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.

Spectroscopy of ultrathin epitaxial rutile TiO[sub 2](110) films grown on W(100)

Epitaxial ultrathin titanium dioxide films of 0.3 to similar to 7 nm thickness on a metal single crystal substrate have been investigated by high resolution vibrational and electron spectroscopies. The data complement previous morphological data provided by scanned probe microscopy and low energy electron diffraction to provide very complete characterization of this system. The thicker films display electronic structure consistent with a stoichiometric TiO2 phase. The thinner films appear nonstoichiometric due to band bending and charge transfer from the metal substrate, while work function measurements also show a marked thickness dependence. The vibrational spectroscopy shows three clear phonon bands at 368, 438, and 829 cm(-1) (at 273 K), which confirms a rutile structure. The phonon band intensity scales linearly with film thickness and shift slightly to lower frequencies with increasing temperature, in accord with results for single crystals. (c) 2007 American Institute of Physics.

Structure of adsorbed organometallic rhodium: model single atom catalysts

We have determined the structure of a complex rhodium carbonyl chloride [Rh(CO)(2)Cl] molecule adsorbed on the TiO2 (110) surface by the normal incidence x-ray standing wave technique. The data show that the technique is applicable to reducible oxide systems and that the dominant adsorbed species is undissociated with Rh binding atop bridging oxygen and to the Cl found close to the fivefold coordinated Ti ions in the surface. A minority geminal dicarboryl species, where Rh-Cl bond scission has occurred, is found bridging the bridging oxygen ions forming a high-symmetry site.

Modeling of complex-valued Wiener systems using B-spline neural network

In this brief, a new complex-valued B-spline neural network is introduced in order to model the complex-valued Wiener system using observational input/output data. The complex-valued nonlinear static function in the Wiener system is represented using the tensor product from two univariate B-spline neural networks, using the real and imaginary parts of the system input. Following the use of a simple least squares parameter initialization scheme, the Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first-order derivatives recursion. Numerical examples, including a nonlinear high-power amplifier model in communication systems, are used to demonstrate the efficacy of the proposed approaches.

B-spline neural network based digital baseband predistorter solution using the inverse of De Boor algorithm

In this paper a new nonlinear digital baseband predistorter design is introduced based on direct learning, together with a new Wiener system modeling approach for the high power amplifiers (HPA) based on the B-spline neural network. The contribution is twofold. Firstly, by assuming that the nonlinearity in the HPA is mainly dependent on the input signal amplitude the complex valued nonlinear static function is represented by two real valued B-spline neural networks, one for the amplitude distortion and another for the phase shift. The Gauss-Newton algorithm is applied for the parameter estimation, in which the De Boor recursion is employed to calculate both the B-spline curve and the first order derivatives. Secondly, we derive the predistorter algorithm calculating the inverse of the complex valued nonlinear static function according to B-spline neural network based Wiener models. The inverse of the amplitude and phase shift distortion are then computed and compensated using the identified phase shift model. Numerical examples have been employed to demonstrate the efficacy of the proposed approaches.

A Wiener model for memory high power amplifiers using B-spline function approximation

In this paper we introduce a new Wiener system modeling approach for memory high power amplifiers in communication systems using observational input/output data. By assuming that the nonlinearity in the Wiener model is mainly dependent on the input signal amplitude, the complex valued nonlinear static function is represented by two real valued B-spline curves, one for the amplitude distortion and another for the phase shift, respectively. The Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first order derivatives recursion. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.