in the Tai Chi arm. Secondary outcomes for PWD include functional balance, static balance, fear of falling, global cognitive functioning, visual-spatial cognitive functioning, quality of life, and falls. Secondary outcomes for carers include dynamic balance, static balance, quality of life, costs, and carer burden. Discussion: This trial is the first in the UK to test the effectiveness of Tai Chi to improve balance among PWD. The trial will inform a future study that will be the first in the world to use Tai Chi in a trial to prevent falls among PWD. Trial registration: NCT02864056

Thin coherent configurations and groupoids

Published: 2 September 2014In this paper, we will investigate thin coherent configurations. We will show that thin coherent configurations are equivalent to finite connected groupoids. Also, we will investigate their representations