Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.

Meaning of the λ parameter of skew–normal and log–skew normal distributions in fluid geochemistry

The literature related to skew–normal distributions has grown rapidly in recent years but at the moment few applications concern the description of natural phenomena with this type of probability models, as well as the interpretation of their parameters. The skew–normal distributions family represents an extension of the normal family to which a parameter (λ) has been added to regulate the skewness. The development of this theoretical field has followed the general tendency in Statistics towards more flexible methods to represent features of the data, as adequately as possible, and to reduce unrealistic assumptions as the normality that underlies most methods of univariate and multivariate analysis. In this paper an investigation on the shape of the frequency distribution of the logratio ln(Cl−/Na+) whose components are related to waters composition for 26 wells, has been performed. Samples have been collected around the active center of Vulcano island (Aeolian archipelago, southern Italy) from 1977 up to now at time intervals of about six months. Data of the logratio have been tentatively modeled by evaluating the performance of the skew–normal model for each well. Values of the λ parameter have been compared by considering temperature and spatial position of the sampling points. Preliminary results indicate that changes in λ values can be related to the nature of environmental processes affecting the data

Fault diagnosis by refining the parameter uncertainty space of nonlinear dynamic systems

This paper deals with fault detection and isolation problems for nonlinear dynamic systems. Both problems are stated as constraint satisfaction problems (CSP) and solved using consistency techniques. The main contribution is the isolation method based on consistency techniques and uncertainty space refining of interval parameters. The major advantage of this method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements, and model errors. Interval calculations bring independence from the assumption of monotony considered by several approaches for fault isolation which are based on observers. An application to a well known alcoholic fermentation process model is presented

Catalase in fluvial biofilms: a comparison between different extraction methods and example of application in a metal-polluted river

Antioxidant enzymes are involved in important processes of cell detoxification during oxidative stress and have, therefore, been used as biomarkers in algae. Nevertheless, their limited use in fluvial biofilms may be due to the complexity of such communities. Here, a comparison between different extraction methods was performed to obtain a reliable method for catalase extraction from fluvial biofilms. Homogenization followed by glass bead disruption appeared to be the best compromise for catalase extraction. This method was then applied to a field study in a metal-polluted stream (Riou Mort, France). The most polluted sites were characterized by a catalase activity 4–6 times lower than in the low-polluted site. Results of the comparison process and its application are promising for the use of catalase activity as an early warning biomarker of toxicity using biofilms in the laboratory and in the field

Variational data assimilation for parameter estimation: application to a simple morphodynamic model

Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce state and parameter estimates that most accurately approximate the current and future states of the true system. The technique is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var, Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more complex morphodynamic models.

Sequential extraction and single-step cold-acid extraction: A feasibility study for use with freshwater-canal sediments

This investigation examines metal release from freshwater sediment using sequential extraction and single-step cold-acid leaching. The concentrations of Cd, Cr, Cu, Fe, Ni, Pb and Zn released using a standard 3-step sequential extraction (Rauret et al., 1999) are compared to those released using a 0.5 M HCl; leach. The results show that the three sediments behave in very different ways when subject to the same leaching experiments: the cold-acid extraction appears to remove higher relative concentrations of metals from the iron-rich sediment than from the other two sediments. Cold-acid extraction appears to be more effective at removing metals from sediments with crystalline iron oxides than the "reducible" step of the sequential extraction. The results show that a single-step acid leach can be just as effective as sequential extractions at removing metals from sediment and are a great deal less time-consuming.

Fate of prions in soil: Detergent extraction of PrP from soils

The transmissible spongiform encephalopathies (TSEs) are caused by infectious agents whose structures have not been fully characterized but include abnormal forms of the host protein PrP, designated PrPSc, which are deposited in infected tissues. The transmission routes of scrapie and chronic wasting disease (CWD) seem to include environmental spread in their epidemiology, yet the fate of TSE agents in the environment is poorly understood. There are concerns that, for example, buried carcasses may remain a potential reservoir of infectivity for many years. Experimental determination of the environmental fate requires methods for assessing binding/elution of TSE infectivity, or its surrogate marker PrPSc, to and from materials with which it might interact. We report a method using Sarkosyl for the extraction of murine PrPSc, and its application to soils containing recombinant ovine PrP (recPrP). Elution properties suggest that PrP binds strongly to one or more soil components. Elution from a clay soil also required proteinase K digestion, suggesting that in the clay soil binding occurs via the N-terminal of PrP to a component that is absent from the sandy soils tested.

Parameter sensitivity and predictive uncertainty in a new water quality model, Q(2)

A new dynamic model of water quality, Q(2), has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q(2) for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q(2) model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.