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.

A hybrid approach to combining CART and logistic regression for stock ranking

The benefits of applying tree-based methods to the purpose of modelling financial assets as opposed to linear factor analysis are increasingly being understood by market practitioners. Tree-based models such as CART (classification and regression trees) are particularly well suited to analysing stock market data which is noisy and often contains non-linear relationships and high-order interactions. CART was originally developed in the 1980s by medical researchers disheartened by the stringent assumptions applied by traditional regression analysis (Brieman et al. [1984]). In the intervening years, CART has been successfully applied to many areas of finance such as the classification of financial distress of firms (see Frydman, Altman and Kao [1985]), asset allocation (see Sorensen, Mezrich and Miller [1996]), equity style timing (see Kao and Shumaker [1999]) and stock selection (see Sorensen, Miller and Ooi [2000])...

Modeling and multiway analysis of chatroom tensors

This work identifies the limitations of n-way data analysis techniques in multidimensional stream data, such as Internet chat room communications data, and establishes a link between data collection and performance of these techniques. Its contributions are twofold. First, it extends data analysis to multiple dimensions by constructing n-way data arrays known as high order tensors. Chat room tensors are generated by a simulator which collects and models actual communication data. The accuracy of the model is determined by the Kolmogorov-Smirnov goodness-of-fit test which compares the simulation data with the observed (real) data. Second, a detailed computational comparison is performed to test several data analysis techniques including svd [1], and multi-way techniques including Tucker1, Tucker3 [2], and Parafac [3].

The impact of construction organisations’ learning capabilities on collaborative projects

Dynamic capability theory asserts that the learning capabilities of construction organisations influence the degree to which value-for-money (VfM) is achieved on collaborative projects. However, there has been little study conducted to verify this relationship. The evidence is particularly limited within the empirical context of infrastructure delivery in Australia. Primarily drawing on the theoretical perspectives of the resource-based view of the firm (e.g. Barney 1991), dynamic capabilities (e.g. Helfat et al. 2007), absorptive capacity (e.g. Lane et al. 2006) and knowledge management (e.g. Nonaka 1994), this paper conceptualises learning capability as a knowledge-based dynamic capability. Learning capability builds on the micro-foundations of high-order learning routines, which are deliberately developed by construction organisations for managing collaborative projects. Based on this conceptualisation of learning capability, an exploratory case study was conducted. The study investigated the operational and higher-order learning routines adopted by a project alliance team to successfully achieve VfM. The case study demonstrated that the learning routines of the alliance project were developed and modified by the continual joint learning activities of participant organisations. Project-level learning routines were found to significantly influence the development of organisational-level learning routines. In turn, the learning outcomes generated from the alliance project appeared to significantly influence the development of project management routines and contractual arrangements applied by the participant organisations in subsequent collaborative projects. The case study findings imply that the higher-order learning routines that underpin the learning capability of construction organisations have the potential to influence the VfM achieved on both current and future collaborative projects.

A threshold analysis of dengue transmission in terms of weather variables and imported dengue cases in Australia

Dengue virus (DENV) transmission in Australia is driven by weather factors and imported dengue fever (DF) cases. However, uncertainty remains regarding the threshold effects of high-order interactions among weather factors and imported DF cases and the impact of these factors on autochthonous DF. A time-series regression tree model was used to assess the threshold effects of natural temporal variations of weekly weather factors and weekly imported DF cases in relation to incidence of weekly autochthonous DF from 1 January 2000 to 31 December 2009 in Townsville and Cairns, Australia. In Cairns, mean weekly autochthonous DF incidence increased 16.3-fold when the 3-week lagged moving average maximum temperature was <32 °C, the 4-week lagged moving average minimum temperature was ≥24 °C and the sum of imported DF cases in the previous 2 weeks was >0. When the 3-week lagged moving average maximum temperature was ≥32 °C and the other two conditions mentioned above remained the same, mean weekly autochthonous DF incidence only increased 4.6-fold. In Townsville, the mean weekly incidence of autochthonous DF increased 10-fold when 3-week lagged moving average rainfall was ≥27 mm, but it only increased 1.8-fold when rainfall was <27 mm during January to June. Thus, we found different responses of autochthonous DF incidence to weather factors and imported DF cases in Townsville and Cairns. Imported DF cases may also trigger and enhance local outbreaks under favorable climate conditions.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

A sub‒domain smoothed Galerkin method for solid mechanics problems

A sub‒domain smoothed Galerkin method is proposed to integrate the advantages of mesh‒free Galerkin method and FEM. Arbitrarily shaped sub‒domains are predefined in problems domain with mesh‒free nodes. In each sub‒domain, based on mesh‒free Galerkin weak formulation, the local discrete equation can be obtained by using the moving Kriging interpolation, which is similar to the discretization of the high‒order finite elements. Strain smoothing technique is subsequently applied to the nodal integration of sub‒domain by dividing the sub‒domain into several smoothing cells. Moreover, condensation of DOF can also be introduced into the local discrete equations to improve the computational efficiency. The global governing equations of present method are obtained on the basis of the scheme of FEM by assembling all local discrete equations of the sub‒domains. The mesh‒free properties of Galerkin method are retained in each sub‒domain. Several 2D elastic problems have been solved on the basis of this newly proposed method to validate its computational performance. These numerical examples proved that the newly proposed sub‒domain smoothed Galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency, good accuracy, and convergence.

Facilitating query decomposition in query language modeling by association rule mining using multiple sliding windows

This paper presents a novel framework to further advance the recent trend of using query decomposition and high-order term relationships in query language modeling, which takes into account terms implicitly associated with different subsets of query terms. Existing approaches, most remarkably the language model based on the Information Flow method are however unable to capture multiple levels of associations and also suffer from a high computational overhead. In this paper, we propose to compute association rules from pseudo feedback documents that are segmented into variable length chunks via multiple sliding windows of different sizes. Extensive experiments have been conducted on various TREC collections and our approach significantly outperforms a baseline Query Likelihood language model, the Relevance Model and the Information Flow model.

Controller synthesis of a bidirectional inductive power interface for electric vehicles

Bidirectional Inductive Power Transfer (IPT) systems are preferred for Vehicle-to-Grid (V2G) applications. Typically, bidirectional IPT systems consist of high order resonant networks, and therefore, the control of bidirectional IPT systems has always been a difficulty. To date several different controllers have been reported, but these have been designed using steady-state models, which invariably, are incapable of providing an accurate insight into the dynamic behaviour of the system A dynamic state-space model of a bidirectional IPT system has been reported. However, currently this model has not been used to optimise the design of controllers. Therefore, this paper proposes an optimised controller based on the dynamic model. To verify the operation of the proposed controller simulated results of the optimised controller and simulated results of another controller are compared. Results indicate that the proposed controller is capable of accurately and stably controlling the power flow in a bidirectional IPT system.

Topological localization using optical flow descriptors

We propose a topological localization method based on optical flow information. We analyse the statistical characteristics of the optical flow signal and demonstrate that the flow vectors can be used to identify and describe key locations in the environment. The key locations (nodes) correspond to significant scene changes and depth discontinuities. Since optical flow vectors contain position, magnitude and angle information, for each node, we extract low and high order statistical moments of the vectors and use them as descriptors for that node. Once a database of nodes and their corresponding optical flow features is created, the robot can perform topological localization by using the Mahalanobis distance between the current frame and the database. This is supported by field trials, which illustrate the repeatability of the proposed method for detecting and describing key locations in indoor and outdoor environments in challenging and diverse lighting conditions.

Text mining with semantic annotation : using enriched text representation for entity-oriented retrieval, semantic relation identification and text clustering

This project is a step forward in the study of text mining where enhanced text representation with semantic information plays a significant role. It develops effective methods of entity-oriented retrieval, semantic relation identification and text clustering utilizing semantically annotated data. These methods are based on enriched text representation generated by introducing semantic information extracted from Wikipedia into the input text data. The proposed methods are evaluated against several start-of-art benchmarking methods on real-life data-sets. In particular, this thesis improves the performance of entity-oriented retrieval, identifies different lexical forms for an entity relation and handles clustering documents with multiple feature spaces.

Robust clustering of multi-type relational data via a heterogeneous manifold ensemble

High-Order Co-Clustering (HOCC) methods have attracted high attention in recent years because of their ability to cluster multiple types of objects simultaneously using all available information. During the clustering process, HOCC methods exploit object co-occurrence information, i.e., inter-type relationships amongst different types of objects as well as object affinity information, i.e., intra-type relationships amongst the same types of objects. However, it is difficult to learn accurate intra-type relationships in the presence of noise and outliers. Existing HOCC methods consider the p nearest neighbours based on Euclidean distance for the intra-type relationships, which leads to incomplete and inaccurate intra-type relationships. In this paper, we propose a novel HOCC method that incorporates multiple subspace learning with a heterogeneous manifold ensemble to learn complete and accurate intra-type relationships. Multiple subspace learning reconstructs the similarity between any pair of objects that belong to the same subspace. The heterogeneous manifold ensemble is created based on two-types of intra-type relationships learnt using p-nearest-neighbour graph and multiple subspaces learning. Moreover, in order to make sure the robustness of clustering process, we introduce a sparse error matrix into matrix decomposition and develop a novel iterative algorithm. Empirical experiments show that the proposed method achieves improved results over the state-of-art HOCC methods for FScore and NMI.

An improved computational method in structural dynamics

Purpose – In structural, earthquake and aeronautical engineering and mechanical vibration, the solution of dynamic equations for a structure subjected to dynamic loading leads to a high order system of differential equations. The numerical methods are usually used for integration when either there is dealing with discrete data or there is no analytical solution for the equations. Since the numerical methods with more accuracy and stability give more accurate results in structural responses, there is a need to improve the existing methods or develop new ones. The paper aims to discuss these issues. Design/methodology/approach – In this paper, a new time integration method is proposed mathematically and numerically, which is accordingly applied to single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. Finally, the results are compared to the existing methods such as Newmark’s method and closed form solution. Findings – It is concluded that, in the proposed method, the data variance of each set of structural responses such as displacement, velocity, or acceleration in different time steps is less than those in Newmark’s method, and the proposed method is more accurate and stable than Newmark’s method and is capable of analyzing the structure at fewer numbers of iteration or computation cycles, hence less time-consuming. Originality/value – A new mathematical and numerical time integration method is proposed for the computation of structural responses with higher accuracy and stability, lower data variance, and fewer numbers of iterations for computational cycles.

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.

Generalizing the use of geographical weights in biodiversity modelling

Aim Determining how ecological processes vary across space is a major focus in ecology. Current methods that investigate such effects remain constrained by important limiting assumptions. Here we provide an extension to geographically weighted regression in which local regression and spatial weighting are used in combination. This method can be used to investigate non-stationarity and spatial-scale effects using any regression technique that can accommodate uneven weighting of observations, including machine learning. Innovation We extend the use of spatial weights to generalized linear models and boosted regression trees by using simulated data for which the results are known, and compare these local approaches with existing alternatives such as geographically weighted regression (GWR). The spatial weighting procedure (1) explained up to 80% deviance in simulated species richness, (2) optimized the normal distribution of model residuals when applied to generalized linear models versus GWR, and (3) detected nonlinear relationships and interactions between response variables and their predictors when applied to boosted regression trees. Predictor ranking changed with spatial scale, highlighting the scales at which different species–environment relationships need to be considered. Main conclusions GWR is useful for investigating spatially varying species–environment relationships. However, the use of local weights implemented in alternative modelling techniques can help detect nonlinear relationships and high-order interactions that were previously unassessed. Therefore, this method not only informs us how location and scale influence our perception of patterns and processes, it also offers a way to deal with different ecological interpretations that can emerge as different areas of spatial influence are considered during model fitting.