On Liouville's twelve squares theorem

A simple proof is given of a formula for the number of representations of a positive integer as the sum of twelve squares

Thickness Estimation of Epitaxial Graphene on SiC using Attenuation of Substrate Raman Intensity

A simple, non-invasive method using Raman spectroscopy for the estimation of the thickness of graphene layers grown epitaxially on silicon carbide (SiC) is presented, enabling simultaneous determination of thickness, grain size and disorder using the spectra. The attenuation of the substrate Raman signal due to the graphene overlayer is found to be dependent on the graphene film thickness deduced from X-ray photoelectron spectroscopy and transmission electron microscopy of the surfaces. We explain this dependence using an absorbing overlayer model. This method can be used for mapping graphene thickness over a region and is capable of estimating thickness of multilayer graphene films beyond that possible by XPS and Auger electron spectroscopy (AES).Comment: 14 pages, 9 figure

The Relationship of Suicides, Guns and Mass Shootings in the United States: An Ethical Dilemma

Suicides have been a reality of life due to many factors across nations. In the United States alone, about 30,000 to 40,000 individuals are likely to take their own life this year. During the Covid-19 Corona virus months, telephone calls to the suicide hotlines in the United States have increased significantly. As such, suicide is a huge, complex and costly problem in our society even when people are not dealing with a pandemic like Covid-19 and racial inequalities. In this study, we look at the relationship between suicides, guns and mass shootings based on age, gender and ethnicity, using data of 3,238-recorded suicides in South Florida’s Broward County

Cats, connectivity and conservation: incorporating datasets and integrating scales for wildlife management

Understanding resource selection and quantifying habitat connectivity are fundamental to conservation planning for both land-use and species management plans. However, datasets available to management authorities for resource selection and connectivity analyses are often highly limited and fragmentary. As a result, measuring connectivity is challenging, and often poorly integrated within conservation planning and wildlife management. To exacerbate the challenge, scale-dependent resource use makes inference across scales problematic, resource use is often modelled in areas where the species is not present, and connectivity is typically measured using a source-to-sink approach, erroneously assuming animals possess predefined destinations. Here, we used a large carnivore, the leopard Panthera pardus, to characterise resource use and landscape connectivity across a vast, biodiverse region of southern Africa. Using a range of datasets to counter data deficiencies inherent in carnivore management, we overcame methodological limitations by employing occupancy modelling and resource selection functions across three orders of selection, and estimated landscape-scale habitat connectivity – independent of a priori source and sink locations – using circuit theory. We evaluated whether occupancy modelling on its own was capable of accurately informing habitat connectivity, and identified conservation priorities necessary for applied management. We detected markedly different scale-dependent relationships across all selection orders. Our multi-data, multi-scale approach accurately predicted resource use across multiple scales and demonstrates how management authorities can more suitably utilise fragmentary datasets. We further developed an unbiased landscape-scale depiction of habitat connectivity, and identified key linkages in need of targeted management. We did not find support for the use of occupancy modelling as a proxy for landscape-scale habitat connectivity and further caution its use within a management context. Synthesis and applications. Maintaining habitat connectivity remains a fundamental component of wildlife management and conservation, yet data to inform these biological and ecological processes are often scarce. We present a robust approach that incorporates multi-scale fragmentary datasets (e.g. mortality data, permit data, sightings data), routinely collected by management authorities, to inform wildlife management and land-use planning. We recommend that management authorities employ a multi-data, multi-scale connectivity approach—as we present here—to identify management units at risk of low connectivity

What is the evidence-base for atopic eczema treatments? A summary of published randomised controlled trials

Atopic eczema (AE) is a common chronic inflammatory skin condition. Whilst many AE treatment options are available, the evidence to support their efficacy varies in depth and quality. In 2000, an NIHR HTA systematic review identified and evaluated existing randomised controlled trials (RCTs) of AE treatments. To ensure continuing utility, the NIHR commissioned an update to the review. Here, we present an overview of the updated report and key findings. Systematic reviews and RCTs of AE treatments that included participants with AE (criteria based or diagnosed) were identified using: MEDLINE, EMBASE, CENTRAL, LILACS, AMED, CINAHL and Cochrane Skin Group Specialised Register (searched to August 31st 2013 (RCTs) and 31st December 2015 (systematic reviews)). Outcome measures included: symptoms, AE severity, quality-of-life, and adverse effects. Study quality was assessed using the Cochrane Collaboration risk of bias tool. Of the 287 new RCTs identified, only 22 (8%) were judged to be low risk of bias. When combined with RCTs from the previous review (n= 254), we found ‘reasonable evidence of benefit’ for corticosteroids, calcineurin inhibitors, Atopiclair™, ciclosporin, azathioprine, ultraviolet light and education programmes. Interventions with reasonable evidence of ‘no benefit’ included some dietary interventions, ion exchange water softeners, multiple daily applications of topical corticosteroids and antibiotic-containing corticosteroids for non-infected AE. Many common treatments lack evidence of efficacy and warrant further evaluation. The evidence base for AE is still hampered by poor trial design and reporting. The trials included in this review were used to establish the Global Resource of Eczema Trials (GREAT) Database

Nanolithography and manipulation of graphene using an atomic force microscope

We use an atomic force microscope (AFM) to manipulate graphene films on a nanoscopic length scale. By means of local anodic oxidation with an AFM we are able to structure isolating trenches into single-layer and few-layer graphene flakes, opening the possibility of tabletop graphene based device fabrication. Trench sizes of less than 30 nm in width are attainable with this technique. Besides oxidation we also show the influence of mechanical peeling and scratching with an AFM of few layer graphene sheets placed on different substrates.Comment: 11 pages text, 5 figure

Atom gratings produced by large angle atom beam splitters

An asymptotic theory of atom scattering by large amplitude periodic potentials is developed in the Raman-Nath approximation. The atom grating profile arising after scattering is evaluated in the Fresnel zone for triangular, sinusoidal, magneto-optical, and bichromatic field potentials. It is shown that, owing to the scattering in these potentials, two \QTR{em}{groups} of momentum states are produced rather than two distinct momentum components. The corresponding spatial density profile is calculated and found to differ significantly from a pure sinusoid.Comment: 16 pages, 7 figure

Gravitation and inertia; a rearrangement of vacuum in gravity

We address the gravitation and inertia in the framework of 'general gauge principle', which accounts for 'gravitation gauge group' generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear realization of the Lie group of 'distortion' of local internal properties of six-dimensional flat space, which is assumed as a toy model underlying four-dimensional Minkowski space. The agreement between proposed gravitational theory and available observational verifications is satisfactory. We construct relativistic field theory of inertia and derive the relativistic law of inertia. This theory furnishes justification for introduction of the Principle of Equivalence. We address the rearrangement of vacuum state in gravity resulting from these ideas.Comment: 17 pages, no figures, revtex4, Accepted for publication in Astrophys. Space Sc

Effectiveness and cost-effectiveness of daily all-over-body application of emollient during the first year of life for preventing atopic eczema in high-risk children (The BEEP trial): protocol for a randomised controlled trial.

BACKGROUND: Atopic eczema (AE) is a common skin problem that impairs quality of life and is associated with the development of other atopic diseases including asthma, food allergy and allergic rhinitis. AE treatment is a significant cost burden for health care providers. The purpose of the trial is to investigate whether daily application of emollients for the first year of life can prevent AE developing in high-risk infants (first-degree relative with asthma, AE or allergic rhinitis). METHODS: This is a protocol for a pragmatic, two-arm, randomised controlled, multicentre trial. Up to 1400 term infants at high risk of developing AE will be recruited through the community, primary and secondary care in England. Participating families will be randomised in a 1:1 ratio to receive general infant skin-care advice, or general skin-care advice plus emollients with advice to apply daily to the infant for the first year of life. Families will not be blinded to treatment allocation. The primary outcome will be a blinded assessment of AE at 24 months of age using the UK Working Party Diagnostic Criteria for Atopic Eczema. Secondary outcomes are other definitions of AE, time to AE onset, severity of AE (EASI and POEM), presence of other allergic diseases including food allergy, asthma and hay fever, allergic sensitisation, quality of life, cost-effectiveness and safety of the emollients. Subgroup analyses are planned for the primary outcome according to filaggrin genotype and the number of first-degree relatives with AE and other atopic diseases. Families will be followed up by online and postal questionnaire at 3, 6, 12 and 18 months with a face-to-face visit at 24 months. Long-term follow-up until 60 months will be via annual questionnaires. DISCUSSION: This trial will demonstrate whether skin-barrier enhancement through daily emollient for the first year of life can prevent AE from developing in high-risk infants. If effective, this simple and cheap intervention has the potential to result in significant cost savings for health care providers throughout the world by preventing AE and possibly other associated allergic diseases. TRIAL REGISTRATION: ISRCTN registry; ID: ISRCTN21528841 . Registered on 25 July 2014