Rigorous Numerical Verification of Uniqueness and Smoothness in a Surface Growth Model

Based on numerical data and a-posteriori analysis we verify rigorously the uniqueness and smoothness of global solutions to a scalar surface growth model with striking similarities to the 3D Navier--Stokes equations, for certain initial data for which analytical approaches fail. The key point is the derivation of a scalar ODE controlling the norm of the solution, whose coefficients depend on the numerical data. Instead of solving this ODE explicitly, we explore three different numerical methods that provide rigorous upper bounds for its solutio

Observations of the Geometry of Horizon-Based Optical Navigation

NASA's Orion Project has sparked a renewed interest in horizon-based optical navigation(OPNAV) techniques for spacecraft in the Earth-Moon system. Some approaches have begun to explore the geometry of horizon-based OPNAV and exploit the fact that it is a conic section problem. Therefore, the present paper focuses more deeply on understanding and leveraging the various geometric interpretations of horizon-based OPNAV. These results provide valuable insight into the fundamental workings of OPNAV solution methods, their convergence properties, and associated estimate covariance. Most importantly, the geometry and transformations uncovered in this paper lead to a simple and non-iterative solution to the generic horizon-based OPNAV problem. This represents a significant theoretical advancement over existing methods. Thus, we find that a clear understanding of geometric relationships is central to the prudent design, use, and operation of horizon-based OPNAV techniques

Comparing predictive accuracy under long memory: With an application to volatility forecasting

This paper extends the popular Diebold-Mariano test to situations when the forecast error loss differential exhibits long memory. It is shown that this situation can arise frequently, since long memory can be transmitted from forecasts and the forecast objective to forecast error loss differentials. The nature of this transmission mainly depends on the (un)biasedness of the forecasts and whether the involved series share common long memory. Further results show that the conventional Diebold-Mariano test is invalidated under these circumstances. Robust statistics based on a memory and autocorrelation consistent estimator and an extended fixed-bandwidth approach are considered. The subsequent Monte Carlo study provides a novel comparison of these robust statistics. As an empirical application, we conduct forecast comparison tests for the realized volatility of the Standard and Poors 500 index among recent extensions of the heterogeneous autoregressive model. While we find that forecasts improve significantly if jumps in the log-price process are considered separately from continuous components, improvements achieved by the inclusion of implied volatility turn out to be insignificant

Random fluctuation leads to forbidden escape of particles

A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser (KAM) islands escape within finite time. The non-hyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperbolic-like time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate this phenomena with a numerical study applying random maps.Comment: 6 pages, 6 figures - Up to date with corrections suggested by referee

HLA gene expression is altered in whole blood and placenta from women who later developed preeclampsia

Preeclampsia is a multi-system disease that significantly contributes to maternal and fetal morbidity and mortality. In this study, we used a non-biased microarray approach to identify dysregulated genes in maternal whole blood samples which may be associated with the development of preeclampsia. Whole blood samples were obtained at 28 weeks of gestation from 5 women who later developed preeclampsia (cases) and 10 matched women with normotensive pregnancies (controls). Placenta samples were obtained from an independent cohort of 19 women with preeclampsia matched with 19 women with normotensive pregnancies. We studied gene expression profiles using Illumina microarray in blood and validated changes in gene expression in whole blood and placenta tissue by qPCR. We found a transcriptional profile differentiating cases from controls; 236 genes were significantly dysregulated in blood from women who developed preeclampsia. Functional annotation of microarray results indicated that most of the genes found to be dysregulated were involved in inflammatory pathways. Whilst general trends were preserved, only HLA-A was validated in whole blood samples from cases using qPCR (2.30 ± 0.9 fold change) whereas in placental tissue HLA-DRB1 expression was found to be significantly increased in samples from women with preeclampsia (5.88 ± 2.24 fold change). We have identified that HLA-A is up-regulated in the circulation of women who went on to develop preeclampsia. In placenta of women with preeclampsia we identified that HLA-DRB1 is up-regulated. Our data provide further evidence for involvement of the HLA gene family in the pathogenesis of preeclampsia

Longitudinal effects of experimental floods on stream benthos downstream from a large dam

We examined the longitudinal effects of 3 experimental floods on seston, periphyton, and macroinvertebrates in a regulated river downstream from a large reservoir in the Swiss Alps. In addition, suspended organic sediments, in conjunction with conductivity and turbidity, were measured during each flood. Three study reaches were selected downstream from the reservoir: an Upper site ca 150 m, a Middle site at 1.2 km, and a Lower site at 2.3 km from the dam. The Upper site was located upstream of any significant source of sediments. No flood effect was observed on water temperature, although river temperatures and diel amplitudes increased progressively downstream from the dam. Most organic sediments were mobilized and transported within the first few hours of each flood, with the pulse in sediments typically occuring later (after peak discharge) and being more prolonged at the Lower site. Turbidity generally decreased during the flood season, perhaps in response to lower amounts of fines and reductions in periphyton biomass. Seston concentrations (as chlorophyll a and AFDM) were lowest at the Upper site, and typically decreased following each flood. The flood response in seston was lowest at the Upper site and more pronounced at the Middle and Lower sites. Periphyton biomass also was lowest at the Upper site, and the flood effects were significant only in the Middle and Lower sites. In contrast, macroinvertebrate densities were similar between the Upper and Lower sites, and both sites exhibited a similar response to the floods. These results indicate a longitudinal response of river benthos to flooding below the reservoir that partly reflects the examined benthic constituent (periphyton or zoobenthos) and the longitudinal differences in the degree and type (e.g., flow in combination with sediment mobility and scouring) of disturbanc

Space and Ground Based Pulsation Data of Eta Bootis Explained with Stellar Models Including Turbulence

The space telescope MOST is now providing us with extremely accurate low frequency p-mode oscillation data for the star Eta Boo. We demonstrate in this paper that these data, when combined with ground based measurements of the high frequency p-mode spectrum, can be reproduced with stellar models that include the effects of turbulence in their outer layers. Without turbulence, the l=0 modes of our models deviate from either the ground based or the space data by about 1.5-4.0 micro Hz. This discrepancy can be completely removed by including turbulence in the models and we can exactly match 12 out of 13 MOST frequencies that we identified as l=0 modes in addition to 13 out of 21 ground based frequencies within their observational 2 sigma tolerances. The better agreement between model frequencies and observed ones depends for the most part on the turbulent kinetic energy which was taken from a 3D convection simulation for the Sun.Comment: 13 pages, 7 figures, ApJ in pres

Differential expression of microRNA-206 and its target genes in pre-eclampsia

Objectives: Pre-eclampsia is a multi-system disease that significantly contributes to maternal and fetal morbidity and mortality. In this study, we used a non-biased microarray approach to identify novel circulating miRNAs in maternal plasma that may be associated with pre-eclampsia. Methods: Plasma samples were obtained at 16 and 28 weeks of gestation from 18 women who later developed pre-eclampsia (cases) and 18 matched women with normotensive pregnancies (controls). We studied miRNA expression profiles in plasma and subsequently confirmed miRNA and target gene expression in placenta samples. Placental samples were obtained from an independent cohort of 19 women with pre-eclampsia matched with 19 women with normotensive pregnancies. Results: From the microarray, we identified 1 miRNA that was significantly differentially expressed between cases and controls at 16 weeks of gestation and 6 miRNAs that were significantly differentially expressed at 28 weeks. Following qPCR validation only one, miR-206, was found to be significantly increased in 28 week samples in women who later developed pre-eclampsia (1.4 fold change ± 0.2). The trend for increase in miR-206 expression was mirrored within placental tissue from women with pre-eclampsia. In parallel, IGF-1, a target gene of miR-206, was also found to be down-regulated (0.41 ± 0.04) in placental tissue from women with pre-eclampsia. miR-206 expression was also detectable in myometrium tissue and trophoblast cell lines. Conclusions: Our pilot study has identified miRNA-206 as a novel factor up-regulated in pre-eclampsia within the maternal circulation and in placental tissue