Isometric Immersions and the Waving of Flags

In this article we propose a novel geometric model to study the motion of a physical flag. In our approach a flag is viewed as an isometric immersion from the square with values into $\mathbb R^3$ satisfying certain boundary conditions at the flag pole. Under additional regularity constraints we show that the space of all such flags carries the structure of an infinite dimensional manifold and can be viewed as a submanifold of the space of all immersions. The submanifold result is then used to derive the equations of motion, after equipping the space of isometric immersions with its natural kinetic energy. This approach can be viewed in a similar spirit as Arnold's geometric picture for the motion of an incompressible fluid.Comment: 25 pages, 1 figur

A relaxed approach for curve matching with elastic metrics

In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the family of $H^2$-metrics with constant coefficients and scale-invariant $H^2$-metrics on both open and closed immersed curves. These families include as particular cases the class of first-order elastic metrics. An essential difference with prior approaches is the way that boundary constraints are dealt with. By leveraging varifold-based similarity metrics we propose a relaxed variational formulation for the matching problem that avoids the necessity of optimizing over the reparametrization group. Furthermore, we show that we can also quotient out finite-dimensional similarity groups such as translation, rotation and scaling groups. The different properties and advantages are illustrated through numerical examples in which we also provide a comparison with related diffeomorphic methods used in shape registration.Comment: 27 page

Risk Factors for Being Seronegative following SARS-CoV-2 Infection in a Large Cohort of Health Care Workers in Denmark

Most individuals seroconvert after infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), but being seronegative is observed in 1 to 9%. We aimed to investigate the risk factors associated with being seronegative following PCR-confirmed SARS-CoV-2 infection. In a prospective cohort study, we screened health care workers (HCW) in the Capital Region of Denmark for SARS-CoV-2 antibodies. We performed three rounds of screening from April to October 2020 using an enzyme-linked immunosorbent assay (ELISA) method targeting SARS-CoV-2 total antibodies. Data on all participants’ PCR for SARS-CoV-2 RNA were captured from national registries. The Kaplan-Meier method and Cox proportional hazards models were applied to investigate the probability of being seronegative and the related risk factors, respectively. Of 36,583 HCW, 866 (2.4%) had a positive PCR before or during the study period. The median (interquartile range [IQR]) age of 866 HCW was 42 (31 to 53) years, and 666 (77%) were female. After a median of 132 (range, 35 to 180) days, 21 (2.4%) of 866 were seronegative. In a multivariable model, independent risk factors for being seronegative were self-reported asymptomatic or mild infection hazard ratio (HR) of 6.6 (95% confidence interval [CI], 2.6 to 17; P < 0.001) and body mass index (BMI) of ≥30, HR 3.1 (95% CI, 1.1 to 8.8; P = 0.039). Only a few (2.4%) HCW were not seropositive. Asymptomatic or mild infection as well as a BMI above 30 were associated with being seronegative. Since the presence of antibodies against SARS-CoV-2 reduces the risk of reinfection, efforts to protect HCW with risk factors for being seronegative may be needed in future COVID-19 surges. IMPORTANCE Most individuals seroconvert after infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), but negative serology is observed in 1 to 9%. We found that asymptomatic or mild infection as well as a BMI above 30 were associated with being seronegative. Since the presence of antibodies against SARS-CoV-2 reduces the risk of reinfection, efforts to protect HCW with risk factors for being seronegative may be needed in future COVID-19 surges

Effect of remote ischaemic conditioning on clinical outcomes in patients with acute myocardial infarction (CONDI-2/ERIC-PPCI): a single-blind randomised controlled trial.

BACKGROUND: Remote ischaemic conditioning with transient ischaemia and reperfusion applied to the arm has been shown to reduce myocardial infarct size in patients with ST-elevation myocardial infarction (STEMI) undergoing primary percutaneous coronary intervention (PPCI). We investigated whether remote ischaemic conditioning could reduce the incidence of cardiac death and hospitalisation for heart failure at 12 months. METHODS: We did an international investigator-initiated, prospective, single-blind, randomised controlled trial (CONDI-2/ERIC-PPCI) at 33 centres across the UK, Denmark, Spain, and Serbia. Patients (age >18 years) with suspected STEMI and who were eligible for PPCI were randomly allocated (1:1, stratified by centre with a permuted block method) to receive standard treatment (including a sham simulated remote ischaemic conditioning intervention at UK sites only) or remote ischaemic conditioning treatment (intermittent ischaemia and reperfusion applied to the arm through four cycles of 5-min inflation and 5-min deflation of an automated cuff device) before PPCI. Investigators responsible for data collection and outcome assessment were masked to treatment allocation. The primary combined endpoint was cardiac death or hospitalisation for heart failure at 12 months in the intention-to-treat population. This trial is registered with ClinicalTrials.gov (NCT02342522) and is completed. FINDINGS: Between Nov 6, 2013, and March 31, 2018, 5401 patients were randomly allocated to either the control group (n=2701) or the remote ischaemic conditioning group (n=2700). After exclusion of patients upon hospital arrival or loss to follow-up, 2569 patients in the control group and 2546 in the intervention group were included in the intention-to-treat analysis. At 12 months post-PPCI, the Kaplan-Meier-estimated frequencies of cardiac death or hospitalisation for heart failure (the primary endpoint) were 220 (8·6%) patients in the control group and 239 (9·4%) in the remote ischaemic conditioning group (hazard ratio 1·10 [95% CI 0·91-1·32], p=0·32 for intervention versus control). No important unexpected adverse events or side effects of remote ischaemic conditioning were observed. INTERPRETATION: Remote ischaemic conditioning does not improve clinical outcomes (cardiac death or hospitalisation for heart failure) at 12 months in patients with STEMI undergoing PPCI. FUNDING: British Heart Foundation, University College London Hospitals/University College London Biomedical Research Centre, Danish Innovation Foundation, Novo Nordisk Foundation, TrygFonden