Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.

Dynamics of Shifting Cultivation Landscapes in Northern Lao PDR Between 2000 and 2009 Based on an Analysis of MODIS Time Series and Landsat Images

The rotational nature of shifting cultivation poses several challenges to its detection by remote sensing. Consequently, there is a lack of spatial data on the dynamics of shifting cultivation landscapes on a regional, i.e. sub-national, or national level. We present an approach based on a time series of Landsat and MODIS data and landscape metrics to delineate the dynamics of shifting cultivation landscapes. Our results reveal that shifting cultivation is a land use system still widely and dynamically utilized in northern Laos. While there is an overall reduction in the areas dominated by shifting cultivation, some regions also show an expansion. A review of relevant reports and articles indicates that policies tend to lead to a reduction while market forces can result in both expansion and reduction. For a better understanding of the different factors affecting shifting cultivation landscapes in Laos, further research should focus on spatially explicit analyses.

Radiocarbon impact in a nearby tree of a light-water VVER type nuclear power plant, Paks, Hungary

Tree-ring series were collected for radiocarbon analyses from the vicinity of Paks nuclear power plant (NPP) and a background area (Dunaföldvár) for a 10-yr period (2000–2009). Samples of holocellulose were prepared from the wood and converted to graphite for accelerator mass spectrometry (AMS) 14C measurement using the MICADAS at ETH Zürich. The 14C concentration data from these tree rings was compared to the background tree rings for each year. The global decreasing trend of atmospheric 14C activity concentration was observed in the annual tree rings both in the background area and in the area of the NPP. As an average of the past 10 yr, the excess 14C emitted by the pressurized-water reactor (PWR) NPP to the atmosphere shows only a slight systematic excess (~6‰) 14C in the annual rings. The highest 14C excess was 13‰ (in 2006); however, years with the same 14C level as the background were quite frequent in the tree-ring series.

Detecting determinism with improved sensitivity in time series: Rank-based nonlinear predictability score

The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).

Renal microvascular assembly and repair: power and promise of molecular definition.

Developmental assembly of the renal microcirculation is a precise and coordinated process now accessible to experimental scrutiny. Although definition of the cellular and molecular determinants is incomplete, recent findings have reframed concepts and questions about the origins of vascular cells in the glomerulus and the molecules that direct cell recruitment, specialization and morphogenesis. New findings illustrate principles that may be applied to defining critical steps in microvascular repair following glomerular injury. Developmental assembly of endothelial, mesangial and epithelial cells into glomerular capillaries requires that a coordinated, temporally defined series of steps occur in an anatomically ordered sequence. Recent evidence shows that both vasculogenic and angiogenic processes participate. Local signals direct cell migration, proliferation, differentiation, cell-cell recognition, formation of intercellular connections, and morphogenesis. Growth factor receptor tyrosine kinases on vascular cells are important mediators of many of these events. Cultured cell systems have suggested that basic fibroblast growth factor (bFGF), hepatocyte growth factor (HGF), and vascular endothelial growth factor (VEGF) promote endothelial cell proliferation, migration or morphogenesis, while genetic deletion experiments have defined an important role for PDGF beta receptors and platelet-derived growth factor (PDGF) B in glomerular development. Receptor tyrosine kinases that convey non-proliferative signals also contribute in kidney and other sites. The EphB1 receptor, one of a diverse class of Eph receptors implicated in neural cell targeting, directs renal endothelial migration, cell-cell recognition and assembly, and is expressed with its ligand in developing glomeruli. Endothelial TIE2 receptors bind angiopoietins (1 and 2), the products of adjacent supportive cells, to signals direct capillary maturation in a sequence that defines cooperative roles for cells of different lineages. Ultimately, definition of the cellular steps and molecular sequence that direct microvascular cell assembly promises to identify therapeutic targets for repair and adaptive remodeling of injured glomeruli.