A note on boundedness of operators in Grand Grand Morrey spaces

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder\'on-Zygmund operators in the framework of grand grand Morrey spaces.Comment: 8 page

Two-loop Yang-Mills diagrams from superstring amplitudes

Starting from the superstring amplitude describing interactions among D-branes with a constant world-volume field strength, we present a detailed analysis of how the open string degeneration limits reproduce the corresponding field theory Feynman diagrams. A key ingredient in the string construction is represented by the twisted (Prym) super differentials, as their periods encode the information about the background field. We provide an efficient method to calculate perturbatively the determinant of the twisted period matrix in terms of sets of super-moduli appropriate to the degeneration limits. Using this result we show that there is a precise one-to-one correspondence between the degeneration of different factors in the superstring amplitudes and one-particle irreducible Feynman diagrams capturing the gauge theory effective action at the two-loop level.Comment: 42 pages plus appendices, 10 figure

Discrete gradient methods for solving variational image regularisation models

Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting

Vitamin A, carotenoid and vitamin E plasma concentrations in children from Laos in relation to sex and growth failure

BACKGROUND: Deficiencies of vitamin A and its precursors, the carotenoids are common problems in developing countries. Plasma levels of these components are used as biomarkers of their availability. The study was conducted to evaluate whether blood plasma obtained from capillaries can be compared with plasma obtained from venous blood with regard to its levels of retinol, carotenoids and α-tocopherol and secondly to apply this technique to evaluate the levels of these components in children in a region with possible deficiencies. METHODS: The survey was conducted in a region of Laos in 81 children (age 35 to 59 months). Dietary intake was assessed by a questionnaire. Retinol, carotenoids and α-tocopherol were determined by HPLC. Blood plasma was obtained either from capillary blood collected into microcapillaries and for reasons of methodological comparison in 14 adults from venous blood. RESULTS: The comparison between capillary and venous blood revealed that all components except zeaxanthin were 9 – 23 % higher in plasma obtained from capillary blood. Results in Laotian children showed that all investigated components except retinol were significantly lower (P < 0.01) compared to European children of slightly older age. Contrary to children in Europe, most components were significantly lower in boys compared to girls. In children from Laos, lutein was the dominant carotenoid, while in children in Europe, β-carotene was dominant. Within the Laotian children only a few differences were observed between stunted and non-stunted children and between children from lowland areas and high land areas. CONCLUSIONS: Results show that in consideration of slightly lower levels than in venous blood, capillary blood can be used to evaluate retinol, carotenoids and α-tocopherol as biomarkers of intake or status and to evaluate the possible effect of diet on absolute and relative carotenoid composition in children from Europe and Laos. Observed sex related differences might not be related to diet and would need further investigation

Misconceptions about Aerobic and Anaerobic Energy Expenditure

The measurement of gas exchange has played an invaluable role in metabolic interpretation. The uptake of 1 liter of oxygen is often converted into an energy expenditure estimate of 21.1 kilojoules (e.g., 1 L O2 = 21.1 kJ or ~5 kcal). This article demonstrates both the importance of such a conversion and the potential for misinterpretation. Oxygen uptake during heavy and severe exercise will also be discussed

Rare coding SNP in DZIP1 gene associated with late-onset sporadic Parkinson's disease

We present the first application of the hypothesis-rich mathematical theory to genome-wide association data. The Hamza et al. late-onset sporadic Parkinson's disease genome-wide association study dataset was analyzed. We found a rare, coding, non-synonymous SNP variant in the gene DZIP1 that confers increased susceptibility to Parkinson's disease. The association of DZIP1 with Parkinson's disease is consistent with a Parkinson's disease stem-cell ageing theory.Comment: 14 page

Quantifying the Detrimental Impacts of Land-Use and Management Change on European Forest Bird Populations

The ecological impacts of changing forest management practices in Europe are poorly understood despite European forests being highly managed. Furthermore, the effects of potential drivers of forest biodiversity decline are rarely considered in concert, thus limiting effective conservation or sustainable forest management. We present a trait-based framework that we use to assess the detrimental impact of multiple land-use and management changes in forests on bird populations across Europe. Major changes to forest habitats occurring in recent decades, and their impact on resource availability for birds were identified. Risk associated with these changes for 52 species of forest birds, defined as the proportion of each species' key resources detrimentally affected through changes in abundance and/or availability, was quantified and compared to their pan-European population growth rates between 1980 and 2009. Relationships between risk and population growth were found to be significantly negative, indicating that resource loss in European forests is an important driver of decline for both resident and migrant birds. Our results demonstrate that coarse quantification of resource use and ecological change can be valuable in understanding causes of biodiversity decline, and thus in informing conservation strategy and policy. Such an approach has good potential to be extended for predictive use in assessing the impact of possible future changes to forest management and to develop more precise indicators of forest health

A role for core planar polarity proteins in cell contact-mediated orientation of planar cell division across the mammalian embryonic skin

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. © The Author(s) 2017. Supplementary information accompanies this paper at doi:10.1038/s41598-017-01971-2.The question of how cell division orientation is determined is fundamentally important for understanding tissue and organ shape in both healthy or disease conditions. Here we provide evidence for cell contact-dependent orientation of planar cell division in the mammalian embryonic skin. We propose a model where the core planar polarity proteins Celsr1 and Frizzled-6 (Fz6) communicate the long axis orientation of interphase basal cells to neighbouring basal mitoses so that they align their horizontal division plane along the same axis. The underlying mechanism requires a direct, cell surface, planar polarised cue, which we posit depends upon variant post-translational forms of Celsr1 protein coupled to Fz6. Our hypothesis has parallels with contact-mediated division orientation in early C. elegans embryos suggesting functional conservation between the adhesion-GPCRs Celsr1 and Latrophilin-1. We propose that linking planar cell division plane with interphase neighbour long axis geometry reinforces axial bias in skin spreading around the mouse embryo body.Peer reviewe