Series in vector spherical harmonics : an efficient tool for solution of nonlinear problems in spherical plasmas

The series expansion of the plasma fields and currents in vector spherical harmonics has been demonstrated to be an efficient technique for solution of nonlinear problems in spherically bounded plasmas. Using this technique, it is possible to describe the nonlinear plasma response to the rotating high-frequency magnetic field applied to the magnetically confined plasma sphere. The effect of the external magnetic field on the current drive and field configuration is studied. The results obtained are important for continuous current drive experiments in compact toruses. © 2000 American Institute of Physics.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

Patterns, heuristics for architectural design support: making use of evolutionary modelling in design

Software used by architectural and industrial designers – has moved from becoming a tool for drafting, towards use in verification, simulation, project management and project sharing remotely. In more advanced models, parameters for the designed object can be adjusted so a family of variations can be produced rapidly. With advances in computer aided design technology, numerous design options can now be generated and analyzed in real time. However the use of digital tools to support design as an activity is still at an early stage and has largely been limited in functionality with regard to the design process. To date, major CAD vendors have not developed an integrated tool that is able to both leverage specialized design knowledge from various discipline domains (known as expert knowledge systems) and support the creation of design alternatives that satisfy different forms of constraints. We propose that evolutionary computing and machine learning be linked with parametric design techniques to record and respond to a designer’s own way of working and design history. It is expected that this will lead to results that impact on future work on design support systems-(ergonomics and interface) as well as implicit constraint and problem definition for problems that are difficult to quantify.

Evaluation of spectral and texture features for object-based vegetation species classification using Support Vector Machines

The use of appropriate features to characterize an output class or object is critical for all classification problems. This paper evaluates the capability of several spectral and texture features for object-based vegetation classification at the species level using airborne high resolution multispectral imagery. Image-objects as the basic classification unit were generated through image segmentation. Statistical moments extracted from original spectral bands and vegetation index image are used as feature descriptors for image objects (i.e. tree crowns). Several state-of-art texture descriptors such as Gray-Level Co-Occurrence Matrix (GLCM), Local Binary Patterns (LBP) and its extensions are also extracted for comparison purpose. Support Vector Machine (SVM) is employed for classification in the object-feature space. The experimental results showed that incorporating spectral vegetation indices can improve the classification accuracy and obtained better results than in original spectral bands, and using moments of Ratio Vegetation Index obtained the highest average classification accuracy in our experiment. The experiments also indicate that the spectral moment features also outperform or can at least compare with the state-of-art texture descriptors in terms of classification accuracy.

Optimization problems for controlled mechanical systems : bridging the gap between theory and application

Mechanical control systems have become a part of our everyday life. Systems such as automobiles, robot manipulators, mobile robots, satellites, buildings with active vibration controllers and air conditioning systems, make life easier and safer, as well as help us explore the world we live in and exploit it’s available resources. In this chapter, we examine a specific example of a mechanical control system; the Autonomous Underwater Vehicle (AUV). Our contribution to the advancement of AUV research is in the area of guidance and control. We present innovative techniques to design and implement control strategies that consider the optimization of time and/or energy consumption. Recent advances in robotics, control theory, portable energy sources and automation increase our ability to create more intelligent robots, and allows us to conduct more explorations by use of autonomous vehicles. This facilitates access to higher risk areas, longer time underwater, and more efficient exploration as compared to human occupied vehicles. The use of underwater vehicles is expanding in every area of ocean science. Such vehicles are used by oceanographers, archaeologists, geologists, ocean engineers, and many others. These vehicles are designed to be agile, versatile and robust, and thus, their usage has gone from novelty to necessity for any ocean expedition.

Negative mood, implicit alcohol-related memory, and alcohol use in young adults: The moderating effect of alcohol expectancy

Objective Alcohol-related implicit (preconscious) cognitive processes are established and unique predictors of alcohol use, but most research in this area has focused on alcohol-related implicit cognition and anxiety. This study extends this work into the area of depressed mood by testing a cognitive model that combines traditional explicit (conscious and considered) beliefs, implicit alcohol-related memory associations (AMAs), and self-reported drinking behavior. Method Using a sample of 106 university students, depressed mood was manipulated using a musical mood induction procedure immediately prior to completion of implicit then explicit alcohol-related cognition measures. A bootstrapped two-group (weak/strong expectancies of negative affect and tension reduction) structural equation model was used to examine how mood changes and alcohol-related memory associations varied across groups. Results Expectancies of negative affect moderated the association of depressed mood and AMAs, but there was no such association for tension reduction expectancy. Conclusion Subtle mood changes may unconsciously trigger alcohol-related memories in vulnerable individuals. Results have implications for addressing subtle fluctuations in depressed mood among young adults at risk of alcohol problems.

Improving matching process in social network using implicit and explicit user information

Personalised social matching systems can be seen as recommender systems that recommend people to others in the social networks. However, with the rapid growth of users in social networks and the information that a social matching system requires about the users, recommender system techniques have become insufficiently adept at matching users in social networks. This paper presents a hybrid social matching system that takes advantage of both collaborative and content-based concepts of recommendation. The clustering technique is used to reduce the number of users that the matching system needs to consider and to overcome other problems from which social matching systems suffer, such as cold start problem due to the absence of implicit information about a new user. The proposed system has been evaluated on a dataset obtained from an online dating website. Empirical analysis shows that accuracy of the matching process is increased, using both user information (explicit data) and user behavior (implicit data).

Whole-proteome phylogeny of large dsDNA viruses and parvoviruses through a composition vector method related to dynamical language model

Background The vast sequence divergence among different virus groups has presented a great challenge to alignment-based analysis of virus phylogeny. Due to the problems caused by the uncertainty in alignment, existing tools for phylogenetic analysis based on multiple alignment could not be directly applied to the whole-genome comparison and phylogenomic studies of viruses. There has been a growing interest in alignment-free methods for phylogenetic analysis using complete genome data. Among the alignment-free methods, a dynamical language (DL) method proposed by our group has successfully been applied to the phylogenetic analysis of bacteria and chloroplast genomes. Results In this paper, the DL method is used to analyze the whole-proteome phylogeny of 124 large dsDNA viruses and 30 parvoviruses, two data sets with large difference in genome size. The trees from our analyses are in good agreement to the latest classification of large dsDNA viruses and parvoviruses by the International Committee on Taxonomy of Viruses (ICTV). Conclusions The present method provides a new way for recovering the phylogeny of large dsDNA viruses and parvoviruses, and also some insights on the affiliation of a number of unclassified viruses. In comparison, some alignment-free methods such as the CV Tree method can be used for recovering the phylogeny of large dsDNA viruses, but they are not suitable for resolving the phylogeny of parvoviruses with a much smaller genome size.

Implicit online learning

Online learning algorithms have recently risen to prominence due to their strong theoretical guarantees and an increasing number of practical applications for large-scale data analysis problems. In this paper, we analyze a class of online learning algorithms based on fixed potentials and nonlinearized losses, which yields algorithms with implicit update rules. We show how to efficiently compute these updates, and we prove regret bounds for the algorithms. We apply our formulation to several special cases where our approach has benefits over existing online learning methods. In particular, we provide improved algorithms and bounds for the online metric learning problem, and show improved robustness for online linear prediction problems. Results over a variety of data sets demonstrate the advantages of our framework.

Enriching XML documents clustering by using concise structure and content

With the growing number of XML documents on theWeb it becomes essential to effectively organise these XML documents in order to retrieve useful information from them. A possible solution is to apply clustering on the XML documents to discover knowledge that promotes effective data management, information retrieval and query processing. However, many issues arise in discovering knowledge from these types of semi-structured documents due to their heterogeneity and structural irregularity. Most of the existing research on clustering techniques focuses only on one feature of the XML documents, this being either their structure or their content due to scalability and complexity problems. The knowledge gained in the form of clusters based on the structure or the content is not suitable for reallife datasets. It therefore becomes essential to include both the structure and content of XML documents in order to improve the accuracy and meaning of the clustering solution. However, the inclusion of both these kinds of information in the clustering process results in a huge overhead for the underlying clustering algorithm because of the high dimensionality of the data. The overall objective of this thesis is to address these issues by: (1) proposing methods to utilise frequent pattern mining techniques to reduce the dimension; (2) developing models to effectively combine the structure and content of XML documents; and (3) utilising the proposed models in clustering. This research first determines the structural similarity in the form of frequent subtrees and then uses these frequent subtrees to represent the constrained content of the XML documents in order to determine the content similarity. A clustering framework with two types of models, implicit and explicit, is developed. The implicit model uses a Vector Space Model (VSM) to combine the structure and the content information. The explicit model uses a higher order model, namely a 3- order Tensor Space Model (TSM), to explicitly combine the structure and the content information. This thesis also proposes a novel incremental technique to decompose largesized tensor models to utilise the decomposed solution for clustering the XML documents. The proposed framework and its components were extensively evaluated on several real-life datasets exhibiting extreme characteristics to understand the usefulness of the proposed framework in real-life situations. Additionally, this research evaluates the outcome of the clustering process on the collection selection problem in the information retrieval on the Wikipedia dataset. The experimental results demonstrate that the proposed frequent pattern mining and clustering methods outperform the related state-of-the-art approaches. In particular, the proposed framework of utilising frequent structures for constraining the content shows an improvement in accuracy over content-only and structure-only clustering results. The scalability evaluation experiments conducted on large scaled datasets clearly show the strengths of the proposed methods over state-of-the-art methods. In particular, this thesis work contributes to effectively combining the structure and the content of XML documents for clustering, in order to improve the accuracy of the clustering solution. In addition, it also contributes by addressing the research gaps in frequent pattern mining to generate efficient and concise frequent subtrees with various node relationships that could be used in clustering.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

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.

Performance assessment of exponential Rosenbrock method for large systems of ODE

This paper studies time integration methods for large stiff systems of ordinary differential equations (ODEs) of the form u'(t) = g(u(t)). For such problems, implicit methods generally outperform explicit methods, since the time step is usually less restricted by stability constraints. Recently, however, explicit so-called exponential integrators have become popular for stiff problems due to their favourable stability properties. These methods use matrix-vector products involving exponential-like functions of the Jacobian matrix, which can be approximated using Krylov subspace methods that require only matrix-vector products with the Jacobian. In this paper, we implement exponential integrators of second, third and fourth order and demonstrate that they are competitive with well-established approaches based on the backward differentiation formulas and a preconditioned Newton-Krylov solution strategy.

Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.