A benchmark method for global optimization problems in structure determination from powder diffraction data

Quasi-Newton-Raphson minimization and conjugate gradient minimization have been used to solve the crystal structures of famotidine form B and capsaicin from X-ray powder diffraction data and characterize the chi(2) agreement surfaces. One million quasi-Newton-Raphson minimizations found the famotidine global minimum with a frequency of ca 1 in 5000 and the capsaicin global minimum with a frequency of ca 1 in 10 000. These results, which are corroborated by conjugate gradient minimization, demonstrate the existence of numerous pathways from some of the highest points on these chi(2) agreement surfaces to the respective global minima, which are passable using only downhill moves. This important observation has significant ramifications for the development of improved structure determination algorithms.

Detection of polycyclic aromatic hydrocarbons using quartz crystal microbalances

A chemically coated piezoelectric sensor has been developed for the determination of PAHs in the liquid phase. An organic monolayer attached to the surface of a gold electrode of a quartz crystal microbalance (QCM) via a covalent thiol-gold link complete with an ionically bound recognition element has been produced. This study has employed the PAH derivative 9-anthracene carboxylic acid which, once bound to the alkane thiol, functions as the recognition element. Binding of anthracene via pi-pi interaction has been observed as a frequency shift in the QCM with a detectability of the target analyte of 2 ppb and a response range of 0-50 ppb. The relative response of the sensor altered for different PAHs despite pi-pi interaction being the sole communication between recognition element and analyte. It is envisaged that such a sensor could be employed in the identification of key marker compounds and, as such, give an indication of total PAH flux in the environment.

Enantioselective detection of L-serine

An acoustic wave sensor coated with an artificial biomimetic recognition element has been developed to selectively detect the amino acid L-serine. A highly specific non-covalently imprinted polymer was cast on one electrode of a quartz crystal microbalance (QCM) as a thin permeable film. Selective rebinding of the L-serine was observed as a frequency shift in the QCM with a detection limit of 2 ppb and for concentrations up to 0.4 ppm. The sensor binding is shown to be capable of discrimination between L- and D-stereoisomers of serine as a result of the enantioselectivity of the imprinted binding sites. (C) 2002 Elsevier Science B.V. All rights reserved.

A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

Modified radial basis function neural network using output transformation

A modified radial basis function (RBF) neural network and its identification algorithm based on observational data with heterogeneous noise are introduced. The transformed system output of Box-Cox is represented by the RBF neural network. To identify the model from observational data, the singular value decomposition of the full regression matrix consisting of basis functions formed by system input data is initially carried out and a new fast identification method is then developed using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator (MLE) for a model base spanned by the largest eigenvectors. Finally, the Box-Cox transformation-based RBF neural network, with good generalisation and sparsity, is identified based on the derived optimal Box-Cox transformation and an orthogonal forward regression algorithm using a pseudo-PRESS statistic to select a sparse RBF model with good generalisation. The proposed algorithm and its efficacy are demonstrated with numerical examples.

A forward-constrained regression algorithm for sparse kernel density estimation

Using the classical Parzen window (PW) estimate as the target function, the sparse kernel density estimator is constructed in a forward-constrained regression (FCR) manner. The proposed algorithm selects significant kernels one at a time, while the leave-one-out (LOO) test score is minimized subject to a simple positivity constraint in each forward stage. The model parameter estimation in each forward stage is simply the solution of jackknife parameter estimator for a single parameter, subject to the same positivity constraint check. For each selected kernels, the associated kernel width is updated via the Gauss-Newton method with the model parameter estimate fixed. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

Hammerstein model identification algorithm using Bezier-Bernstein approximation

A new identification algorithm is introduced for the Hammerstein model consisting of a nonlinear static function followed by a linear dynamical model. The nonlinear static function is characterised by using the Bezier-Bernstein approximation. The identification method is based on a hybrid scheme including the applications of the inverse of de Casteljau's algorithm, the least squares algorithm and the Gauss-Newton algorithm subject to constraints. The related work and the extension of the proposed algorithm to multi-input multi-output systems are discussed. Numerical examples including systems with some hard nonlinearities are used to illustrate the efficacy of the proposed approach through comparisons with other approaches.

The importance of the relationship between scale and process in understanding long-term DOC dynamics

Concentrations of dissolved organic carbon have increased in many, but not all, surface waters across acid impacted areas of Europe and North America over the last two decades. Over the last eight years several hypotheses have been put forward to explain these increases, but none are yet accepted universally. Research in this area appears to have reached a stalemate between those favouring declining atmospheric deposition, climate change or land management as the key driver of long-term DOC trends. While it is clear that many of these factors influence DOC dynamics in soil and stream waters, their effect varies over different temporal and spatial scales. We argue that regional differences in acid deposition loading may account for the apparent discrepancies between studies. DOC has shown strong monotonic increases in areas which have experienced strong downward trends in pollutant sulphur and/or seasalt deposition. Elsewhere climatic factors, that strongly influence seasonality, have also dominated inter-annual variability, and here long-term monotonic DOC trends are often difficult to detect. Furthermore, in areas receiving similar acid loadings, different catchment characteristics could have affected the site specific sensitivity to changes in acidity and therefore the magnitude of DOC release in response to changes in sulphur deposition. We suggest that confusion over these temporal and spatial scales of investigation has contributed unnecessarily to the disagreement over the main regional driver(s) of DOC trends, and that the data behind the majority of these studies is more compatible than is often conveyed.