Covariant Poisson equation with compact Lie algebras

The covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for the existence and smoothness of solutions to the covariant Poisson equation. These conditions require, apart from suitable continuity, appropriate local integrability of the gauge potentials and global weighted integrability of the curvature form and the source. The possibility of nontrivial asymptotic behaviour of a solution is also considered. As a by-product, weighted covariant generalisations of Sobolev embeddings are established.Comment: 31 pages, LaTeX2

Sharp constants in weighted trace inequalities on Riemannian manifolds

We establish some sharp weighted trace inequalities W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M) on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of $M$ and $\sigma\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page

Pigmentary retinopathy can indicate the presence of pathogenic LAMP2 variants even in somatic mosaic carriers with no additional signs of Danon disease

PURPOSE: Danon disease (DD) is a rare X-linked disorder caused by pathogenic variants in LAMP2. DD primarily manifests as a severe cardiomyopathy. An early diagnosis is crucial for patient survival. The aim of the study was to determine the usefulness of ocular examination for identification of DD. METHODS: Detailed ocular examination in 10 patients with DD (3 males, 7 females) and a 45-year-old asymptomatic female somatic mosaic carrier of a LAMP2 disease-causing variant. RESULTS: All patients with manifest cardiomyopathy had pigmentary retinopathy with altered autofluorescence and diffuse visual field loss. Best corrected visual acuity (BCVA) was decreased (<0.63) in 8 (40%) out of 20 eyes. The severity of retinal pathology increased with age, resulting in marked cone-rod involvement overtime. Spectral-domain optical coherence tomography in younger patients revealed focal loss of photoreceptors, disruption and deposition at the retinal pigment epithelium/Bruch's membrane layer (corresponding to areas of marked increased autofluorescence), and hyperreflective foci in the outer nuclear layer. Cystoid macular oedema was seen in one eye. In the asymptomatic female with somatic mosaicism, the BCVA was 1.0 bilaterally. An abnormal autofluorescence pattern in the left eye was present; while full-field electroretinography was normal. CONCLUSIONS: Detailed ocular examination may represent a sensitive and quick screening tool for the identification of carriers of LAMP2 pathogenic variants, even in somatic mosaicism. Hence, further investigation should be undertaken in all patients with pigmentary retinal dystrophy as it may be a sign of a life-threatening disease

Interpolation in variable exponent spaces

In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale

Axial Globe Position Measurement: A Prospective Multicenter Study by the International Thyroid Eye Disease Society

Identify a reproducible measure of axial globe position (AGP) for multicenter studies on patients with thyroid eye disease (TED)

Nutritional management of children with cerebral palsy: a practical guide

Peer reviewedFinal Published versio

Prediction of Psilocybin Response in Healthy Volunteers

Responses to hallucinogenic drugs, such as psilocybin, are believed to be critically dependent on the user's personality, current mood state, drug pre-experiences, expectancies, and social and environmental variables. However, little is known about the order of importance of these variables and their effect sizes in comparison to drug dose. Hence, this study investigated the effects of 24 predictor variables, including age, sex, education, personality traits, drug pre-experience, mental state before drug intake, experimental setting, and drug dose on the acute response to psilocybin. The analysis was based on the pooled data of 23 controlled experimental studies involving 409 psilocybin administrations to 261 healthy volunteers. Multiple linear mixed effects models were fitted for each of 15 response variables. Although drug dose was clearly the most important predictor for all measured response variables, several non-pharmacological variables significantly contributed to the effects of psilocybin. Specifically, having a high score in the personality trait of Absorption, being in an emotionally excitable and active state immediately before drug intake, and having experienced few psychological problems in past weeks were most strongly associated with pleasant and mystical-type experiences, whereas high Emotional Excitability, low age, and an experimental setting involving positron emission tomography most strongly predicted unpleasant and/or anxious reactions to psilocybin. The results confirm that non-pharmacological variables play an important role in the effects of psilocybin