A weighted reduced basis method for parabolic PDEs with random data

This work considers a weighted POD-greedy method to estimate statistical outputs parabolic PDE problems with parametrized random data. The key idea of weighted reduced basis methods is to weight the parameter-dependent error estimate according to a probability measure in the set-up of the reduced space. The error of stochastic finite element solutions is usually measured in a root mean square sense regarding their dependence on the stochastic input parameters. An orthogonal projection of a snapshot set onto a corresponding POD basis defines an optimum reduced approximation in terms of a Monte Carlo discretization of the root mean square error. The errors of a weighted POD-greedy Galerkin solution are compared against an orthogonal projection of the underlying snapshots onto a POD basis for a numerical example involving thermal conduction. In particular, it is assessed whether a weighted POD-greedy solutions is able to come significantly closer to the optimum than a non-weighted equivalent. Additionally, the performance of a weighted POD-greedy Galerkin solution is considered with respect to the mean absolute error of an adjoint-corrected functional of the reduced solution.Comment: 15 pages, 4 figure

Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints

Finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems

Increased HIV Incidence in Men Who Have Sex with Men Despite High Levels of ART-Induced Viral Suppression: Analysis of an Extensively Documented Epidemic

Background: There is interest in expanding ART to prevent HIV transmission, but in the group with the highest levels of ART use, men-who-have-sex-with-men (MSM), numbers of new infections diagnosed each year have not decreased as ART coverage has increased for reasons which remain unclear. Methods: We analysed data on the HIV-epidemic in MSM in the UK from a range of sources using an individual-based simulation model. Model runs using parameter sets found to result in good model fit were used to infer changes in HIV-incidence and risk behaviour. Results: HIV-incidence has increased (estimated mean incidence 0.30/100 person-years 1990–1997, 0.45/100 py 1998–2010), associated with a modest (26%) rise in condomless sex. We also explored counter-factual scenarios: had ART not been introduced, but the rise in condomless sex had still occurred, then incidence 2006–2010 was 68% higher; a policy of ART initiation in all diagnosed with HIV from 2001 resulted in 32% lower incidence; had levels of HIV testing been higher (68% tested/year instead of 25%) incidence was 25% lower; a combination of higher testing and ART at diagnosis resulted in 62% lower incidence; cessation of all condom use in 2000 resulted in a 424% increase in incidence. In 2010, we estimate that undiagnosed men, the majority in primary infection, accounted for 82% of new infections. Conclusion: A rise in HIV-incidence has occurred in MSM in the UK despite an only modest increase in levels of condomless sex and high coverage of ART. ART has almost certainly exerted a limiting effect on incidence. Much higher rates of HIV testing combined with initiation of ART at diagnosis would be likely to lead to substantial reductions in HIV incidence. Increased condom use should be promoted to avoid the erosion of the benefits of ART and to prevent other serious sexually transmitted infections

Capturing the Surface Texture and Shape of Pollen: A Comparison of Microscopy Techniques

Research on the comparative morphology of pollen grains depends crucially on the application of appropriate microscopy techniques. Information on the performance of microscopy techniques can be used to inform that choice. We compared the ability of several microscopy techniques to provide information on the shape and surface texture of three pollen types with differing morphologies. These techniques are: widefield, apotome, confocal and two-photon microscopy (reflected light techniques), and brightfield and differential interference contrast microscopy (DIC) (transmitted light techniques). We also provide a first view of pollen using super-resolution microscopy. The three pollen types used to contrast the performance of each technique are: Croton hirtus (Euphorbiaceae), Mabea occidentalis (Euphorbiaceae) and Agropyron repens (Poaceae). No single microscopy technique provided an adequate picture of both the shape and surface texture of any of the three pollen types investigated here. The wavelength of incident light, photon-collection ability of the optical technique, signal-to-noise ratio, and the thickness and light absorption characteristics of the exine profoundly affect the recovery of morphological information by a given optical microscopy technique. Reflected light techniques, particularly confocal and two-photon microscopy, best capture pollen shape but provide limited information on very fine surface texture. In contrast, transmitted light techniques, particularly differential interference contrast microscopy, can resolve very fine surface texture but provide limited information on shape. Texture comprising sculptural elements that are spaced near the diffraction limit of light (∼250 nm; NDL) presents an acute challenge to optical microscopy. Super-resolution structured illumination microscopy provides data on the NDL texture of A. repens that is more comparable to textural data from scanning electron microscopy than any other optical microscopy technique investigated here. Maximizing the recovery of morphological information from pollen grains should lead to more robust classifications, and an increase in the taxonomic precision with which ancient vegetation can be reconstructed

Treatment of stage I seminoma: is it time to change your practice?

At the plenary session of the 2008 annual meeting of the American Society of Clinical Oncology, updated results were presented from a large randomized phase III trial comparing adjuvant radiation therapy (RT) and one cycle of Carboplatin for the adjuvant treatment of Stage I seminoma. Results of this Medical Research Council (MRC) trial led its investigators to conclude that one cycle of carboplatin was equivalent in safety and efficacy and less toxic than RT. In this editorial, the trial's design, statistics, toxicity, and length of follow-up are discussed within the context of historical treatments of this disease. With a 1.3% increase in relapse rate (5.3% with carboplatin vs. 4.0% with radiation), a 3% or greater increase in relapse rate could not be excluded, the primary endpoint of the study. A decrease in second testicular germ cell tumors was observed, but was equivalent to the increase in relapse rate. Acute toxicity was generally less with carboplatin. However, the extent of late toxicity, including late second neoplasms, cannot be evaluated because of the short median follow-up. Carboplatin is not yet a standard of care. Surveillance-based strategies, including risk-adapted policies that limit RT to patients with the greatest likelihood of relapse remain prudent at this time

Analysis of the Human Kinome Using Methods Including Fold Recognition Reveals Two Novel Kinases

Background: Protein sequence similarity is a commonly used criterion for inferring the unknown function of a protein from a protein of known function. However, proteins can diverge significantly over time such that sequence similarity is difficult, if not impossible, to find. In some cases, a structural similarity remains over long evolutionary time scales and once detected can be used to predict function. Methodology/Principal Findings: Here we employed a high-throughput approach to assign structural and functional annotation to the human proteome, focusing on the collection of human protein kinases, the human kinome. We compared human protein sequences to a library of domains from known structures using WU-BLAST, PSI-BLAST, and 123D. This approach utilized both sequence comparison and fold recognition methods. The resulting set of potential protein kinases was cross-checked against previously identified human protein kinases, and analyzed for conserved kinase motifs. Conclusions/Significance: We demonstrate that our structure-based method can be used to identify both typical and atypical human protein kinases. We also identify two potentially novel kinases that contain an interesting combination o

NeuralHydrology -- Interpreting LSTMs in Hydrology

Despite the huge success of Long Short-Term Memory networks, their applications in environmental sciences are scarce. We argue that one reason is the difficulty to interpret the internals of trained networks. In this study, we look at the application of LSTMs for rainfall-runoff forecasting, one of the central tasks in the field of hydrology, in which the river discharge has to be predicted from meteorological observations. LSTMs are particularly well-suited for this problem since memory cells can represent dynamic reservoirs and storages, which are essential components in state-space modelling approaches of the hydrological system. On basis of two different catchments, one with snow influence and one without, we demonstrate how the trained model can be analyzed and interpreted. In the process, we show that the network internally learns to represent patterns that are consistent with our qualitative understanding of the hydrological system.Comment: Pre-print of published book chapter. See journal reference and DOI for more inf