Decay estimates for the quadratic tilt-excess of integral varifolds

This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise and almost everywhere decay results for the quadratic tilt-excess are established for those varifolds. The results are optimal in terms of the dimension of the varifold and the exponent of the Lebesgue space in most cases, for example if the varifold is not two-dimensional

Weakly differentiable functions on varifolds

The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts identities for certain compositions with smooth functions. In this class the idea of zero boundary values is realised using the relative perimeter of superlevel sets. Results include a variety of Sobolev Poincar\'e type embeddings, embeddings into spaces of continuous and sometimes H\"older continuous functions, pointwise differentiability results both of approximate and integral type as well as coarea formulae. As prerequisite for this study decomposition properties of such varifolds and a relative isoperimetric inequality are established. Both involve a concept of distributional boundary of a set introduced for this purpose. As applications the finiteness of the geodesic distance associated to varifolds with suitable summability of the mean curvature and a characterisation of curvature varifolds are obtained

A Sobolev Poincar\'e type inequality for integral varifolds

In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.Comment: v1: 27 pages, no figures; v2: replaced citations of the author's dissertation by proofs, material of sections 1 and 3 reorganised, slightly more general results in section 2, some remarks, some discussion and some references added, 40 pages, no figure

Podocytic PKC-Alpha Is Regulated in Murine and Human Diabetes and Mediates Nephrin Endocytosis

Background: Microalbuminuria is an early lesion during the development of diabetic nephropathy. The loss of high molecular weight proteins in the urine is usually associated with decreased expression of slit diaphragm proteins. Nephrin, is the major component of the glomerular slit diaphragm and loss of nephrin has been well described in rodent models of experimental diabetes as well as in human diabetic nephropathy. Methodology/Principal Findings: In this manuscript we analyzed the role of PKC-alpha (PKCa) on endocytosis of nephrin in podocytes. We found that treatment of diabetic mice with a PKCa-inhibitor (GÖ6976) leads to preserved nephrin expression and reduced proteinuria. In vitro, we found that high glucose stimulation would induce PKCa protein expression in murine and human podocytes. We can demonstrate that PKCa mediates nephrin endocytosis in podocytes and that overexpression of PKCa leads to an augmented endocytosis response. After PKC-activation, we demonstrate an inducible association of PKCa, PICK1 and nephrin in podocytes. Moreover, we can demonstrate a strong induction of PKCa in podocytes of patients with diabetic nephropathy. Conclusions/Significance: We therefore conclude that activation of PKCa is a pathomechanistic key event during the development of diabetic nephropathy. PKCa is involved in reduction of nephrin surface expression and therefore PKC

The gender perspective in climate change and global health

Background: Population health is a primary goal of sustainable development. United Nations international conferences like the Beijing Platform for Action have highlighted the key role of women in ensuring sustainable development. In the context of climate change, women are affected the most while they display knowledge and skills to orient themselves toward climate adaptation activities within their societies. Objective: To investigate how the gender perspective is addressed as an issue in research and policy-making concerning climate change and global health. Methods: A broad literature search was undertaken using the databases Pubmed and Web of Science to explore the terms ‘climate change,’ ‘health,’ ‘gender,’ and ‘policy.’ Climate change and health-related policy documents of the World Health Organization (WHO) and National Communications and National Adaptation Programs of Action reports submitted to the United Nations Framework Convention on Climate Change of selected countries were studied. Assessment guidelines to review these reports were developed from this study's viewpoint. Results: The database search results showed almost no articles when the four terms were searched together. The WHO documents lacked a gender perspective in their approach and future recommendations on climate policies. The reviewed UN reports were also neutral to gender perspective except one of the studied documents. Conclusion: Despite recognizing the differential effects of climate change on health of women and men as a consequence of complex social contexts and adaptive capacities, the study finds gender to be an underrepresented or non-existing variable both in research and studied policy documents in the field of climate change and health

Planar cyclotron motion in unidirectional superlattices defined by strong magnetic and electric fields: Traces of classical orbits in the energy spectrum

We compare the quantum and the classical description of the two-dimensional motion of electrons subjected to a perpendicular magnetic field and a one-dimensional lateral superlattice defined by spatially periodic magnetic and electric fields of large amplitudes. We explain in detail the complicated energy spectra, consisting of superimposed branches of strong and of weak dispersion, by the correspondence between the respective eigenstates and the ``channeled'' and ``drifting'' orbits of the classical description.Comment: 11 pages, 11 figures, to appear in Physical Review

Social sciences research in neglected tropical diseases 2: A bibliographic analysis

The official published version of the article can be found at the link below.Background There are strong arguments for social science and interdisciplinary research in the neglected tropical diseases. These diseases represent a rich and dynamic interplay between vector, host, and pathogen which occurs within social, physical and biological contexts. The overwhelming sense, however, is that neglected tropical diseases research is a biomedical endeavour largely excluding the social sciences. The purpose of this review is to provide a baseline for discussing the quantum and nature of the science that is being conducted, and the extent to which the social sciences are a part of that. Methods A bibliographic analysis was conducted of neglected tropical diseases related research papers published over the past 10 years in biomedical and social sciences. The analysis had textual and bibliometric facets, and focussed on chikungunya, dengue, visceral leishmaniasis, and onchocerciasis. Results There is substantial variation in the number of publications associated with each disease. The proportion of the research that is social science based appears remarkably consistent (<4%). A textual analysis, however, reveals a degree of misclassification by the abstracting service where a surprising proportion of the "social sciences" research was pure clinical research. Much of the social sciences research also tends to be "hand maiden" research focused on the implementation of biomedical solutions. Conclusion There is little evidence that scientists pay any attention to the complex social, cultural, biological, and environmental dynamic involved in human pathogenesis. There is little investigator driven social science and a poor presence of interdisciplinary science. The research needs more sophisticated funders and priority setters who are not beguiled by uncritical biomedical promises

Existence of Integral mm-Varifolds minimizing ∫∣A∣p\int |A|^p and ∫∣H∣p\int |H|^p, p>mp>m, in Riemannian Manifolds

We prove existence and partial regularity of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2\leq mm$, under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in $\mathbb{R}^S$ involving $\int |H|^p$, to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.Comment: 33 pages; this second submission corresponds to the published version of the paper, minor typos are fixe