Two isoperimetric inequalities for the Sobolev constant

In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.Comment: 11 page

The Link between the Baryonic Mass Distribution and the Rotation Curve Shape

The observed rotation curves of disc galaxies, ranging from late-type dwarf galaxies to early-type spirals, can be fit remarkably well simply by scaling up the contributions of the stellar and HI discs. This `baryonic scaling model' can explain the full breadth of observed rotation curves with only two free parameters. For a small fraction of galaxies, in particular early-type spiral galaxies, HI scaling appears to fail in the outer parts, possibly due to observational effects or ionization of the HI. The overall success of the baryonic scaling model suggests that the well-known global coupling between the baryonic mass of a galaxy and its rotation velocity (known as the baryonic Tully-Fisher relation), applies at a more local level as well, and it seems to imply a link between the baryonic mass distribution and the distribution of total mass (including dark matter).Comment: 10 pages, accepted for publication in MNRA

Antlia Dwarf Galaxy: Distance, quantitative morphology and recent formation history via statistical field correction

We apply a statistical field correction technique originally designed to determine membership of high redshift galaxy clusters to Hubble Space Telescope imaging of the Antlia Dwarf Galaxy; a galaxy at the very edge of the Local Group. Using the tip of the red giant branch standard candle method coupled with a simple Sobel edge detection filter we find a new distance to Antlia of 1.31 +/- 0.03 Mpc. For the first time for a Local Group Member, we compute the concentration, asymmetry and clumpiness (CAS) quantitative morphology parameters for Antlia from the distribution of resolved stars in the HST/ACS field, corrected with a new method for contaminants and complement these parameters with the Gini coefficient (G) and the second order moment of the brightest 20 per cent of the flux (M_20). We show that it is a classic dwarf elliptical (C = 2.0, A = 0.063, S = 0.077, G = 0.39 and M_20 = -1.17 in the F814W band), but has an appreciable blue stellar population at its core, confirming on-going star-formation. The values of asymmetry and clumpiness, as well as Gini and M_20 are consistent with an undisturbed galaxy. Although our analysis suggests that Antlia may not be tidally influenced by NGC 3109 it does not necessarily preclude such interaction.Comment: Accepted for publication in MNRA

Think Small: Zebrafish as a Model System of Human Pathology

Although human pathologies have mostly been modeled using higher mammal systems such as mice, the lower vertebrate zebrafish has gained tremendous attention as a model system. The advantages of zebrafish over classical vertebrate models are multifactorial and include high genetic and organ system homology to humans, high fecundity, external fertilization, ease of genetic manipulation, and transparency through early adulthood that enables powerful imaging modalities. This paper focuses on four areas of human pathology that were developed and/or advanced significantly in zebrafish in the last decade. These areas are (1) wound healing/restitution, (2) gastrointestinal diseases, (3) microbe-host interactions, and (4) genetic diseases and drug screens. Important biological processes and pathologies explored include wound-healing responses, pancreatic cancer, inflammatory bowel diseases, nonalcoholic fatty liver disease, and mycobacterium infection. The utility of zebrafish in screening for novel genes important in various pathologies such as polycystic kidney disease is also discussed

Mass-to-light ratio gradients in early-type galaxy haloes

Since the near future should see a rapidly expanding set of probes of the halo masses of individual early-type galaxies, we introduce a convenient parameter for characterising the halo masses from both observational and theoretical results: \dML, the logarithmic radial gradient of the mass-to-light ratio. Using halo density profiles from LCDM simulations, we derive predictions for this gradient for various galaxy luminosities and star formation efficiencies $\epsilon_{SF}$. As a pilot study, we assemble the available \dML\ data from kinematics in early-type galaxies - representing the first unbiassed study of halo masses in a wide range of early-type galaxy luminosities - and find a correlation between luminosity and \dML, such that the brightest galaxies appear the most dark-matter dominated. We find that the gradients in most of the brightest galaxies may fit in well with the LCDM predictions, but that there is also a population of fainter galaxies whose gradients are so low as to imply an unreasonably high star formation efficiency $\epsilon_{SF} > 1$. This difficulty is eased if dark haloes are not assumed to have the standard LCDM profiles, but lower central concentrations.Comment: 17 pages, 13 figures. Accepted for publication on MNRA

The ethics of digital well-being: a multidisciplinary perspective

This chapter serves as an introduction to the edited collection of the same name, which includes chapters that explore digital well-being from a range of disciplinary perspectives, including philosophy, psychology, economics, health care, and education. The purpose of this introductory chapter is to provide a short primer on the different disciplinary approaches to the study of well-being. To supplement this primer, we also invited key experts from several disciplines—philosophy, psychology, public policy, and health care—to share their thoughts on what they believe are the most important open questions and ethical issues for the multi-disciplinary study of digital well-being. We also introduce and discuss several themes that we believe will be fundamental to the ongoing study of digital well-being: digital gratitude, automated interventions, and sustainable co-well-being