Using interior point algorithms for the solution of linear programs with special structural features

Linear Programming (LP) is a powerful decision making tool extensively used in various economic and engineering activities. In the early stages the success of LP was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is reported here. The preconditional conjugate gradient method is one of the most powerful tools for the solution of the least square problem, present in every iteration of all interior point methods. The effect of using different preconditioners on a range of problems with various condition numbers is presented. Decomposition algorithms has been one of the main fields of research in linear programming over the last few years. After reviewing the latest decomposition techniques, three promising methods were chosen the implemented. Sparsity is again a consideration and suggestions have been included to allow improvements when solving problems with these methods. Finally, experimental results on randomly generated data are reported and compared with an interior point method. The efficient implementation of the decomposition methods considered in this study requires the solution of quadratic subproblems. A review of recent work on algorithms for convex quadratic was performed. The most promising algorithms are discussed and implemented taking sparsity into account. The related performance of these algorithms on randomly generated separable and non-separable problems is also reported.

System identification of linear vibrating structures

Methods of dynamic modelling and analysis of structures, for example the finite element method, are well developed. However, it is generally agreed that accurate modelling of complex structures is difficult and for critical applications it is necessary to validate or update the theoretical models using data measured from actual structures. The techniques of identifying the parameters of linear dynamic models using Vibration test data have attracted considerable interest recently. However, no method has received a general acceptance due to a number of difficulties. These difficulties are mainly due to (i) Incomplete number of Vibration modes that can be excited and measured, (ii) Incomplete number of coordinates that can be measured, (iii) Inaccuracy in the experimental data (iv) Inaccuracy in the model structure. This thesis reports on a new approach to update the parameters of a finite element model as well as a lumped parameter model with a diagonal mass matrix. The structure and its theoretical model are equally perturbed by adding mass or stiffness and the incomplete number of eigen-data is measured. The parameters are then identified by an iterative updating of the initial estimates, by sensitivity analysis, using eigenvalues or both eigenvalues and eigenvectors of the structure before and after perturbation. It is shown that with a suitable choice of the perturbing coordinates exact parameters can be identified if the data and the model structure are exact. The theoretical basis of the technique is presented. To cope with measurement errors and possible inaccuracies in the model structure, a well known Bayesian approach is used to minimize the least squares difference between the updated and the initial parameters. The eigen-data of the structure with added mass or stiffness is also determined using the frequency response data of the unmodified structure by a structural modification technique. Thus, mass or stiffness do not have to be added physically. The mass-stiffness addition technique is demonstrated by simulation examples and Laboratory experiments on beams and an H-frame.

Cortical activity during rotational and linear transformations

Neuroimaging studies of cortical activation during image transformation tasks have shown that mental rotation may rely on similar brain regions as those underlying visual perceptual mechanisms. The V5 complex, which is specialised for visual motion, is one region that has been implicated. We used functional magnetic resonance imaging (fMRI) to investigate rotational and linear transformation of stimuli. Areas of significant brain activation were identified for each of the primary mental transformation tasks in contrast to its own perceptual reference task which was cognitively matched in all respects except for the variable of interest. Analysis of group data for perception of rotational and linear motion showed activation in areas corresponding to V5 as defined in earlier studies. Both rotational and linear mental transformations activated Brodman Area (BA) 19 but did not activate V5. An area within the inferior temporal gyrus, representing an inferior satellite area of V5, was activated by both the rotational perception and rotational transformation tasks, but showed no activation in response to linear motion perception or transformation. The findings demonstrate the extent to which neural substrates for image transformation and perception overlap and are distinct as well as revealing functional specialisation within perception and transformation processing systems.

A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples. ACM Computing Classification System (1998): G.1.3.

In vitro studies of drug transformations: application to forensic toxicology

The forensic toxicologist faces challenges in the detection of drugs and poisons in biological samples due to transformations which occur both during life and after death. For example, changes can result from drug metabolism during life or from the use of formalin solution for post mortem embalming purposes. The former requires the identification of drug metabolites and the latter the identification of chemical reaction products in order to know which substances had been administered. The work described in this thesis was aimed at providing ways of tackling these challenges and was divided into two parts. Part 1 investigated the use of in vitro drug metabolism by human liver microsomes (HLM) to obtain information on drug metabolites and Part 2 investigated the chemical reactions of drugs and a carbamate pesticide with formalin solution and formalin-blood. The initial aim of part I was to develop an in vitro metabolism method using HLM, based on a literature review of previous studies of this type. MDMA was chosen as a model compound to develop the HLM method because its metabolism was known and standards of its metabolites were commercially available. In addition, a sensitive and selective method was developed for the identification and quantitation of hydrophilic phase I drug metabolites using LC/MS/MS with a conventional reverse-phase (C18) column. In order to obtain suitable retention factors for polar drug metabolites on this column, acetyl derivatives were evaluated for converting the metabolites to more lipophilic compounds and an optimal separation system was developed. Acetate derivatives were found to be stable in the HPLC mobile phase and to provide good chromatographic separation of the target analytes. In vitro metabolism of MDMA and, subsequently, of other drugs involved incubation of 4 µg drug substance in pH 7.4 buffer with an NADPH generating system (NGS) at 37oC for 90 min with addition of more NGS after 30 min. The reaction was stopped at 90 min by the addition of acetonitrile before extraction of the metabolites. Acetate derivatives of MDMA metabolites were identified by LC/MS/MS using multiple reaction monitoring (MRM). Three phase I metabolites (both major and minor metabolites) of MDMA were detected in HLM samples. 3,4-dihydroxy-methamphetamine and 4-hydroxy-3-methoxymethamphetamine were found to be major metabolites of MDMA whereas 3,4-methylenedioxyamphetamine was found to be a minor metabolite. Subsequently, ten MDMA positive urines were analysed to compare the metabolite patterns with those produced by HLM. An LC/MS method for MDMA and its metabolites in urine samples was developed and validated. The method demonstrated good linearity, accuracy and precision and insignificant matrix effects, with limits of quantitation of 0.025 µg/ml. Moreover, derivatives of MDMA and its metabolites were quantified in all 10 positive human urine samples. The urine metabolite pattern was found to be similar to that from HLM. The second aim of Part 1 was to use the HLM system to study the metabolism of some new psychoactive substances, whose misuse worldwide has necessitated the development of analytical methods for these drugs in biological specimens. Methylone and butylone were selected as representative cathinones and para-methoxyamphetamine (PMA) was chosen as a representative ring-substituted amphetamine, because of the involvement of these drugs in recent drug-related deaths, because of a relative lack of information on their metabolism, and because reference standards of their metabolites were not commercially available. An LC/MS/MS method for the analysis of methylone, butylone, PMA and their metabolites was developed. Three phase I metabolites of methylone and butylone were detected in HLM samples. Ketone reduction to β-OH metabolites and demethylenation to dihydroxy-metabolites were found to be major phase I metabolic pathways of butylone and methylone whereas N-demethylation to nor-methylone and nor-butylone were found to be minor pathways. Also, demethylation to para-hydroxyamphetamine was found to be a major phase I metabolic pathway of PMA whereas β-hydroxylation to β-OH-PMA was found to be a minor pathway. Formaldehyde is used for embalming, to reduce decomposition and preserve cadavers, especially in tropical countries such as Thailand. Drugs present in the body can be exposed to formaldehyde resulting in decreasing concentrations of the original compounds and production of new substances. The aim of part II of the study was to evaluate the in vitro reactions of formaldehyde with selected drug groups including amphetamines (amphetamine, methamphetamine and MDMA), benzodiazepines (alprazolam and diazepam), opiates (morphine, hydromorphone, codeine and hydrocodone) and with a carbamate insecticide (carbosulfan). The study would identify degradation products to serve as markers for the parent compounds when these were no longer detectable. Drugs standards were spiked in 10% formalin solution and 10% formalin blood. Water and whole blood without formalin were used for controls. Samples were analysed by LC/MS/MS at different times from the start, over periods of up to 30 days. Amphetamine, methamphetamine and MDMA were found to rapidly convert to methamphetamine, DMA and MDDMA respectively, in both formalin solution and formalin blood, confirming the Eschweiler-Clarke reaction between amine-containing compounds and formaldehyde. Alprazolam was found to be unstable whereas diazepam was found to be stable in both formalin solution and water. Both were found to hydrolyse in formalin solution and to give open-ring alprazolam and open-ring diazepam. Other alprazolam conversion products attached to paraformaldehyde were detected in both formalin solution and formalin blood. Morphine and codeine were found to be more stable than hydromorphone and hydrocodone in formalin solution. Conversion products of hydromorphone and hydrocodone attached to paraformaldehyde were tentatively identified in formalin solution. Moreover, hydrocodone and hydromorphone rapidly decreased within 24 h in formalin blood and could not be detected after 7 days. Carbosulfan was found to be unstable in formalin solution and was rapidly hydrolysed within 24 h, whereas in water it was stable up to 48 h. Carbofuran was the major degradation product, plus smaller amounts of other products, 3-ketocarbofuran and 3-hydrocarbofuran. By contrast, carbosulfan slowly hydrolysed in formalin-blood and was still detected after 15 days. It was concluded that HLM provide a useful tool for human drug metabolism studies when ethical considerations preclude their controlled administration to humans. The use of chemical derivatisation for hydrophilic compounds such as polar drug metabolites for analysis by LC/MS/MS with a conventional C18 column is effective and inexpensive, and suitable for routine use in the identification and quantitation of drugs and their metabolites. The detection of parent drugs and their metabolites or conversion and decomposition products is potentially very useful for the interpretation of cases in forensic toxicology, especially when the original compounds cannot be observed.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

Study on the method of freeway incident detection using wireless positioning terminal

Improving the performance of a incident detection system was essential to minimize the effect of incidents. A new method of incident detection was brought forward in this paper based on an in-car terminal which consisted of GPS module, GSM module and control module as well as some optional parts such as airbag sensors, mobile phone positioning system (MPPS) module, etc. When a driver or vehicle discovered the freeway incident and initiated an alarm report the incident location information located by GPS, MPPS or both would be automatically send to a transport management center (TMC), then the TMC would confirm the accident with a closed-circuit television (CCTV) or other approaches. In this method, detection rate (DR), time to detect (TTD) and false alarm rate (FAR) were more important performance targets. Finally, some feasible means such as management mode, education mode and suitable accident confirming approaches had been put forward to improve these targets.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

A method of lines approach for modelling saltwater intrusion in coastal aquifiers

The equations governing saltwater intrusion in coastal aquifers are complex. Backward Euler time stepping approaches are often used to advance the solution to these equations in time, which typically requires that small time steps be taken in order to ensure that an accurate solution is obtained. We show that a method of lines approach incorporating variable order backward differentiation formulas can greatly improve the efficiency of the time stepping process.

Moderating drinking by correspondence : an evaluation of a new method of intervention

Recognizing the need to offer alternative methods of brief interventions, this study developed correspondence treatments for low-dependent problem drinkers and evaluated their impact. One hundred and twenty-one problem drinkers were recruited by media advertisements and were randomly allocated to a full cognitive behavioural treatment programme (CBT) or to a minimal intervention condition (MI) that gave information regarding alcohol misuse and instructions to record drinking. As predicted, CBT was more effective than MI in reducing alcohol consumption over the 4-month controlled trial period. CBT produced a 50% fall in consumption, bringing the average intake of subjects within recommended maximum levels. Treatment gains at 6 months were well maintained to 12 months. High levels of consumer satisfaction, a high representation of women and a substantial participation from isolated rural areas attested to the feasibility of the correspondence programme as an alternative treatment. However, some drinking occasions still involved high intake for a significant subgroup of subjects, and this issue will be addressed in future programmes. The results supported the use of correspondence delivery as a means of promoting early engagement and equity of access between city and country areas.

A pilot study utilising cross-age peer tutoring as a method of intervention for anxious adolescents

Anxiety disorders are the most common psychopathology experienced by young people, with up to 18% of adolescents developing an anxiety disorder. The consequences of these disorders, if left untreated, include impaired peer relationships, school absenteeism and self-concept problems. In addition, anxiety disorders may play a causal role in the development of depression in young people, precede eating disorders and predispose adolescents to substance abuse disorders. While the school is often chosen as a place to provide early intervention for this debilitating disorder, the fact that excessive anxiety is often not recognised in school and that young people are reluctant to seek help, makes identifying these adolescents difficult. Even when these young people are identified, there are problems in providing sensitive programs which are not stigmatising to them within a school setting. One method which may engage this adolescent population could be cross-age peer tutoring. This paper reports on a small pilot study using the “Worrybusters” program and a cross-age peer tutoring method to engage the anxious adolescents. These anxious secondary school students planned activities for teacher-referred anxious primary school students for a term in the high school setting and then delivered those activities to the younger students weekly in the next term in the primary school. Although the secondary school students decreased their scores on anxiety self-report measures there were no significant differences for primary school students’ self-reports. However, the primary school parent reports indicated a significant decrease in their child’s anxiety.