Sums of magnetic eigenvalues are maximal on rotationally symmetric domains

The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3 on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n=1).Comment: 19 pages, 1 figur

Maximizing Neumann fundamental tones of triangles

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proved for the harmonic and arithmetic means of the first two nonzero eigenvalues

Attendance in a national screening program for diabetic retinopathy:a population-based study of 205,970 patients

AIMS: A nationwide diabetic retinopathy (DR) screening program has been established in Denmark since 2013. We aimed to perform an evaluation of adherence to DR screenings and to examine whether non-adherence was correlated to DR progression. METHODS: The population consisted of a register-based cohort, who participated in the screening program from 2013 to 2018. We analyzed age, gender, marital status, DR level (International Clinical DR severity scale, none, mild-, moderate-, severe non-proliferative DR (NPDR) and proliferative DR (PDR)), comorbidities and socioeconomic factors. The attendance pattern of patients was grouped as either timely (no delays > 33%), delayed (delays > 33%) or one-time attendance (unexplained). RESULTS: We included 205,970 patients with 591,136 screenings. Rates of timely, delayed and one-time attendance were 53.0%, 35.5% and 11.5%, respectively. DR level at baseline was associated with delays (mild-, moderate-, severe NPDR and PDR) and one-time attendance (moderate-, severe NPDR and PDR) with relative risk ratios (RRR) of 1.68, 2.27, 3.14, 2.44 and 1.18, 2.07, 1.26, respectively (P < 0.05). Delays at previous screenings were associated with progression to severe NPDR or PDR (hazard ratio (HR) 2.27, 6.25 and 12.84 for 1, 2 and 3+ delays, respectively). Any given delay doubled the risk of progression (HR 2.28). CONCLUSIONS: In a national cohort of 205,970 patients, almost half of the patients attended DR screening later than scheduled or dropped out after first screening episode. This was, in particular, true for patients with any levels of DR at baseline. DR progression in patients with delayed attendance, increased with the number of missed appointments

Diabetic retinopathy as a potential marker of Parkinson's disease:a register-based cohort study

Neurodegeneration is an early event in the pathogenesis of diabetic retinopathy, and an association between diabetic retinopathy and Parkinson’s disease has been proposed. In this nationwide register-based cohort study, we investigated the prevalence and incidence of Parkinson’s disease among patients screened for diabetic retinopathy in a Danish population-based cohort. Cases (n = 173 568) above 50 years of age with diabetes included in the Danish Registry of Diabetic Retinopathy between 2013 and 2018 were matched 1:5 by gender and birth year with a control population without diabetes (n = 843 781). At index date, the prevalence of Parkinson’s disease was compared between cases and controls. To assess the longitudinal relationship between diabetic retinopathy and Parkinson’s disease, a multivariable Cox proportional hazard model was estimated. The prevalence of Parkinson’s disease was 0.28% and 0.44% among cases and controls, respectively. While diabetic retinopathy was not associated with present (adjusted odds ratio 0.93, 95% confidence interval 0.72–1.21) or incident Parkinson’s disease (adjusted hazard ratio 0.77, 95% confidence interval 0.56–1.05), cases with diabetes were in general less likely to have or to develop Parkinson’s disease compared to controls without diabetes (adjusted odds ratio 0.79, 95% confidence interval 0.71–0.87 and adjusted hazard ratio 0.88, 95% confidence interval 0.78–1.00). In a national cohort of more than 1 million persons, patients with diabetes were 21% and 12% were less likely to have prevalent and develop incident Parkinson’s disease, respectively, compared to an age- and gender-matched control population without diabetes. We found no indication for diabetic retinopathy as an independent risk factor for incident Parkinson’s disease

The methylation inhibitor 3DZNep promotes HDR pathway choice during CRISPR-Cas9 genome editing

Alteration of specific epigenetic marks might promote homology directed repair (HDR) during CRISPR-Cas9 genome editing. Testing several epigenetic inhibitors in a traffic light reporter assay, the histone methylation inhibitor 3DZNep showed a significant HDR promoting effect, while non-homologous end joining mediated repair was not significantly changed. This HDR promoting effect was largely independent of the target gene and its expression levels but showed a limited cell type specificity. HDR promotion was independent of the best described target of 3DZNep, the H3K27 methyltransferase EZH2, and of altered gene expression, but correlated partially with increased frequency of S/G2 cell cycle stage

Reproducing subgroups of Sp(2,R)Sp(2,\mathbb{R}). Part I: algebraic classification

We classify the connected Lie subgroups of the symplectic group $Sp(2,\mathbb{R})$ whose elements are matrices in block lower triangular form. The classification is up to conjugation within $Sp(2,\mathbb{R})$. Their study is motivated by the need of a unified approach to continuous 2D signal analyses, as those provided by wavelets and shearlets.Comment: 26 page

Study protocol for a randomised trial of nicotine-free cigarettes as an adjunct to usual NRT-based cessation practice, in people who wish to stop smoking

This trial is funded by a programme grant from the Health Research Council of New Zealand.