Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions. (c) 2006 Optical Society of America.

Modeling phytoplankton dynamics in the River Darling (Australia) using the radial basis function neural network

A radial basis function neural network was employed to model the abundance of cyanobacteria. The trained network could predict the populations of two bloom forming algal taxa with high accuracy, Nostocales spp. and Anabaena spp., in the River Darling, Australia. To elucidate the population dynamics for both Nostocales spp. and Anabaena spp., sensitivity analysis was performed with the following results. Total Kjeldahl nitrogen had a very strong influence on the abundance of the two algal taxa, electrical conductivity had a very strong negative relationship with the population of the two algal species, and flow was identified as one dominant factor influencing algal blooms after a scatter plot revealed that high flow could significantly reduce the algal biomass for both Nostocales spp. and Anabaena spp. Other variables such as turbidity, color, and pH were less important in determining the abundance and succession of the algal blooms.

DISTRIBUTION FUNCTION OF A DRIFTING ELECTRON-GAS FOR GENERAL ENERGY-BAND STRUCTURES

The usual application of the Lei-Ting balance equation method for treating electron transport problems makes use of a Fermi distribution function for the electron motion relative to the center of mass. It is pointed out that this presumes the existence of a moving frame of reference that is dynamically equivalent to the rest frame of reference, and this is only true for electrons with a constant effective mass. The method is thus inapplicable to problems where electrons governed by a general energy-band dispersion E(k) are important (such as in miniband conduction). It is demonstrated that this difficulty can be overcome by introducing a distribution function for a drifting electron gas by maximizing the entropy subject to a prescribed average drift velocity. The distribution function reduces directly to the usual Fermi distribution for electron motion relative to the center of mass in the special case of E(k)=($) over bar h(2)\k\(2)/2m*. This maximum entropy treatment of a drifting electron gas provides a physically more direct as well as a more general basis for the application of the balance equation method.

A Radial Basis Function Approach to Financial Time Series Analysis

Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining'' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.

Automated cross-modal mapping in robotic eye/hand systems using plastic radial basis function networks

Q. Meng and M. H Lee, Automated cross-modal mapping in robotic eye/hand systems using plastic radial basis function networks, Connection Science, 19(1), pp 25-52, 2007.

Two-stage mixed discrete-continuous identification of radial basis function (RBF) neural models for nonlinear systems

The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete-continuous; identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm.