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.

Modulation of the SHBG signalling axis

Sex hormone-binding globulin (SHBG) is a homodimeric plasma glycoprotein that is the major sex steroid carrier-protein in the bloodstream and functions also as a key regulator of steroid bioavailability within target tissues, such as the prostate. Additionally, SHBG binds to prostatic cell membranes via the putative and unidentified SHBG receptor (RSHBG), activating a signal transduction pathway implicated in stimulating both proliferation and expression of prostate specific antigen (PSA) in prostate cell lines in vitro. A yeast-two hybrid assay suggested an interaction between SHBG and kallikrein-related protease (KLK) 4, which is a serine protease implicated in the progression of prostate cancer. The potential interaction between these two proteins was investigated in this PhD thesis to determine whether SHBG is a proteolytic substrate of KLK4 and other members of the KLK family including KLK3/PSA, KLK7 and KLK14. Furthermore, the effects from SHBG proteolytic degradation on SHBG-regulated steroid bioavailability and the activation of the putative RSHBG signal transduction pathway were examined in the LNCaP prostate cancer cell line. SHBG was found to be a proteolytic substrate of the trypsin-like KLK4 and KLK14 in vitro, yielding several proteolysis fragments. Both chymotrypsin-like PSA and KLK7 displayed insignificant proteolytic activity against SHBG. The kinetic parameters of SHBG proteolysis by KLK4 and KLK14 demonstrate a strong enzyme-substrate binding capacity, possessing a Km of 1.2 ± 0.7 µM and 2.1 ± 0.6 µM respectively. The catalytic efficiencies (kcat/Km) of KLK4 and KLK14 proteolysis of SHBG were 1.6 x 104 M-1s-1 and 3.8 x 104 M-1s-1 respectively, which were comparable to parameters previously reported for peptide substrates. N-terminal sequencing of the fragments revealed cleavage near the junction of the N- and C-terminal laminin globulin-like (G-like) domains of SHBG, resulting in the division of the two globulins and ultimately the full degradation of these fragments by KLK4 and KLK14 over time. Proteolytic fragments that may retain steroid binding were rapidly degraded by both proteases, while fragments containing residues beyond the steroid binding pocket were less degraded over the same period of time. Degradation of SHBG was inhibited by the divalent metal cations calcium and zinc for KLK4, and calcium, zinc and magnesium for KLK14. The human secreted serine protease inhibitors (serpins), α1-antitrypsin and α2-antiplasmin, inhibited KLK4 and KLK14 proteolysis of SHBG; α1-antichymotrypsin inhibited KLK4 but not KLK14 activity. The inhibition by these serpins was comparable and in some cases more effective than general trypsin protease inhibitors such as aprotinin and phenylmethanesulfonyl fluoride (PMSF). The binding of 5α-dihydrotestosterone (DHT) to SHBG modulated interactions with KLK4 and KLK14. Steroid-free SHBG was more readily digested by both enzymes than DHT-bound SHBG. Moreover, a binding interaction exists between SHBG and pro-KLK4 and pro-KLK14, with DHT strengthening the binding to pro-KLK4 only. The inhibition of androgen uptake by cultured prostate cancer cells, mediated by SHBG steroid-binding, was examined to assess whether SHBG proteolysis by KLK4 and KLK14 modulated this process. Proteolytic digestion eliminated the ability of SHBG to inhibit the uptake of DHT from conditioned media into LNCaP cells. Therefore, the proteolysis of SHBG by KLK4 and KLK14 increased steroid bioavailability in vitro, leading to an increased uptake of androgens by prostate cancer cells. Interestingly, different transcriptional responses of PSA and KLK2, which are androgen-regulated genes, to DHT-bounsd SHBG treatment were observed between low and high passage number LNCaP cells (lpLNCaP and hpLNCaP respectively). HpLNCaP cells treated with DHT-bound SHBG demonstrated a significant synergistic upregulation of PSA and KLK2 above DHT or SHBG treatment alone, which is similar to previously reported downstream responses from RSHBG-mediated signaling activation. As this result was not seen in lpLNCaP cells, only hpLNCaP cells were further investigated to examine the modulation of potential RSHBG activity by KLK4 and KLK14 proteolysis of SHBG. Contrary to reported results, no increase in intracellular cAMP was observed in hpLNCaP cells when treated with SHBG in the presence and absence of either DHT or estradiol. As a result, the modulation of RSHBG-mediated signaling activation could not be determined. Finally, the identification of the RSHBG from both breast (MCF-7) and prostate cancer (LNCaP) cell lines was attempted. Fluorescently labeled peptides corresponding to the putative receptor binding domain (RBD) of SHBG were shown to be internalized by MCF-7 cells. Crosslinking of the RBD peptide to the cell surfaces of both MCF-7 and LNCaP cells, demonstrated the interaction of the peptide with several targets. These targets were then captured using RBD peptides synthesized onto a hydrophilic scaffold and analysed by mass spectrometry. The samples captured by the RBD peptide returned statistically significantly matches for cytokeratin 8, 18 and 19 as well as microtubule-actin crosslinking factor 1, which may indicate a novel interaction between SHBG and these proteins, but ultimately failed to detect a membrane receptor potentially responsible for the putative RSHBG-mediated signaling. This PhD project has reported the proteolytic processing of SHBG by two members of the kallikrein family, KLK4 and KLK14. The effect of SHBG proteolysis by KLK4 and KLK14 on RSHBG-mediated signaling activation was unable to be determined as the reported signal transduction pathway was not activated after treatment with SHBG, in combination with either DHT or estradiol. However, the digestion of SHBG by these two proteases positively regulated androgen bioavailability to prostate cancer cells in vitro. The increased uptake of androgens is deleterious in prostate cancer due to the promotion of proliferation, metastasis, invasion and the inhibition of apoptosis. The increased bioavailability of androgens, from SHBG proteolysis by KLK4 and KLK14, may therefore promote both carcinogenesis and progression of prostate cancer. Finally, this information may contribute to the development of therapeutic treatment strategies for prostate cancer by inhibiting the proteolysis of SHBG, by KLK4 and KLK14, to prevent the increased uptake of androgens by hormone-dependent cancerous tissues.

Theoretical investigation of thermal tweezers for parallel manipulation of atoms and nanoparticles on surfaces

A major focus of research in nanotechnology is the development of novel, high throughput techniques for fabrication of arbitrarily shaped surface nanostructures of sub 100 nm to atomic scale. A related pursuit is the development of simple and efficient means for parallel manipulation and redistribution of adsorbed atoms, molecules and nanoparticles on surfaces – adparticle manipulation. These techniques will be used for the manufacture of nanoscale surface supported functional devices in nanotechnologies such as quantum computing, molecular electronics and lab-on-achip, as well as for modifying surfaces to obtain novel optical, electronic, chemical, or mechanical properties. A favourable approach to formation of surface nanostructures is self-assembly. In self-assembly, nanostructures are grown by aggregation of individual adparticles that diffuse by thermally activated processes on the surface. The passive nature of this process means it is generally not suited to formation of arbitrarily shaped structures. The self-assembly of nanostructures at arbitrary positions has been demonstrated, though these have typically required a pre-patterning treatment of the surface using sophisticated techniques such as electron beam lithography. On the other hand, a parallel adparticle manipulation technique would be suited for directing the selfassembly process to occur at arbitrary positions, without the need for pre-patterning the surface. There is at present a lack of techniques for parallel manipulation and redistribution of adparticles to arbitrary positions on the surface. This is an issue that needs to be addressed since these techniques can play an important role in nanotechnology. In this thesis, we propose such a technique – thermal tweezers. In thermal tweezers, adparticles are redistributed by localised heating of the surface. This locally enhances surface diffusion of adparticles so that they rapidly diffuse away from the heated regions. Using this technique, the redistribution of adparticles to form a desired pattern is achieved by heating the surface at specific regions. In this project, we have focussed on the holographic implementation of this approach, where the surface is heated by holographic patterns of interfering pulsed laser beams. This implementation is suitable for the formation of arbitrarily shaped structures; the only condition is that the shape can be produced by holographic means. In the simplest case, the laser pulses are linearly polarised and intersect to form an interference pattern that is a modulation of intensity along a single direction. Strong optical absorption at the intensity maxima of the interference pattern results in approximately a sinusoidal variation of the surface temperature along one direction. The main aim of this research project is to investigate the feasibility of the holographic implementation of thermal tweezers as an adparticle manipulation technique. Firstly, we investigate theoretically the surface diffusion of adparticles in the presence of sinusoidal modulation of the surface temperature. Very strong redistribution of adparticles is predicted when there is strong interaction between the adparticle and the surface, and the amplitude of the temperature modulation is ~100 K. We have proposed a thin metallic film deposited on a glass substrate heated by interfering laser beams (optical wavelengths) as a means of generating very large amplitude of surface temperature modulation. Indeed, we predict theoretically by numerical solution of the thermal conduction equation that amplitude of the temperature modulation on the metallic film can be much greater than 100 K when heated by nanosecond pulses with an energy ~1 mJ. The formation of surface nanostructures of less than 100 nm in width is predicted at optical wavelengths in this implementation of thermal tweezers. Furthermore, we propose a simple extension to this technique where spatial phase shift of the temperature modulation effectively doubles or triples the resolution. At the same time, increased resolution is predicted by reducing the wavelength of the laser pulses. In addition, we present two distinctly different, computationally efficient numerical approaches for theoretical investigation of surface diffusion of interacting adparticles – the Monte Carlo Interaction Method (MCIM) and the random potential well method (RPWM). Using each of these approaches we have investigated thermal tweezers for redistribution of both strongly and weakly interacting adparticles. We have predicted that strong interactions between adparticles can increase the effectiveness of thermal tweezers, by demonstrating practically complete adparticle redistribution into the low temperature regions of the surface. This is promising from the point of view of thermal tweezers applied to directed self-assembly of nanostructures. Finally, we present a new and more efficient numerical approach to theoretical investigation of thermal tweezers of non-interacting adparticles. In this approach, the local diffusion coefficient is determined from solution of the Fokker-Planck equation. The diffusion equation is then solved numerically using the finite volume method (FVM) to directly obtain the probability density of adparticle position. We compare predictions of this approach to those of the Ermak algorithm solution of the Langevin equation, and relatively good agreement is shown at intermediate and high friction. In the low friction regime, we predict and investigate the phenomenon of ‘optimal’ friction and describe its occurrence due to very long jumps of adparticles as they diffuse from the hot regions of the surface. Future research directions, both theoretical and experimental are also discussed.

Phenyl-ring disorder in the two-dimensional hydrogen-bonded structure of the 1:1 proton-transfer salt of the diazo-dye precursor 4-(phenyldiazenyl)aniline (aniline yellow) with L-tartaric acid

The structure of the 1:1 proton-transfer compound from the reaction of L-tartaric acid with the azo-dye precursor aniline yellow [4-(phenylazo)aniline], 4-(phenyldiazenyl)anilinium hydrogen 2R,3R-tartrate C12H12N3+ . C4H6O6- has been determined at 200 K. The asymmetric unit of the compound contains two independent phenylazoanilinium cations and two hydrogen L-tartrate anions. The structure is unusual in that all four phenyl rings of both cations have identical 50% rotational disorder. The two hydrogen L-tartrate anions form independent but similar chains through head-to-tail carboxylic O--H...O~carboxyl~ hydrogen bonds [graph set C7] which are then extended into a two-dimensional hydrogen-bonded sheet structure through hydroxyl O--H...O hydrogen-bonding links. The anilinium groups of the phenyldiazenyl cations are incorporated into the sheets and also provide internal hydrogen-bonding extensions while their aromatic tails layer in the structure without significant interaction except for weak \p--\p interactions [minimum ring centroid separation, 3.844(3) \%A]. The hydrogen L-tartrate residues of both anions have the common short intramolecular hydroxyl O--H...O~carboxyl~ hydogen bonds. This work has provided a solution to the unusual disorder problem inherent in the structure of this salt as well as giving another example of the utility of the hydrogen tartrate in the generation of sheet substructures in molecular assembly processes.

The Validity of the Brief Michigan Alcohol Screening Test (bMAST) as a Problem Drinking Severity Measure

Objective: The Brief Michigan Alcoholism Screening Test (bMAST) is a 10-item test derived from the 25-item Michigan Alcoholism Screening Test (MAST). It is widely used in the assessment of alcohol dependence. In the absence of previous validation studies, the principal aim of this study was to assess the validity and reliability of the bMAST as a measure of the severity of problem drinking. Method: There were 6,594 patients (4,854 men, 1,740 women) who had been referred for alcohol-use disorders to a hospital alcohol and drug service who voluntarily participated in this study. Results: An exploratory factor analysis defined a two-factor solution, consisting of Perception of Current Drinking and Drinking Consequences factors. Structural equation modeling confirmed that the fit of a nine-item, two-factor model was superior to the original one-factor model. Concurrent validity was assessed through simultaneous administration of the Alcohol Use Disorders Identification Test (AUDIT) and associations with alcohol consumption and clinically assessed features of alcohol dependence. The two-factor bMAST model showed moderate correlations with the AUDIT. The two-factor bMAST and AUDIT were similarly associated with quantity of alcohol consumption and clinically assessed dependence severity features. No differences were observed between the existing weighted scoring system and the proposed simple scoring system. Conclusions: In this study, both the existing bMAST total score and the two-factor model identified were as effective as the AUDIT in assessing problem drinking severity. There are additional advantages of employing the two-factor bMAST in the assessment and treatment planning of patients seeking treatment for alcohol-use disorders. (J. Stud. Alcohol Drugs 68: 771-779,2007)

Initial psychometric evaluation of the Wayfinding Effectiveness Scale

This study evaluates three versions of the Wayfinding Effectiveness Scale (WES), developed to differentiate problems of wayfinding and wandering behavior of community-residing elders with dementia (EWD), in 266 dyads (EWD and caregiver) recruited from Alzheimer's Association chapters. Factor analyses yield a five-factor solution (explained variance = 62.6%): complex wayfinding goals, analytic strategies, global strategies, simple wayfinding goals, and being stimulus bound. Overall, internal consistencies are high: WES (.94-.95), and subscales are stable across all versions. Testretest reliability is acceptable for the overall WES and two subscales (complex and simple wayfinding goals) for the care recipient current behavior version. Construct validity is supported by the pattern of correlations among subscales and analyses of variance (ANOVAs) showing significant differences among the care recipient (current vs. prior behavior) and caregiver versions overall and for all subscales. Results support the WES as a valid and reliable measure of wayfinding effectiveness in persons with dementia.

Psychometric analysis of the Brisbane Practice Environment Measure (B-PEM)

Purpose: To undertake rigorous psychometric testing of the newly developed contemporary work environment measure (the Brisbane Practice Environment Measure [B-PEM]) using exploratory factor analysis and confirmatory factor analysis. Methods: Content validity of the 33-item measure was established by a panel of experts. Initial testing involved 195 nursing staff using principal component factor analysis with varimax rotation (orthogonal) and Cronbach's alpha coefficients. Confirmatory factor analysis was conducted using data from a further 983 nursing staff. Results: Principal component factor analysis yielded a four-factor solution with eigenvalues greater than 1 that explained 52.53% of the variance. These factors were then verified using confirmatory factor analysis. Goodness-of-fit indices showed an acceptable fit overall with the full model, explaining 21% to 73% of the variance. Deletion of items took place throughout the evolution of the instrument, resulting in a 26-item, four-factor measure called the Brisbane Practice Environment Measure-Tested. Conclusions: The B-PEM has undergone rigorous psychometric testing, providing evidence of internal consistency and goodness-of-fit indices within acceptable ranges. The measure can be utilised as a subscale or total score reflective of a contemporary nursing work environment. Clinical Relevance: An up-to-date instrument to measure practice environment may be useful for nursing leaders to monitor the workplace and to assist in identifying areas for improvement, facilitating greater job satisfaction and retention.

Observation of the suppression of water uptake by marine particles

A 4 week intensive measurement campaign was conducted in March–April 2007 at Agnes Water, a remote coastal site on the east coast of Australia. A Volatility-Hygroscopicity-Tandem Differential Mobility Analyser (VH-TDMA) was used to investigate changes in the hygroscopic properties of ambient particles as volatile components were progressively evaporated. Nine out of 18 VH-TDMA volatility scans detected internally mixed multi-component particles in the nucleation and Aitken modes in clean marine air. Evaporation of a volatile, organic-like component in the VH-TDMA caused significant increases in particle hygroscopicity. In 3 scans the increase in hygroscopicity was so large it was explained by an increase in the absolute volume of water uptake by the particle residuals, and not merely an increase in their relative hygroscopicity. This indicates the presence of organic components that were suppressing the hygroscopic growth of mixed particles on the timescale of humidification in the VH-TDMA (6.5 secs). This observation was supported by ZSR calculations for one scan, which showed that the measured growth factors of mixed particles were up to 18% below those predicted assuming independent water uptake of the individual particle components. The observed suppression of water uptake could be due to a reduced rate of hygroscopic growth caused by the presence of organic films or organic-inorganic interactions in solution droplets that had a negative effect on hygroscopicity.

Who's afraid of the dark? Transpower New Zealand Ltd

On 12 June 2006, the lights went out in New Zealand’s largest city and major commercial centre, Auckland. Business was disrupted and many thousands of people inconvenienced. The unscheduled power cut was the latest in a series of electric power problems in New Zealand over the past decade. Attention turned to state-owned enterprise [SOE] Transpower, which was in charge of maintaining and developing New Zealand’s national electricity grid. The problem of 12 June was traced to two shackles in poor condition, small but essential parts of the electricity grid infrastructure. Closer examination of New Zealand’s electricity sector indicated these shackles were merely the tip of a power supply iceberg. Transpower’s Chief Executive, Ralph Craven, was now answerable to the Prime Minister for the issues creating the problems, and a workable solution to fix them. Transpower Chief Executive Ralph Craven needed to produce answers that went well beyond the problem of the two faulty shackles. The power crisis had brought to the fore wider issues of roles, responsibilities, and expectations in relation to the supply of electric power in New Zealand. Transpower was contending with these issues on a daily basis; however, the incident on 12 June publicly highlighted the urgent need for solutions that served the stakeholders in this critical industry.

Effects of opening in the cross girders of the flat bottom rail wagons to the load transferring mechanisms when used as road bridge deck

A Flat Bed Rail Wagon (FBRW) has been proposed as an alternative solution for replacing bridges on low traffic volume roads. The subject matter for this paper is to investigate the impediment to load transfer from cross girders to main girder, through visually identifiable structural flaws. Namely, the effect of having large openings at close proximity to the connection of the main girder to the cross girder of a FBRW was examined. It was clear that openings locally reduce the section modulus of the secondary members; however it was unclear how these reductions would affect the load transfer to the main girder. The results are presented through modeling grillage action for which the loads applied onto the FBRW were distributed through cross girders to the main girder.

Numerical solution to the Saffman-Taylor finger problem with kinetic undercooling regularisation

The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

Preliminary characterisation of the surface of cartilage following exposure to saturated and unsaturated synthetic lipids

Articular cartilage is covered by a microscopic structure known as surface amorphous layer. This surface structure is often the first victim of attack during cartilage degeneration, thereby resulting in a gross impairment in cartilage function such as lubrication and load bearing. We hypothesize that incubation of degraded cartilage in solutions of different species of synthetic surface active phospholipids (saturated and unsaturated species) can remodel this lost surface structure. To test this hypothesis, the structural configuration of the surface of articular cartilage was studied and characterised with the lipid filled surface amorphous layer intact using the AFM. The results were then compared with those obtained following a systematic removal (delipidization) and replacement (relipidization) of this layer. Our results show that the unsaturated surfactant partially restored the lost surface amorphous layer while the saturated surfactant specie settled on the surface due to its poor solubility in aqueous solution.