A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

Uncertainty analysis of pollutant build-up modelling based on a Bayesian Weighted Least Squares approach

Reliable pollutant build-up prediction plays a critical role in the accuracy of urban stormwater quality modelling outcomes. However, water quality data collection is resource demanding compared to streamflow data monitoring, where a greater quantity of data is generally available. Consequently, available water quality data sets span only relatively short time scales unlike water quantity data. Therefore, the ability to take due consideration of the variability associated with pollutant processes and natural phenomena is constrained. This in turn gives rise to uncertainty in the modelling outcomes as research has shown that pollutant loadings on catchment surfaces and rainfall within an area can vary considerably over space and time scales. Therefore, the assessment of model uncertainty is an essential element of informed decision making in urban stormwater management. This paper presents the application of a range of regression approaches such as ordinary least squares regression, weighted least squares Regression and Bayesian Weighted Least Squares Regression for the estimation of uncertainty associated with pollutant build-up prediction using limited data sets. The study outcomes confirmed that the use of ordinary least squares regression with fixed model inputs and limited observational data may not provide realistic estimates. The stochastic nature of the dependent and independent variables need to be taken into consideration in pollutant build-up prediction. It was found that the use of the Bayesian approach along with the Monte Carlo simulation technique provides a powerful tool, which attempts to make the best use of the available knowledge in the prediction and thereby presents a practical solution to counteract the limitations which are otherwise imposed on water quality modelling.

Characterisation of humidity dependence of a metal oxide semiconductor (MOS) sensor array using Partial Least Squares (PLS)

Metal oxide semiconductor (MOS) sensors are a class of chemical sensor that have potential for being a practical core sensor module for an electronic nose system in various environmental monitoring applications. However, the responses of these sensors may be affected by changes in humidity and this must be taken into consideration when developing calibration models. This paper characterises the humidity dependence of a sensor array which consists of 12 MOS sensors. The results were used to develop calibration models using partial least squares. Effects of humidity on the response of the sensor array and predictive ability of partial least squares are discussed. It is shown that partial least squares can provide proper calibration models to compensate for effects caused by changes in humidity.

Characterisation of humidity dependence of a metal oxide semiconductor sensor array using partial least squares

Metal oxide semiconductor (MOS) sensors are a class of chemical sensors that have potential for being a practical core sensor module for an electronic nose system in various environmental monitoring applications. However, the responses of these sensors may be affected by changes in humidity and this must be taken into consideration when developing calibration models. This paper characterises the humidity dependence of a sensor array which consists of 12 MOS sensors. The results were used to develop calibration models using partial least squares (PLS). Effects of humidity on the response of the sensor array and predictive ability of partial least squares are discussed. It is shown that partial least squares can provide proper calibration models to compensate for effects caused by changes in humidity. Special Issue: Selected Paper from the 12th International Symposium on Olfaction and Electronic Noses - ISOEN 2007, International Symposium on Olfaction and Electronic Noses.

Fast FIR Algorithms for the Continuous Wavelet Transform From Constrained Least Squares

New algorithms for the continuous wavelet transform are developed that are easy to apply, each consisting of a single-pass finite impulse response (FIR) filter, and several times faster than the fastest existing algorithms. The single-pass filter, named WT-FIR-1, is made possible by applying constraint equations to least-squares estimation of filter coefficients, which removes the need for separate low-pass and high-pass filters. Non-dyadic two-scale relations are developed and it is shown that filters based on them can work more efficiently than dyadic ones. Example applications to the Mexican hat wavelet are presented.

High-Throughput Prediction of Acacia and Eucalypt Lignin Syringyl/Guaiacyl Content Using FT-Raman Spectroscopy and Partial Least Squares Modeling

High-throughput techniques are necessary to efficiently screen potential lignocellulosic feedstocks for the production of renewable fuels, chemicals, and bio-based materials, thereby reducing experimental time and expense while supplanting tedious, destructive methods. The ratio of lignin syringyl (S) to guaiacyl (G) monomers has been routinely quantified as a way to probe biomass recalcitrance. Mid-infrared and Raman spectroscopy have been demonstrated to produce robust partial least squares models for the prediction of lignin S/G ratios in a diverse group of Acacia and eucalypt trees. The most accurate Raman model has now been used to predict the S/G ratio from 269 unknown Acacia and eucalypt feedstocks. This study demonstrates the application of a partial least squares model composed of Raman spectral data and lignin S/G ratios measured using pyrolysis/molecular beam mass spectrometry (pyMBMS) for the prediction of S/G ratios in an unknown data set. The predicted S/G ratios calculated by the model were averaged according to plant species, and the means were not found to differ from the pyMBMS ratios when evaluating the mean values of each method within the 95 % confidence interval. Pairwise comparisons within each data set were employed to assess statistical differences between each biomass species. While some pairwise appraisals failed to differentiate between species, Acacias, in both data sets, clearly display significant differences in their S/G composition which distinguish them from eucalypts. This research shows the power of using Raman spectroscopy to supplant tedious, destructive methods for the evaluation of the lignin S/G ratio of diverse plant biomass materials.

A modified least squares algorithm to treat associations in liquid alloys

The associated model for binary systems has been modified to include volume effects and excess entropy arising from preferential interactions between the associate and the free atoms or between the free atoms. Equations for thermodynamic mixing functions have been derived. An optimization procedure using a modified conjugate gradient method has been used to evaluate the enthalpy and entropy interaction energies, the free energy of dissociation of the complex, its temperature dependance and the size of the associate. An expression for the concentration—concentration structure factor [Scc (0)] has been deduced from the modified associated solution model. The analysis has been applied to the thermodynamic mixing functions of liquid Ga-Te alloys at 1120 K, believed to contain Ga2Te3 associates. It is observed that the modified associated solution model incorporating volume effects and terms for the temperature dependance of interaction energies, describes the thermodynamic properties of Ga-Te system satisfactorily.

Parameter estimation in water-distribution systems by least squares

The weighted-least-squares method using sensitivity-analysis technique is proposed for the estimation of parameters in water-distribution systems. The parameters considered are the Hazen-Williams coefficients for the pipes. The objective function used is the sum of the weighted squares of the differences between the computed and the observed values of the variables. The weighted-least-squares method can elegantly handle multiple loading conditions with mixed types of measurements such as heads and consumptions, different sets and number of measurements for each loading condition, and modifications in the network configuration due to inclusion or exclusion of some pipes affected by valve operations in each loading condition. Uncertainty in parameter estimates can also be obtained. The method is applied for the estimation of parameters in a metropolitan urban water-distribution system in India.

Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

Probabilistic least squares approach to ordinal regression

This paper proposes a novel approach to solve the ordinal regression problem using Gaussian processes. The proposed approach, probabilistic least squares ordinal regression (PLSOR), obtains the probability distribution over ordinal labels using a particular likelihood function. It performs model selection (hyperparameter optimization) using the leave-one-out cross-validation (LOO-CV) technique. PLSOR has conceptual simplicity and ease of implementation of least squares approach. Unlike the existing Gaussian process ordinal regression (GPOR) approaches, PLSOR does not use any approximation techniques for inference. We compare the proposed approach with the state-of-the-art GPOR approaches on some synthetic and benchmark data sets. Experimental results show the competitiveness of the proposed approach.