Analytic Benchmark Solutions for Open-Channel Flows

An important test of the quality of a computational model is its ability to reproduce standard test cases or benchmarks. For steady open–channel flow based on the Saint Venant equations some benchmarks exist for simple geometries from the work of Bresse, Bakhmeteff and Chow but these are tabulated in the form of standard integrals. This paper provides benchmark solutions for a wider range of cases, which may have a nonprismatic cross section, nonuniform bed slope, and transitions between subcritical and supercritical flow. This makes it possible to assess the underlying quality of computational algorithms in more difficult cases, including those with hydraulic jumps. Several new test cases are given in detail and the performance of a commercial steady flow package is evaluated against two of them. The test cases may also be used as benchmarks for both steady flow models and unsteady flow models in the steady limit.

Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.

On computational algorithms for pole assignment

A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct procedures do not necessarily produce robust solutions to the problem, however, in the sense that the assigned poles are insensitive to perturbalions in the closed-loop system. This difficulty is illustrated here with results from a recent algorithm presented in this TRANSACTIONS and its causes are examined. A measure of robustness is described, and techniques for testing and improving robustness are indicated.

Algorithms for Robust Pole Assignment in Singular Systems

The solution of the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil. A robustness measure is defined, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ∈ X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

The REFLEX project: Comparing different algorithms and implementations for the inversion of a terrestrial ecosystem model against eddy covariance data

We describe a model-data fusion (MDF) inter-comparison project (REFLEX), which compared various algorithms for estimating carbon (C) model parameters consistent with both measured carbon fluxes and states and a simple C model. Participants were provided with the model and with both synthetic net ecosystem exchange (NEE) of CO2 and leaf area index (LAI) data, generated from the model with added noise, and observed NEE and LAI data from two eddy covariance sites. Participants endeavoured to estimate model parameters and states consistent with the model for all cases over the two years for which data were provided, and generate predictions for one additional year without observations. Nine participants contributed results using Metropolis algorithms, Kalman filters and a genetic algorithm. For the synthetic data case, parameter estimates compared well with the true values. The results of the analyses indicated that parameters linked directly to gross primary production (GPP) and ecosystem respiration, such as those related to foliage allocation and turnover, or temperature sensitivity of heterotrophic respiration, were best constrained and characterised. Poorly estimated parameters were those related to the allocation to and turnover of fine root/wood pools. Estimates of confidence intervals varied among algorithms, but several algorithms successfully located the true values of annual fluxes from synthetic experiments within relatively narrow 90% confidence intervals, achieving >80% success rate and mean NEE confidence intervals <110 gC m−2 year−1 for the synthetic case. Annual C flux estimates generated by participants generally agreed with gap-filling approaches using half-hourly data. The estimation of ecosystem respiration and GPP through MDF agreed well with outputs from partitioning studies using half-hourly data. Confidence limits on annual NEE increased by an average of 88% in the prediction year compared to the previous year, when data were available. Confidence intervals on annual NEE increased by 30% when observed data were used instead of synthetic data, reflecting and quantifying the addition of model error. Finally, our analyses indicated that incorporating additional constraints, using data on C pools (wood, soil and fine roots) would help to reduce uncertainties for model parameters poorly served by eddy covariance data.

Ensemble clustering in deterministic ensemble Kalman filters

Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M−1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF.

In vitro evaluation of the fermentation properties and potential prebiotic activity of caprine cheese whey oligosaccharides in batch culture systems

The prebiotic effect of oligosaccharides recovered and purified from caprine whey, was evaluated by in vitro fermentation under anaerobic conditions using batch cultures at 37ºC with human faeces. Effects on key gut bacterial groups were monitored over 24h by fluorescence in situ hybridisation (FISH), which was used to determine a quantitative prebiotic index score. Production of short-chain fatty acids (SCFAs) as fermentation end products was analysed by high-performance liquid chromatography (HPLC). Growth of Bifidobacterium spp was significantly higher (p ≥ 0.05) with the purified oligosaccharides compared to the negative control. Lactic and propionic acids were the main SCFAs produced. Antimicrobial activity of the oligosaccharides was also tested, revealing no inhibition though a decrease in Staphylococcus aureus and Escherichia coli growth. These findings indicate that naturally extracted oligosaccharides from caprine whey could be used as new and valuable source of prebiotics.

On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

Drug control, human rights, and the right to the highest attainable standard of health: a reply to Saul Takahashi

A recent article in this journal challenged claims that a human rights framework should be applied to drug control. This article questions the author’s assertions and reframes them in the context of socio-legal drug scholarship, aiming to build on the discourse concerning human rights and drug use. It is submitted that a rights-based approach is a necessary, indeed obligatory, ethical and legal framework through which to address drug use and that international human rights law provides the proper scope for determining where interferences with individual human rights might be justified on certain, limited grounds.

Detection of mutations in Salmonella enterica gyrA, gyrB, parC and parE genes by denaturing high performance liquid chromatography (DHPLC) using standard HPLC instrumentation

Aims: Quinolone antibiotics are the agents of choice for treating systemic Salmonella infections. Resistance to quinolones is usually mediated by mutations in the DNA gyrase gene gyrA. Here we report the evaluation of standard HPLC equipment for the detection of mutations (single nucleotide polymorphisms; SNPs) in gyrA, gyrB, parC and parE by denaturing high performance liquid chromatography (DHPLC). Methods: A panel of Salmonella strains was assembled which comprised those with known different mutations in gyrA (n = 8) and fluoroquinolone-susceptible and -resistant strains (n = 50) that had not been tested for mutations in gyrA. Additionally, antibiotic-susceptible strains of serotypes other than Salmonella enterica serovar Typhimurium strains were examined for serotype-specific mutations in gyrB (n = 4), parC (n = 6) and parE (n = 1). Wild-type (WT) control DNA was prepared from Salmonella Typhimurium NCTC 74. The DNA of respective strains was amplified by PCR using Optimase (R) proofreading DNA polymerase. Duplex DNA samples were analysed using an Agilent A1100 HPLC system with a Varian Helix (TM) DNA column. Sequencing was used to validate mutations detected by DHPLC in the strains with unknown mutations. Results: Using this HPLC system, mutations in gyrA, gyrB, parC and parE were readily detected by comparison with control chromatograms. Sequencing confirmed the gyrA predicted mutations as detected by DHPLC in the unknown strains and also confirmed serotype-associated sequence changes in non-Typhimurium serotypes. Conclusions: The results demonstrated that a non-specialist standard HPLC machine fitted with a generally available column can be used to detect SNPs in gyrA, gyrB, parC and parE genes by DHPLC. Wider applications should be possible.

Standardized test to evaluate numerical weather prediction algorithms

In order to assist in comparing the computational techniques used in different models, the authors propose a standardized set of one-dimensional numerical experiments that could be completed for each model. The results of these experiments, with a simplified form of the computational representation for advection, diffusion, pressure gradient term, Coriolis term, and filter used in the models, should be reported in the peer-reviewed literature. Specific recommendations are described in this paper.

A Web Map Service implementation for the visualization of multidimensional gridded environmental data

We describe ncWMS, an implementation of the Open Geospatial Consortium’s Web Map Service (WMS) specification for multidimensional gridded environmental data. ncWMS can read data in a large number of common scientific data formats – notably the NetCDF format with the Climate and Forecast conventions – then efficiently generate map imagery in thousands of different coordinate reference systems. It is designed to require minimal configuration from the system administrator and, when used in conjunction with a suitable client tool, provides end users with an interactive means for visualizing data without the need to download large files or interpret complex metadata. It is also used as a “bridging” tool providing interoperability between the environmental science community and users of geographic information systems. ncWMS implements a number of extensions to the WMS standard in order to fulfil some common scientific requirements, including the ability to generate plots representing timeseries and vertical sections. We discuss these extensions and their impact upon present and future interoperability. We discuss the conceptual mapping between the WMS data model and the data models used by gridded data formats, highlighting areas in which the mapping is incomplete or ambiguous. We discuss the architecture of the system and particular technical innovations of note, including the algorithms used for fast data reading and image generation. ncWMS has been widely adopted within the environmental data community and we discuss some of the ways in which the software is integrated within data infrastructures and portals.