Finite element approximation of a sixth order nonlinear degenerate parabolic equation

We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ?.( b(u)? 2u), where generically b(u) := |u|? for any given ? ? (0,?). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ? 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments in one and two space dimensions are presented.

A 3D stochastic cloud model for investigating the radiative properties of inhomogeneous cirrus clouds

(From author). Comments: First 3D stochastic/fractal model of cirrus; first detailed analysis & explanation of power spectra of ice water content, including first observations of 50-km scale break and mixing-induced steepening of spectrum; first demonstration of the potential effect of wind shear on radiative fluxes by changing fall-streak orientation. Has spawned work on the effect of 3D photon transport on the radiative effects of cirrus clouds.

Simulating current global river runoff with a global hydrological model: model revisions, validation, and sensitivity analysis

Global hydrological models (GHMs) model the land surface hydrologic dynamics of continental-scale river basins. Here we describe one such GHM, the Macro-scale - Probability-Distributed Moisture model.09 (Mac-PDM.09). The model has undergone a number of revisions since it was last applied in the hydrological literature. This paper serves to provide a detailed description of the latest version of the model. The main revisions include the following: (1) the ability for the model to be run for n repetitions, which provides more robust estimates of extreme hydrological behaviour, (2) the ability of the model to use a gridded field of coefficient of variation (CV) of daily rainfall for the stochastic disaggregation of monthly precipitation to daily precipitation, and (3) the model can now be forced with daily input climate data as well as monthly input climate data. We demonstrate the effects that each of these three revisions has on simulated runoff relative to before the revisions were applied. Importantly, we show that when Mac-PDM.09 is forced with monthly input data, it results in a negative runoff bias relative to when daily forcings are applied, for regions of the globe where the day-to-day variability in relative humidity is high. The runoff bias can be up to - 80% for a small selection of catchments but the absolute magnitude of the bias may be small. As such, we recommend future applications of Mac-PDM.09 that use monthly climate forcings acknowledge the bias as a limitation of the model. The performance of Mac-PDM.09 is evaluated by validating simulated runoff against observed runoff for 50 catchments. We also present a sensitivity analysis that demonstrates that simulated runoff is considerably more sensitive to method of PE calculation than to perturbations in soil moisture and field capacity parameters.

The binding site distance test score: a robust method for the assessment of predicted protein binding sites

We propose a novel method for scoring the accuracy of protein binding site predictions – the Binding-site Distance Test (BDT) score. Recently, the Matthews Correlation Coefficient (MCC) has been used to evaluate binding site predictions, both by developers of new methods and by the assessors for the community wide prediction experiment – CASP8. Whilst being a rigorous scoring method, the MCC does not take into account the actual 3D location of the predicted residues from the observed binding site. Thus, an incorrectly predicted site that is nevertheless close to the observed binding site will obtain an identical score to the same number of nonbinding residues predicted at random. The MCC is somewhat affected by the subjectivity of determining observed binding residues and the ambiguity of choosing distance cutoffs. By contrast the BDT method produces continuous scores ranging between 0 and 1, relating to the distance between the predicted and observed residues. Residues predicted close to the binding site will score higher than those more distant, providing a better reflection of the true accuracy of predictions. The CASP8 function predictions were evaluated using both the MCC and BDT methods and the scores were compared. The BDT was found to strongly correlate with the MCC scores whilst also being less susceptible to the subjectivity of defining binding residues. We therefore suggest that this new simple score is a potentially more robust method for future evaluations of protein-ligand binding site predictions.

Translating climate forecasts into agricultural terms: advances and challenges

Seasonal climate prediction offers the potential to anticipate variations in crop production early enough to adjust critical decisions. Until recently, interest in exploiting seasonal forecasts from dynamic climate models (e.g. general circulation models, GCMs) for applications that involve crop simulation models has been hampered by the difference in spatial and temporal scale of GCMs and crop models, and by the dynamic, nonlinear relationship between meteorological variables and crop response. Although GCMs simulate the atmosphere on a sub-daily time step, their coarse spatial resolution and resulting distortion of day-to-day variability limits the use of their daily output. Crop models have used daily GCM output with some success by either calibrating simulated yields or correcting the daily rainfall output of the GCM to approximate the statistical properties of historic observations. Stochastic weather generators are used to disaggregate seasonal forecasts either by adjusting input parameters in a manner that captures the predictable components of climate, or by constraining synthetic weather sequences to match predicted values. Predicting crop yields, simulated with historic weather data, as a statistical function of seasonal climatic predictors, eliminates the need for daily weather data conditioned on the forecast, but must often address poor statistical properties of the crop-climate relationship. Most of the work on using crop simulation with seasonal climate forecasts has employed historic analogs based on categorical ENSO indices. Other methods based on classification of predictors or weather types can provide daily weather inputs to crop models conditioned on forecasts. Advances in climate-based crop forecasting in the coming decade are likely to include more robust evaluation of the methods reviewed here, dynamically embedding crop models within climate models to account for crop influence on regional climate, enhanced use of remote sensing, and research in the emerging area of 'weather within climate'.

Translating climate forecasts into agricultural terms: advances and challenges

Seasonal climate prediction offers the potential to anticipate variations in crop production early enough to adjust critical decisions. Until recently, interest in exploiting seasonal forecasts from dynamic climate models (e.g. general circulation models, GCMs) for applications that involve crop simulation models has been hampered by the difference in spatial and temporal scale of GCMs and crop models, and by the dynamic, nonlinear relationship between meteorological variables and crop response. Although GCMs simulate the atmosphere on a sub-daily time step, their coarse spatial resolution and resulting distortion of day-to-day variability limits the use of their daily output. Crop models have used daily GCM output with some success by either calibrating simulated yields or correcting the daily rainfall output of the GCM to approximate the statistical properties of historic observations. Stochastic weather generators are used to disaggregate seasonal forecasts either by adjusting input parameters in a manner that captures the predictable components of climate, or by constraining synthetic weather sequences to match predicted values. Predicting crop yields, simulated with historic weather data, as a statistical function of seasonal climatic predictors, eliminates the need for daily weather data conditioned on the forecast, but must often address poor statistical properties of the crop-climate relationship. Most of the work on using crop simulation with seasonal climate forecasts has employed historic analogs based on categorical ENSO indices. Other methods based on classification of predictors or weather types can provide daily weather inputs to crop models conditioned on forecasts. Advances in climate-based crop forecasting in the coming decade are likely to include more robust evaluation of the methods reviewed here, dynamically embedding crop models within climate models to account for crop influence on regional climate, enhanced use of remote sensing, and research in the emerging area of 'weather within climate'.

Dual technological development in Botswana agriculture: A Stochastic input distance function approach

To improve the welfare of the rural poor and keep them in the countryside, the government of Botswana has been spending 40% of the value of agricultural GDP on agricultural support services. But can investment make smallholder agriculture prosperous in such adverse conditions? This paper derives an answer by applying a two-output six-input stochastic translog distance function, with inefficiency effects and biased technical change to panel data for the 18 districts and the commercial agricultural sector, from 1979 to 1996 This model demonstrates that herds are the most important input, followed by draft power. land and seeds. Multilateral indices for technical change, technical efficiency and total factor productivity (TFP) show that the technology level of the commercial agricultural sector is more than six times that of traditional agriculture and that the gap has been increasing, due to technological regression in traditional agriculture and modest progress in commercial agriculture. Since the levels of efficiency are similar, the same patient is repeated by the TFP indices. This result highlights the policy dilemma of the trade-off between efficiency and equity objectives.

Stopping clinical trials because of treatment ineffectiveness: a comparison of a futility design with a method of stochastic curtailment

This paper introduces a simple futility design that allows a comparative clinical trial to be stopped due to lack of effect at any of a series of planned interim analyses. Stopping due to apparent benefit is not permitted. The design is for use when any positive claim should be based on the maximum sample size, for example to allow subgroup analyses or the evaluation of safety or secondary efficacy responses. A final frequentist analysis can be performed that is valid for the type of design employed. Here the design is described and its properties are presented. Its advantages and disadvantages relative to the use of stochastic curtailment are discussed. Copyright (C) 2003 John Wiley Sons, Ltd.

Extending Zelterman’s approach for robust estimation of population size to zero-truncated clustered data

Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)