On-line Gaussian mixture density estimator for adaptive minimum bit-error-rate beamforming receivers

We develop an on-line Gaussian mixture density estimator (OGMDE) in the complex-valued domain to facilitate adaptive minimum bit-error-rate (MBER) beamforming receiver for multiple antenna based space-division multiple access systems. Specifically, the novel OGMDE is proposed to adaptively model the probability density function of the beamformer’s output by tracking the incoming data sample by sample. With the aid of the proposed OGMDE, our adaptive beamformer is capable of updating the beamformer’s weights sample by sample to directly minimize the achievable bit error rate (BER). We show that this OGMDE based MBER beamformer outperforms the existing on-line MBER beamformer, known as the least BER beamformer, in terms of both the convergence speed and the achievable BER.

Two fast radiative transfer methods to improve the temporal sampling of clouds in numerical weather prediction and climate models

The high computational cost of calculating the radiative heating rates in numerical weather prediction (NWP) and climate models requires that calculations are made infrequently, leading to poor sampling of the fast-changing cloud field and a poor representation of the feedback that would occur. This paper presents two related schemes for improving the temporal sampling of the cloud field. Firstly, the ‘split time-stepping’ scheme takes advantage of the independent nature of the monochromatic calculations of the ‘correlated-k’ method to split the calculation into gaseous absorption terms that are highly dependent on changes in cloud (the optically thin terms) and those that are not (optically thick). The small number of optically thin terms can then be calculated more often to capture changes in the grey absorption and scattering associated with cloud droplets and ice crystals. Secondly, the ‘incremental time-stepping’ scheme uses a simple radiative transfer calculation using only one or two monochromatic calculations representing the optically thin part of the atmospheric spectrum. These are found to be sufficient to represent the heating rate increments caused by changes in the cloud field, which can then be added to the last full calculation of the radiation code. We test these schemes in an operational forecast model configuration and find a significant improvement is achieved, for a small computational cost, over the current scheme employed at the Met Office. The ‘incremental time-stepping’ scheme is recommended for operational use, along with a new scheme to correct the surface fluxes for the change in solar zenith angle between radiation calculations.

Using high-frequency water quality data to assess sampling strategies for the EU Water Framework Directive

The EU Water Framework Directive (WFD) requires that the ecological and chemical status of water bodies in Europe should be assessed, and action taken where possible to ensure that at least "good" quality is attained in each case by 2015. This paper is concerned with the accuracy and precision with which chemical status in rivers can be measured given certain sampling strategies, and how this can be improved. High-frequency (hourly) chemical data from four rivers in southern England were subsampled to simulate different sampling strategies for four parameters used for WFD classification: dissolved phosphorus, dissolved oxygen, pH and water temperature. These data sub-sets were then used to calculate the WFD classification for each site. Monthly sampling was less precise than weekly sampling, but the effect on WFD classification depended on the closeness of the range of concentrations to the class boundaries. In some cases, monthly sampling for a year could result in the same water body being assigned to three or four of the WFD classes with 95% confidence, due to random sampling effects, whereas with weekly sampling this was one or two classes for the same cases. In the most extreme case, the same water body could have been assigned to any of the five WFD quality classes. Weekly sampling considerably reduces the uncertainties compared to monthly sampling. The width of the weekly sampled confidence intervals was about 33% that of the monthly for P species and pH, about 50% for dissolved oxygen, and about 67% for water temperature. For water temperature, which is assessed as the 98th percentile in the UK, monthly sampling biases the mean downwards by about 1 °C compared to the true value, due to problems of assessing high percentiles with limited data. Low-frequency measurements will generally be unsuitable for assessing standards expressed as high percentiles. Confining sampling to the working week compared to all 7 days made little difference, but a modest improvement in precision could be obtained by sampling at the same time of day within a 3 h time window, and this is recommended. For parameters with a strong diel variation, such as dissolved oxygen, the value obtained, and thus possibly the WFD classification, can depend markedly on when in the cycle the sample was taken. Specifying this in the sampling regime would be a straightforward way to improve precision, but there needs to be agreement about how best to characterise risk in different types of river. These results suggest that in some cases it will be difficult to assign accurate WFD chemical classes or to detect likely trends using current sampling regimes, even for these largely groundwater-fed rivers. A more critical approach to sampling is needed to ensure that management actions are appropriate and supported by data.

Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective

We study discontinuous Galerkin approximations of the p-biharmonic equation for p∈(1,∞) from a variational perspective. We propose a discrete variational formulation of the problem based on an appropriate definition of a finite element Hessian and study convergence of the method (without rates) using a semicontinuity argument. We also present numerical experiments aimed at testing the robustness of the method.

A moment problem for random discrete measures

Let X be a locally compact Polish space. A random measure on X is a probability measure on the space of all (nonnegative) Radon measures on X. Denote by K(X) the cone of all Radon measures η on X which are of the form η =

Molecular design of a discrete chain-folding polyimide for controlled inkjet deposition of supramolecular polymers

A supramolecular polymer based upon two complementary polymer components is formed by sequential deposition from solution in THF, using a piezoelectric drop-on-demand inkjet printer. Highly efficient cycloaddition or ‘click’ chemistry afforded a well-defined poly(ethylene glycol) featuring chain-folding diimide end groups, which possesses greatly enhanced solubility in THF relative to earlier materials featuring random diimide sequences. Blending the new polyimide with a complementary poly(ethylene glycol) system bearing pyrene end groups (which bind to the chain-folding diimide units) overcomes the limited solubility encountered previously with chain-folding polyimides in inkjet printing applications. The solution state properties of the resulting polymer blend were assessed via viscometry to confirm the presence of a supramolecular polymer before depositing the two electronically complementary polymers by inkjet printing techniques. The novel materials so produced offer an insight into ways of controlling the properties of printed materials through tuning the structure of the polymer at the (supra)molecular level.

Sampling and analyzing metals in soils for archaeological prospection: a critique

This paper presents a critique of current methods of sampling and analyzing soils for metals in archaeological prospection. Commonly used methodologies in soil science are shown to be suitable for archaeological investigations, with a concomitant improvement in their resolution. Understanding the soil-fraction location, concentration range, and spatial distribution of autochthonous (native) soil metals is shown to be a vital precursor to archaeological-site investigations, as this is the background upon which anthropogenic deposition takes place. Nested sampling is suggested as the most cost-effective method of investigating the spatial variability in the autochthonous metal concentrations. The use of the appropriate soil horizon (or sampling depth) and point sampling are critical in the preparation of a sampling regime. Simultaneous extraction is proposed as the most efficient method of identifying the location and eventual fate of autochthonous and anthropogenic metals, respectively.

Ectomycorrhizal symbiosis can enhance plant nutrition through improved access to discrete organic nutrient patches of high resource quality

It is known that roots can respond to patches of fertility; however, root proliferation is often too slow to exploit resources fully, and organic nutrient patches may be broken down and leached, immobilized or chemically fixed before they are invaded by the root system. The ability of fungal hyphae to exploit resource patches is far greater than that of roots due to their innate physiological and morphological plasticity, which allows comprehensive exploration and rapid colonization of resource patches in soils. The fungal symbionts of ectomycorrhizal plants excrete significant quantities of enzymes such as chitinases, phosphatases and proteases. These might allow the organic residue to be tapped directly for nutrients such as N and P. Pot experiments conducted with nutrient-stressed ectomycorrhizal and control willow plants showed that when high quality organic nutrient patches were added, they were colonized rapidly by the ectomycorrhizal mycelium. These established willows (0.5 m tall) were colonized by Hebeloma syrjense P. Karst. for 1 year prior to nutrient patch addition. Within days after patch addition, colour changes in the leaves of the mycorrhizal plants (reflecting improved nutrition) were apparent, and after I month the concentration of N and P in the foliage of mycorrhizal plants was significantly greater than that in non-mycorrhizal plants subject to the same nutrient addition. It seems likely that the mycorrhizal plants were able to compete effectively with the wider soil microbiota and tap directly into the high quality organic resource patch via their extra-radical mycelium. We hypothesize that ectomycorrhizal plants may reclaim some of the N and P invested in seed production by direct recycling from failed seeds in the soil. The rapid exploitation of similar discrete, transient, high-quality nutrient patches may have led to underestimations when determining the nutritional benefits of ectomycorrhizal colonization.

Application of dried blood spots to determine vitamin D status in a large nutritional study with unsupervised sampling: the Food4Me project

An efficient and robust method to measure vitamin D (25-hydroxy vitamin D3 (25(OH)D3) and 25-hydroxy vitamin D2 in dried blood spots (DBS) has been developed and applied in the pan-European multi-centre, internet-based, personalised nutrition intervention study Food4Me. The method includes calibration with blood containing endogenous 25(OH)D3, spotted as DBS and corrected for haematocrit content. The methodology was validated following international standards. The performance characteristics did not reach those of the current gold standard liquid chromatography-MS/MS in plasma for all parameters, but were found to be very suitable for status-level determination under field conditions. DBS sample quality was very high, and 3778 measurements of 25(OH)D3 were obtained from 1465 participants. The study centre and the season within the study centre were very good predictors of 25(OH)D3 levels (P<0·001 for each case). Seasonal effects were modelled by fitting a sine function with a minimum 25(OH)D3 level on 20 January and a maximum on 21 July. The seasonal amplitude varied from centre to centre. The largest difference between winter and summer levels was found in Germany and the smallest in Poland. The model was cross-validated to determine the consistency of the predictions and the performance of the DBS method. The Pearson's correlation between the measured values and the predicted values was r 0·65, and the sd of their differences was 21·2 nmol/l. This includes the analytical variation and the biological variation within subjects. Overall, DBS obtained by unsupervised sampling of the participants at home was a viable methodology for obtaining vitamin D status information in a large nutritional study.

Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Sampling uncertainty in gridded sea surface temperature products and Advanced Very High Resolution Radiometer (AVHRR) Global Area Coverage (GAC) data

Sea surface temperature (SST) data are often provided as gridded products, typically at resolutions of order 0.05 degrees from satellite observations to reduce data volume at the request of data users and facilitate comparison against other products or models. Sampling uncertainty is introduced in gridded products where the full surface area of the ocean within a grid cell cannot be fully observed because of cloud cover. In this paper we parameterise uncertainties in SST as a function of the percentage of clear-sky pixels available and the SST variability in that subsample. This parameterisation is developed from Advanced Along Track Scanning Radiometer (AATSR) data, but is applicable to all gridded L3U SST products at resolutions of 0.05-0.1 degrees, irrespective of instrument and retrieval algorithm, provided that instrument noise propagated into the SST is accounted for. We also calculate the sampling uncertainty of ~0.04 K in Global Area Coverage (GAC) Advanced Very High Resolution Radiometer (AVHRR) products, using related methods.