New exact solutions for Hele-Shaw flow in doubly connected regions

Radial Hele-Shaw flows are treated analytically using conformal mapping techniques. The geometry of interest has a doubly-connected annular region of viscous fluid surrounding an inviscid bubble that is either expanding or contracting due to a pressure difference caused by injection or suction of the inviscid fluid. The zero-surface-tension problem is ill-posed for both bubble expansion and contraction, as both scenarios involve viscous fluid displacing inviscid fluid. Exact solutions are derived by tracking the location of singularities and critical points in the analytic continuation of the mapping function. We show that by treating the critical points, it is easy to observe finite-time blow-up, and the evolution equations may be written in exact form using complex residues. We present solutions that start with cusps on one interface and end with cusps on the other, as well as solutions that have the bubble contracting to a point. For the latter solutions, the bubble approaches an ellipse in shape at extinction.

Optimising container processes at multimodal seaport terminals : an integrated approach and application

A Multimodal Seaport Container Terminal (MSCT) is a complex system which requires careful planning and control in order to operate efficiently. It consists of a number of subsystems that require optimisation of the operations within them, as well as synchronisation of machines and containers between the various subsystems. Inefficiency in the terminal can delay ships from their scheduled timetables, as well as cause delays in delivering containers to their inland destinations, both of which can be very costly to their operators. The purpose of this PhD thesis is to use Operations Research methodologies to optimise and synchronise these subsystems as an integrated application. An initial model is developed for the overall MSCT; however, due to a large number of assumptions that had to be made, as well as other issues, it is found to be too inaccurate and infeasible for practical use. Instead, a method of developing models for each subsystem is proposed that then be integrated with each other. Mathematical models are developed for the Storage Area System (SAS) and Intra-terminal Transportation System (ITTS). The SAS deals with the movement and assignment of containers to stacks within the storage area, both when they arrive and when they are rehandled to retrieve containers below them. The ITTS deals with scheduling the movement of containers and machines between the storage areas and other sections of the terminal, such as the berth and road/rail terminals. Various constructive heuristics are explored and compared for these models to produce good initial solutions for large-sized problems, which are otherwise impractical to compute by exact methods. These initial solutions are further improved through the use of an innovative hyper-heuristic algorithm that integrates the SAS and ITTS solutions together and optimises them through meta-heuristic techniques. The method by which the two models can interact with each other as an integrated system will be discussed, as well as how this method can be extended to the other subsystems of the MSCT.

Weighted LDA techniques for I-vector based speaker verification

This paper introduces the Weighted Linear Discriminant Analysis (WLDA) technique, based upon the weighted pairwise Fisher criterion, for the purposes of improving i-vector speaker verification in the presence of high intersession variability. By taking advantage of the speaker discriminative information that is available in the distances between pairs of speakers clustered in the development i-vector space, the WLDA technique is shown to provide an improvement in speaker verification performance over traditional Linear Discriminant Analysis (LDA) approaches. A similar approach is also taken to extend the recently developed Source Normalised LDA (SNLDA) into Weighted SNLDA (WSNLDA) which, similarly, shows an improvement in speaker verification performance in both matched and mismatched enrolment/verification conditions. Based upon the results presented within this paper using the NIST 2008 Speaker Recognition Evaluation dataset, we believe that both WLDA and WSNLDA are viable as replacement techniques to improve the performance of LDA and SNLDA-based i-vector speaker verification.

The scalability and the strategy for EMR database encryption techniques

EMR (Electronic Medical Record) is an emerging technology that is highly-blended between non-IT and IT area. One methodology is to link the non-IT and IT area is to construct databases. Nowadays, it supports before and after-treatment for patients and should satisfy all stakeholders such as practitioners, nurses, researchers, administrators and financial departments and so on. In accordance with the database maintenance, DAS (Data as Service) model is one solution for outsourcing. However, there are some scalability and strategy issues when we need to plan to use DAS model properly. We constructed three kinds of databases such as plan-text, MS built-in encryption which is in-house model and custom AES (Advanced Encryption Standard) - DAS model scaling from 5K to 2560K records. To perform custom AES-DAS better, we also devised Bucket Index using Bloom Filter. The simulation showed the response times arithmetically increased in the beginning but after a certain threshold, exponentially increased in the end. In conclusion, if the database model is close to in-house model, then vendor technology is a good way to perform and get query response times in a consistent manner. If the model is DAS model, it is easy to outsource the database, however, some techniques like Bucket Index enhances its utilization. To get faster query response times, designing database such as consideration of the field type is also important. This study suggests cloud computing would be a next DAS model to satisfy the scalability and the security issues.

Scalability of encryption techniques for electronic health record (EHR) retrieval

Electronic Health Record (EHR) retrieval processes are complex demanding Information Technology (IT) resources exponentially in particular memory usage. Database-as-a-service (DAS) model approach is proposed to meet the scalability factor of EHR retrieval processes. A simulation study using ranged of EHR records with DAS model was presented. The bucket-indexing model incorporated partitioning fields and bloom filters in a Singleton design pattern were used to implement custom database encryption system. It effectively provided faster responses in the range query compared to different types of queries used such as aggregation queries among the DAS, built-in encryption and the plain-text DBMS. The study also presented with constraints around the approach should consider for other practical applications.

Meeting under the “Omei” Tree in the Torres Strait Islands : networks and funds of knowledge of mathematical ideas

This paper focuses on the turning point experiences that worked to transform the researcher during a preliminary consultation process to seek permission to conduct of a small pilot project on one Torres Strait Island. The project aimed to learn from parents how they support their children in their mathematics learning. Drawing on a community research design, a consultative meeting was held with one Torres Strait Islander community to discuss the possibility of piloting a small project that focused on working with parents and children to learn about early mathematics processes. Preliminary data indicated that parents use networks in their community. It highlighted the funds of knowledge of mathematics that exist in the community and which are used to teach their children. Such knowledges are situated within a community’s unique histories, culture and the voices of the people. “Omei” tree means the Tree of Wisdom in the Island community.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Damage quantification techniques in acoustic emission monitoring

Acoustic emission (AE) analysis is one of the several diagnostic techniques available nowadays for structural health monitoring (SHM) of engineering structures. Some of its advantages over other techniques include high sensitivity to crack growth and capability of monitoring a structure in real time. The phenomenon of rapid release of energy within a material by crack initiation or growth in form of stress waves is known as acoustic emission (AE). In AE technique, these stress waves are recorded by means of suitable sensors placed on the surface of a structure. Recorded signals are subsequently analysed to gather information about the nature of the source. By enabling early detection of crack growth, AE technique helps in planning timely retrofitting or other maintenance jobs or even replacement of the structure if required. In spite of being a promising tool, some challenges do still exist behind the successful application of AE technique. Large amount of data is generated during AE testing, hence effective data analysis is necessary, especially for long term monitoring uses. Appropriate analysis of AE data for quantification of damage level is an area that has received considerable attention. Various approaches available for damage quantification for severity assessment are discussed in this paper, with special focus on civil infrastructure such as bridges. One method called improved b-value analysis is used to analyse data collected from laboratory testing.

Improving trust and securing data accessibility for e-health decision making by using data encryption techniques

In the medical and healthcare arena, patients‟ data is not just their own personal history but also a valuable large dataset for finding solutions for diseases. While electronic medical records are becoming popular and are used in healthcare work places like hospitals, as well as insurance companies, and by major stakeholders such as physicians and their patients, the accessibility of such information should be dealt with in a way that preserves privacy and security. Thus, finding the best way to keep the data secure has become an important issue in the area of database security. Sensitive medical data should be encrypted in databases. There are many encryption/ decryption techniques and algorithms with regard to preserving privacy and security. Currently their performance is an important factor while the medical data is being managed in databases. Another important factor is that the stakeholders should decide more cost-effective ways to reduce the total cost of ownership. As an alternative, DAS (Data as Service) is a popular outsourcing model to satisfy the cost-effectiveness but it takes a consideration that the encryption/ decryption modules needs to be handled by trustworthy stakeholders. This research project is focusing on the query response times in a DAS model (AES-DAS) and analyses the comparison between the outsourcing model and the in-house model which incorporates Microsoft built-in encryption scheme in a SQL Server. This research project includes building a prototype of medical database schemas. There are 2 types of simulations to carry out the project. The first stage includes 6 databases in order to carry out simulations to measure the performance between plain-text, Microsoft built-in encryption and AES-DAS (Data as Service). Particularly, the AES-DAS incorporates implementations of symmetric key encryption such as AES (Advanced Encryption Standard) and a Bucket indexing processor using Bloom filter. The results are categorised such as character type, numeric type, range queries, range queries using Bucket Index and aggregate queries. The second stage takes the scalability test from 5K to 2560K records. The main result of these simulations is that particularly as an outsourcing model, AES-DAS using the Bucket index shows around 3.32 times faster than a normal AES-DAS under the 70 partitions and 10K record-sized databases. Retrieving Numeric typed data takes shorter time than Character typed data in AES-DAS. The aggregation query response time in AES-DAS is not as consistent as that in MS built-in encryption scheme. The scalability test shows that the DBMS reaches in a certain threshold; the query response time becomes rapidly slower. However, there is more to investigate in order to bring about other outcomes and to construct a secured EMR (Electronic Medical Record) more efficiently from these simulations.

A new approach to automatically producing schedules for cane railways

The scheduling of locomotive movements on cane railways has proven to be a very complex task. Various optimisation methods have been used over the years to try and produce an optimised schedule that eliminates or minimises bin supply delays to harvesters and the factory, while minimising the number of locomotives, locomotive shifts and cane bins, and also the cane age. This paper reports on a new attempt to develop an automatic scheduler using a mathematical model solved using mixed integer programming and constraint programming approaches and blocking parallel job shop scheduling fundamentals. The model solution has been explored using conventional constraint programming search techniques and found to produce a reasonable schedule for small-scale problems with up to nine harvesters. While more effort is required to complete the development of the full model with metaheuristic search techniques, the work completed to date gives confidence that the metaheuristic techniques will provide near optimal solutions in reasonable time.

PLDA based speaker verification with weighted LDA techniques

This paper investigates the use of the dimensionality-reduction techniques weighted linear discriminant analysis (WLDA), and weighted median fisher discriminant analysis (WMFD), before probabilistic linear discriminant analysis (PLDA) modeling for the purpose of improving speaker verification performance in the presence of high inter-session variability. Recently it was shown that WLDA techniques can provide improvement over traditional linear discriminant analysis (LDA) for channel compensation in i-vector based speaker verification systems. We show in this paper that the speaker discriminative information that is available in the distance between pair of speakers clustered in the development i-vector space can also be exploited in heavy-tailed PLDA modeling by using the weighted discriminant approaches prior to PLDA modeling. Based upon the results presented within this paper using the NIST 2008 Speaker Recognition Evaluation dataset, we believe that WLDA and WMFD projections before PLDA modeling can provide an improved approach when compared to uncompensated PLDA modeling for i-vector based speaker verification systems.

Navigational safety in port waters: Techniques for modeling collision risk

Navigational collisions are one of the major safety concerns for many seaports. Continuing growth of shipping traffic in number and sizes is likely to result in increased number of traffic movements, which consequently could result higher risk of collisions in these restricted waters. This continually increasing safety concern warrants a comprehensive technique for modeling collision risk in port waters, particularly for modeling the probability of collision events and the associated consequences (i.e., injuries and fatalities). A number of techniques have been utilized for modeling the risk qualitatively, semi-quantitatively and quantitatively. These traditional techniques mostly rely on historical collision data, often in conjunction with expert judgments. However, these techniques are hampered by several shortcomings, such as randomness and rarity of collision occurrence leading to obtaining insufficient number of collision counts for a sound statistical analysis, insufficiency in explaining collision causation, and reactive approach to safety. A promising alternative approach that overcomes these shortcomings is the navigational traffic conflict technique (NTCT), which uses traffic conflicts as an alternative to the collisions for modeling the probability of collision events quantitatively. This article explores the existing techniques for modeling collision risk in port waters. In particular, it identifies the advantages and limitations of the traditional techniques and highlights the potentials of the NTCT in overcoming the limitations. In view of the principles of the NTCT, a structured method for managing collision risk is proposed. This risk management method allows safety analysts to diagnose safety deficiencies in a proactive manner, which consequently has great potential for managing collision risk in a fast, reliable and efficient manner.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.