An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

Modelling water droplet movement on a leaf surface

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates

The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and computational load of the integration of the multivariate probability density function. Contributions of this work are twofold. First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid, at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions.

Multiview point cloud kernels for semisupervised learning [Lecture Notes]

In semisupervised learning (SSL), a predictive model is learn from a collection of labeled data and a typically much larger collection of unlabeled data. These paper presented a framework called multi-view point cloud regularization (MVPCR), which unifies and generalizes several semisupervised kernel methods that are based on data-dependent regularization in reproducing kernel Hilbert spaces (RKHSs). Special cases of MVPCR include coregularized least squares (CoRLS), manifold regularization (MR), and graph-based SSL. An accompanying theorem shows how to reduce any MVPCR problem to standard supervised learning with a new multi-view kernel.

Achieving high reliability for ambiguity resolutions with multiple GNSS constellations

Global Navigation Satellite Systems (GNSS)-based observation systems can provide high precision positioning and navigation solutions in real time, in the order of subcentimetre if we make use of carrier phase measurements in the differential mode and deal with all the bias and noise terms well. However, these carrier phase measurements are ambiguous due to unknown, integer numbers of cycles. One key challenge in the differential carrier phase mode is to fix the integer ambiguities correctly. On the other hand, in the safety of life or liability-critical applications, such as for vehicle safety positioning and aviation, not only is high accuracy required, but also the reliability requirement is important. This PhD research studies to achieve high reliability for ambiguity resolution (AR) in a multi-GNSS environment. GNSS ambiguity estimation and validation problems are the focus of the research effort. Particularly, we study the case of multiple constellations that include initial to full operations of foreseeable Galileo, GLONASS and Compass and QZSS navigation systems from next few years to the end of the decade. Since real observation data is only available from GPS and GLONASS systems, the simulation method named Virtual Galileo Constellation (VGC) is applied to generate observational data from another constellation in the data analysis. In addition, both full ambiguity resolution (FAR) and partial ambiguity resolution (PAR) algorithms are used in processing single and dual constellation data. Firstly, a brief overview of related work on AR methods and reliability theory is given. Next, a modified inverse integer Cholesky decorrelation method and its performance on AR are presented. Subsequently, a new measure of decorrelation performance called orthogonality defect is introduced and compared with other measures. Furthermore, a new AR scheme considering the ambiguity validation requirement in the control of the search space size is proposed to improve the search efficiency. With respect to the reliability of AR, we also discuss the computation of the ambiguity success rate (ASR) and confirm that the success rate computed with the integer bootstrapping method is quite a sharp approximation to the actual integer least-squares (ILS) method success rate. The advantages of multi-GNSS constellations are examined in terms of the PAR technique involving the predefined ASR. Finally, a novel satellite selection algorithm for reliable ambiguity resolution called SARA is developed. In summary, the study demonstrats that when the ASR is close to one, the reliability of AR can be guaranteed and the ambiguity validation is effective. The work then focuses on new strategies to improve the ASR, including a partial ambiguity resolution procedure with a predefined success rate and a novel satellite selection strategy with a high success rate. The proposed strategies bring significant benefits of multi-GNSS signals to real-time high precision and high reliability positioning services.

A new ambiguity acceptance test threshold determination method with controllable failure rate

The ambiguity acceptance test is an important quality control procedure in high precision GNSS data processing. Although the ambiguity acceptance test methods have been extensively investigated, its threshold determine method is still not well understood. Currently, the threshold is determined with the empirical approach or the fixed failure rate (FF-) approach. The empirical approach is simple but lacking in theoretical basis, while the FF-approach is theoretical rigorous but computationally demanding. Hence, the key of the threshold determination problem is how to efficiently determine the threshold in a reasonable way. In this study, a new threshold determination method named threshold function method is proposed to reduce the complexity of the FF-approach. The threshold function method simplifies the FF-approach by a modeling procedure and an approximation procedure. The modeling procedure uses a rational function model to describe the relationship between the FF-difference test threshold and the integer least-squares (ILS) success rate. The approximation procedure replaces the ILS success rate with the easy-to-calculate integer bootstrapping (IB) success rate. Corresponding modeling error and approximation error are analysed with simulation data to avoid nuisance biases and unrealistic stochastic model impact. The results indicate the proposed method can greatly simplify the FF-approach without introducing significant modeling error. The threshold function method makes the fixed failure rate threshold determination method feasible for real-time applications.

The Impact of Internal Market Orientation on Staff Service Behaviours

The impact of service direction, service training and staff behaviours on perceptions of service delivery are examined. The impact of managerial behaviour in the form of internal market orientation (IMO) on the attitudes of frontline staff towards the firm and its consequent influence on their customer oriented behaviours is also examined. Frontline service staff working in the consumer transport industry were surveyed to provide subjective data about the constructs of interest in this study, and the data were analysed using structural equations modelling employing partial least squares estimation. The data indicate significant relationships between internal market orientation (IMO), the attitudes of the employees to the firm and their consequent behaviour towards customers. Customer orientation, service direction and service training are all identified as antecedents to high levels of service delivery. The study contributes to marketing theory by providing quantitative evidence to support assumptions that internal marketing has an impact on services success. For marketing practitioners, the research findings offer additional information about the management, training and motivation of service staff towards service excellence.

Trust and strong ties in the selection and evaluation of business advisors by small firms

Principal Topic A small firm is unlikely to possess internally the full range of knowledge and skills that it requires or could benefit from for the development of its business. The ability to acquire suitable external expertise - defined as knowledge or competence that is rare in the firm and acquired from the outside - when needed thus becomes a competitive factor in itself. Access to external expertise enables the firm to focus on its core competencies and removes the necessity to internalize every skill and competence. However, research on how small firms access external expertise is still scarce. The present study contributes to this under-developed discussion by analysing the role of trust and strong ties in the small firm's selection and evaluation of sources of external expertise (henceforth referred to as the 'business advisor' or 'advisor'). Granovetter (1973, 1361) defines the strength of a network tie as 'a (probably linear) combination of the amount of time, the emotional intensity, the intimacy (mutual confiding) and the reciprocal services which characterize the tie'. Strong ties in the context of the present investigation refer to sources of external expertise who are well known to the owner-manager, and who may be either informal (e.g., family, friends) or professional advisors (e.g., consultants, enterprise support officers, accountants or solicitors). Previous research has suggested that strong and weak ties have different fortes and the choice of business advisors could thus be critical to business performance) While previous research results suggest that small businesses favour previously well known business advisors, prior studies have also pointed out that an excessive reliance on a network of well known actors might hamper business development, as the range of expertise available through strong ties is limited. But are owner-managers of small businesses aware of this limitation and does it matter to them? Or does working with a well-known advisor compensate for it? Hence, our research model first examines the impact of the strength of tie on the business advisor's perceived performance. Next, we ask what encourages a small business owner-manager to seek advice from a strong tie. A recent exploratory study by Welter and Kautonen (2005) drew attention to the central role of trust in this context. However, while their study found support for the general proposition that trust plays an important role in the choice of advisors, how trust and its different dimensions actually affect this choice remained ambiguous. The present paper develops this discussion by considering the impact of the different dimensions of perceived trustworthiness, defined as benevolence, integrity and ability, on the strength of tie. Further, we suggest that the dimensions of perceived trustworthiness relevant in the choice of a strong tie vary between professional and informal advisors. Methodology/Key Propositions Our propositions are examined empirically based on survey data comprising 153 Finnish small businesses. The data are analysed utilizing the partial least squares (PLS) approach to structural equation modelling with SmartPLS 2.0. Being non-parametric, the PLS algorithm is particularly well-suited to analysing small datasets with non-normally distributed variables. Results and Implications The path model shows that the stronger the tie, the more positively the advisor's performance is perceived. Hypothesis 1, that strong ties will be associated with higher perceptions of performance is clearly supported. Benevolence is clearly the most significant predictor of the choice of a strong tie for external expertise. While ability also reaches a moderate level of statistical significance, integrity does not have a statistically significant impact on the choice of a strong tie. Hence, we found support for two out of three independent variables included in Hypothesis 2. Path coefficients differed between the professional and informal advisor subsamples. The results of the exploratory group comparison show that Hypothesis 3a regarding ability being associated with strong ties more pronouncedly when choosing a professional advisor was not supported. Hypothesis 3b arguing that benevolence is more strongly associated with strong ties in the context of choosing an informal advisor received some support because the path coefficient in the informal advisor subsample was much larger than in the professional advisor subsample. Hypothesis 3c postulating that integrity would be more strongly associated with strong ties in the choice of a professional advisor was supported. Integrity is the most important dimension of trustworthiness in this context. However, integrity is of no concern, or even negative, when using strong ties to choose an informal advisor. The findings of this study have practical relevance to the enterprise support community. First of all, given that the strength of tie has a significant positive impact on the advisor's perceived performance, this implies that small business owners appreciate working with advisors in long-term relationships. Therefore, advisors are well advised to invest into relationship building and maintenance in their work with small firms. Secondly, the results show that, especially in the context of professional advisors, the advisor's perceived integrity and benevolence weigh more than ability. This again emphasizes the need to invest time and effort into building a personal relationship with the owner-manager, rather than merely maintaining a professional image and credentials. Finally, this study demonstrates that the dimensions of perceived trustworthiness are orthogonal with different effects on the strength of tie and ultimately perceived performance. This means that entrepreneurs and advisors should consider the specific dimensions of ability, benevolence and integrity, rather than rely on general perceptions of trustworthiness in their advice relationships.

Does chemometrics enhance the performance of electroanalysis?

This review explores the question whether chemometrics methods enhance the performance of electroanalytical methods. Electroanalysis has long benefited from the well-established techniques such as potentiometric titrations, polarography and voltammetry, and the more novel ones such as electronic tongues and noses, which have enlarged the scope of applications. The electroanalytical methods have been improved with the application of chemometrics for simultaneous quantitative prediction of analytes or qualitative resolution of complex overlapping responses. Typical methods include partial least squares (PLS), artificial neural networks (ANNs), and multiple curve resolution methods (MCR-ALS, N-PLS and PARAFAC). This review aims to provide the practising analyst with a broad guide to electroanalytical applications supported by chemometrics. In this context, after a general consideration of the use of a number of electroanalytical techniques with the aid of chemometrics methods, several overviews follow with each one focusing on an important field of application such as food, pharmaceuticals, pesticides and the environment. The growth of chemometrics in conjunction with electronic tongue and nose sensors is highlighted, and this is followed by an overview of the use of chemometrics for the resolution of complicated profiles for qualitative identification of analytes, especially with the use of the MCR-ALS methodology. Finally, the performance of electroanalytical methods is compared with that of some spectrophotometric procedures on the basis of figures-of-merit. This showed that electroanalytical methods can perform as well as the spectrophotometric ones. PLS-1 appears to be the method of practical choice if the %relative prediction error of not, vert, similar±10% is acceptable.

Small molecule–biopolymer interactions : Ultraviolet–visible and fluorescence spectroscopy and chemometrics

Interactions between small molecules with biopolymers e.g. the bovine serum albumin (BSA protein), are important, and significant information is recorded in the UV–vis and fluorescence spectra of their reaction mixtures. The extraction of this information is difficult conventionally and principally because there is significant overlapping of the spectra of the three analytes in the mixture. The interaction of berberine chloride (BC) and the BSA protein provides an interesting example of such complex systems. UV–vis and fluorescence spectra of BC and BSA mixtures were investigated in pH 7.4 Tris–HCl buffer at 37 °C. Two sample series were measured by each technique: (1) [BSA] was kept constant and the [BC] was varied and (2) [BC] was kept constant and the [BSA] was varied. This produced four spectral data matrices, which were combined into one expanded spectral matrix. This was processed by the multivariate curve resolution–alternating least squares method (MCR–ALS). The results produced: (1) the extracted pure BC, BSA and the BC–BSA complex spectra from the measured heavily overlapping composite responses, (2) the concentration profiles of BC, BSA and the BC–BSA complex, which are difficult to obtain by conventional means, and (3) estimates of the number of binding sites of BC.

Simultaneous determination of three synthetic glucocorticoids by differential pulse stripping voltammetry with the aid of chemometrics

A novel voltammetric method for simultaneous determination of the glucocorticoid residues prednisone, prednisolone, and dexamethasone was developed. All three compounds were reduced at a mercury electrode in a Britton-Robinson buffer (pH 3.78), and well-defined voltammetric waves were observed. However, the voltammograms of these three compounds overlapped seriously and showed nonlinear character, and thus, it was difficult to analyze the compounds individually in their mixtures. In this work, two chemometrics methods, principal component regression (PCR) and partial least squares (PLS), were applied to resolve the overlapped voltammograms, and the calibration models were established for simultaneous determination of these compounds. Under the optimum experimental conditions, the limits of detection (LOD) were 5.6, 8.3, and 16.8 µg l-1 for prednisone, prednisolone, and dexamethasone, respectively. The proposed method was also applied for the determination of these glucocorticoid residues in the rabbit plasma and human urine samples with satisfactory results.

A differential kinetic spectrophotometric method for determination of three sulphanilamide artificial sweeteners with the aid of chemometrics

A simple and sensitive spectrophotometric method for the simultaneous determination of acesulfame-K, sodium cyclamate and saccharin sodium sweeteners in foodstuff samples has been researched and developed. This analytical method relies on the different kinetic rates of the analytes in their oxidative reaction with KMnO4 to produce the green manganate product in an alkaline solution. As the kinetic rates of acesulfame-K, sodium cyclamate and saccharin sodium were similar and their kinetic data seriously overlapped, chemometrics methods, such as partial least squares (PLS), principal component regression (PCR) and classical least squares (CLS), were applied to resolve the kinetic data. The results showed that the PLS prediction model performed somewhat better. The proposed method was then applied for the determination of the three sweeteners in foodstuff samples, and the results compared well with those obtained by the reference HPLC method.

Simultaneous kinetic-spectrophotometric determination of maltol and ethyl maltol in food samples by using chemometrics

A fast and accurate procedure has been researched and developed for the simultaneous determination of maltol and ethyl maltol, based on their reaction with iron(III) in the presence of o-phenanthroline in sulfuric acid medium. This reaction was the basis for an indirect kinetic spectrophotometric method, which followed the development of the pink ferroin product (λmax = 524 nm). The kinetic data were collected in the 370–900 nm range over 0–30 s. The optimized method indicates that individual analytes followed Beer’s law in the concentration range of 4.0–76.0 mg L−1 for both maltol and ethyl maltol. The LOD values of 1.6 mg L−1 for maltol and 1.4 mg L−1 for ethyl maltol agree well with those obtained by the alternative high performance liquid chromatography with ultraviolet detection (HPLC-UV). Three chemometrics methods, principal component regression (PCR), partial least squares (PLS) and principal component analysis–radial basis function–artificial neural networks (PC–RBF–ANN), were used to resolve the measured data with small kinetic differences between the two analytes as reflected by the development of the pink ferroin product. All three performed satisfactorily in the case of the synthetic verification samples, and in their application for the prediction of the analytes in several food products. The figures of merit for the analytes based on the multivariate models agreed well with those from the alternative HPLC-UV method involving the same samples.