A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Assessing eco-environmental performance of agricultural production in OECD countries : combination of soil surface, soil system and farm gate methods of nutrient auditing

Nitrogen balance is increasingly used as an indicator of the environmental performance of agricultural sector in national, international, and global contexts. There are three main methods of accounting the national nitrogen balance: farm gate, soil surface, and soil system. OECD (2008) recently reported the nitrogen and phosphorus balances for member countries for the 1985 - 2004 period using the soil surface method. The farm gate and soil system methods were also used in some international projects. Some studies have provided the comparison among these methods and the conclusion is mixed. The motivation of this present paper was to combine these three methods to provide a more detailed auditing of the nitrogen balance and flows for national agricultural production. In addition, the present paper also provided a new strategy of using reliable international and national data sources to calculate nitrogen balance using the farm gate method. The empirical study focused on the nitrogen balance of OECD countries for the period from 1985 to 2003. The N surplus sent to the total environment of OECD surged dramatically in early 1980s, gradually decreased during 1990s but exhibited an increasing trends in early 2000s. The overall N efficiency however fluctuated without a clear increasing trend. The eco-environmental ranking shows that Australia and Ireland were the worst while Korea and Greece were the best.

An in-vitro 3-D cell culture model for studying pathomechanisms in AMD

Purpose To develop a novel 3-D cell culture model with the view to studying the pathomechanisms underlying the development of age-related macular degeneration (AMD). Our central hypothesis is that the silk structural protein fibroin used in conjunction with cultured human cells can be used to mimic the structural relationships between the RPE and choriocapillaris in health and disease. Methods Co-cultures of human RPE cells (ARPE-19 cells grown in Miller’s medium) and microvascular endothelial cells (HMEC-1 cells grown in endothelial culture medium) were established on opposing sides of a synthetic Bruch’s membrane (3 microns thick) constructed from B mori silk fibroin. Cell attachment was facilitated by pre-coating the fibroin membrane with vitronectin (for ARPE-19 cells) and gelatin (for HMEC-1 cells) respectively. The effects of tropoelastin on attachment of ARPE-19 cells was also examined. Barrier function was examined by measurement of trans-epithelial resistance (TER) using a voltohmmeter (EVOM-2). The phagocytic activity of the synthetic RPE was tested using vitronectin-coated microspheres (2 micron diameter FluoSpheres). In some cultures, membrane defects were created by puncturing within a 24 G needle. The architecture of the synthetic tissue before and after wounding was examined by confocal microscopy after staining for ZO-1 and F-actin. Results The RPE layer of the 3D model developed a cobblestoned morphology (validated by staining for ZO-1 and F-actin), displayed barrier function (validated by measurement of TER) and demonstrated cytoplasmic uptake of vitronectin-coated microspheres. Attachment of ARPE-19 cells to fibroin was unaffected by tropoelastin. Microvascular endothelial cells attached well to the gelatin-coated surface of the fibroin membrane and remained physically separated from the overlaying RPE layer. The fibroin membranes were amenable to puncturing without collapse thus providing the opportunity to study transmembrane migration of the endothelial cells. Conclusions Synthetic Bruch’s membranes constructed from silk fibroin, vitronectin and gelatin, support the co-cultivation of RPE cells and microvascular endothelial cells. The resulting RPE layer displays functions similar to that of native RPE and the entire tri-layered structure displays potential to be used as an in vitro model of choroidal neovascularization.

Combined expression of KLK4, KLK5, KLK6, and KLK7 by ovarian cancer cells leads to decreased adhesion and paclitaxel-induced chemoresistance.

OBJECTIVE: Chemoresistance is a critical feature of advanced ovarian cancer with only 30% of patients surviving longer than 5 years. We have previously shown that four kallikrein-related (KLK) peptidases, KLK4, KLK5, KLK6 and KLK7 (KLK4-7), are implicated in peritoneal invasion and tumour growth, but underlying mechanisms were not identified. We also reported that KLK7 overexpression confers chemoresistance to paclitaxel, and cell survival via integrins. In this study, we further explored the functional consequenses of overexpression of all four KLKs (KLK4-7) simultaneously in the ovarian cancer cell line, OV-MZ-6, and its impact on integrin expression and signalling, cell adhesion and survival as contributors to chemoresistance and metastatic progression. METHODS: Quantitative gene and protein expression analyses, confocal microscopy, cell adhesion and chemosensitivity assays were performed. RESULTS: Expression of α5β1/αvβ3 integrins was downregulated upon combined stable KLK4-7 overexpression in OV-MZ-6 cells. Accordingly, the adhesion of these cells to vitronectin and fibronectin, the extracellular matrix binding proteins of α5β1/αvβ3 integrins and two predominant proteins of the peritoneal matrix, was decreased. KLK4-7-transfected cells were more resistant to paclitaxel (10-100 nmol/L: 38-54%), but not to carboplatin, which was associated with decreased apoptotic stimuli. However, the KLK4-7-induced paclitaxel resistance was not blocked by the MEK1/2 inhibitor, U0126. CONCLUSIONS: This study demonstrates that combined KLK4-7 expression by ovarian cancer cells promotes reduced integrin expression with consequently less cell-matrix attachment, and insensitivity to paclitaxel mediated by complex integrin and MAPK independent interactions, indicative of a malignant phenotype and disease progression suggesting a role for these KLKs in this process.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, 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. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to 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.

A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Sources of ultrafine particles and chemical species along a traffic corridor : comparison of the results from two receptor models

Particulate matter is common in our environment and has been linked to human health problems particularly in the ultrafine size range. A range of chemical species have been associated with particulate matter and of special concern are the hazardous chemicals that can accentuate health problems. If the sources of such particles can be identified then strategies can be developed for the reduction of air pollution and consequently, the improvement of the quality of life. In this investigation, particle number size distribution data and the concentrations of chemical species were obtained at two sites in Brisbane, Australia. Source apportionment was used to determine the sources (or factors) responsible for the particle size distribution data. The apportionment was performed by Positive Matrix Factorisation (PMF) and Principal Component Analysis/Absolute Principal Component Scores (PCA/APCS), and the results were compared with information from the gaseous chemical composition analysis. Although PCA/APCS resolved more sources, the results of the PMF analysis appear to be more reliable. Six common sources identified by both methods include: traffic 1, traffic 2, local traffic, biomass burning, and two unassigned factors. Thus motor vehicle related activities had the most impact on the data with the average contribution from nearly all sources to the measured concentrations higher during peak traffic hours and weekdays. Further analyses incorporated the meteorological measurements into the PMF results to determine the direction of the sources relative to the measurement sites, and this indicated that traffic on the nearby road and intersection was responsible for most of the factors. The described methodology which utilised a combination of three types of data related to particulate matter to determine the sources could assist future development of particle emission control and reduction strategies.

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.

Depression among Holocaust survivors : a meta-analytic review

The publication of the fourth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV; American Psychiatric Association, 1994) introduced the notion that a life-threatening illness can be a stressor and catalyst for Posttraumatic Stress Disorder (PTSD). Since then a solid body of research has been established investigating the post-diagnosis experience of cancer. These studies have identified a number of short and long-term life changes resulting from a diagnosis of cancer and associated treatments. In this chapter, we discuss the psychosocial response to the cancer experience and the potential for cancer-related distress. Cancer can represent a life-threatening diagnosis that may be associated with aggressive treatments and result in physical and psychological changes. The potential for future trauma through the lasting effects of the disease and treatment, and the possibility of recurrence, can be a source of continued psychological distress. In addition to the documented adverse repercussions of cancer, we also outline the recent shift that has occurred in the psycho-oncology literature regarding positive life change or posttraumatic growth that is commonly reported after a diagnosis of cancer. Adopting a salutogenic framework acknowledges that the cancer experience is a dynamic psychosocial process with both negative and positive repercussions. Next, we describe the situational and individual factors that are associated with posttraumatic growth and the types of positive life change that are prevalent in this context. Finally, we discuss the implications of this research in a therapeutic context and the directions of future posttraumatic growth research with cancer survivors. This chapter will present both quantitative and qualitative research that indicates the potential for personal growth from adversity rather than just mere survival and return to pre-diagnosis functioning. It is important to emphasise however, that the presence of growth and prevalence of resilience does not negate the extremely distressing nature of a cancer diagnosis for the patient and their families and the suffering that can accompany treatment regimes. Indeed, it will be explained that for growth to occur, the experience must be one that quite literally shatters previously held schemas in order to act as a catalyst for change.

Application of multi-criteria decision making methods to compression ignition engine efficiency and gaseous, particulate and greenhouse gas emissions

Compression ignition (CI) engine design is subject to many constraints which presents a multi-criteria optimisation problem that the engine researcher must solve. In particular, the modern CI engine must not only be efficient, but must also deliver low gaseous, particulate and life cycle greenhouse gas emissions so that its impact on urban air quality, human health, and global warming are minimised. Consequently, this study undertakes a multi-criteria analysis which seeks to identify alternative fuels, injection technologies and combustion strategies that could potentially satisfy these CI engine design constraints. Three datasets are analysed with the Preference Ranking Organization Method for Enrichment Evaluations and Geometrical Analysis for Interactive Aid (PROMETHEE-GAIA) algorithm to explore the impact of 1): an ethanol fumigation system, 2): alternative fuels (20 % biodiesel and synthetic diesel) and alternative injection technologies (mechanical direct injection and common rail injection), and 3): various biodiesel fuels made from 3 feedstocks (i.e. soy, tallow, and canola) tested at several blend percentages (20-100 %) on the resulting emissions and efficiency profile of the various test engines. The results show that moderate ethanol substitutions (~20 % by energy) at moderate load, high percentage soy blends (60-100 %), and alternative fuels (biodiesel and synthetic diesel) provide an efficiency and emissions profile that yields the most “preferred” solutions to this multi-criteria engine design problem. Further research is, however, required to reduce Reactive Oxygen Species (ROS) emissions with alternative fuels, and to deliver technologies that do not significantly reduce the median diameter of particle emissions.

Distinguishing new science from calibration effects in the electron-volt neutron spectrometer VESUVIO at ISIS

The "standard" procedure for calibrating the Vesuvio eV neutron spectrometer at the ISIS neutron source, forming the basis for data analysis over at least the last decade, was recently documented in considerable detail by the instrument’s scientists. Additionally, we recently derived analytic expressions of the sensitivity of recoil peak positions with respect to fight-path parameters and presented neutron–proton scattering results that together called in to question the validity of the "standard" calibration. These investigations should contribute significantly to the assessment of the experimental results obtained with Vesuvio. Here we present new results of neutron–deuteron scattering from D2 in the backscattering angular range (theata > 90 degrees) which are accompanied by a striking energy increase that violates the Impulse Approximation, thus leading unequivocally the following dilemma: (A) either the "standard" calibration is correct and then the experimental results represent a novel quantum dynamical effect of D which stands in blatant contradiction of conventional theoretical expectations; (B) or the present "standard" calibration procedure is seriously deficient and leads to artificial outcomes. For Case(A), we allude to the topic of attosecond quantumdynamical phenomena and our recent neutron scattering experiments from H2 molecules. For Case(B),some suggestions as to how the "standard" calibration could be considerably improved are made.

The adoption of e-learning 2.0 in higher education by teachers and students : an investigation using mixed methods approach

This paper describes an approach to investigate the adoption of Web 2.0 in the classroom using a mixed methods study. By using a combination of qualitative or quantitative data collection and analysis techniques, we attempt to synergize the results and provide a more valid understanding of Web 2.0 adoption for learning by both teachers and students. This approach is expected to yield a better holistic view on the adoption issues associated with the e-learning 2.0 concept in current higher education as opposed to single method studies done previously. This paper also presents some early findings of e-learning 2.0 adoption using this research method

Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo

Purpose. The purpose of this article was to present methods capable of estimating the size and shape of the human eye lens without resorting to phakometry or magnetic resonance imaging (MRI). Methods. Previously published biometry and phakometry data of 66 emmetropic eyes of 66 subjects (age range [18, 63] years, spherical equivalent range [−0.75, +0.75] D) were used to define multiple linear regressions for the radii of curvature and thickness of the lens, from which the lens refractive index could be derived. MRI biometry was also available for a subset of 30 subjects, from which regressions could be determined for the vertex radii of curvature, conic constants, equatorial diameter, volume, and surface area. All regressions were compared with the phakometry and MRI data; the radii of curvature regressions were also compared with a method proposed by Bennett and Royston et al. Results. The regressions were in good agreement with the original measurements. This was especially the case for the regressions of lens thickness, volume, and surface area, which each had an R2 > 0.6. The regression for the posterior radius of curvature had an R2 < 0.2, making this regression unreliable. For all other regressions we found 0.25 < R2 < 0.6. The Bennett-Royston method also produced a good estimation of the radii of curvature, provided its parameters were adjusted appropriately. Conclusions. The regressions presented in this article offer a valuable alternative in case no measured lens biometry values are available; however care must be taken for possible outliers.

Riding a mile in their shoes : understanding Australian metropolitan rail passenger perceptions and experiences of crowdedness using mixed-methods research

Metrics such as passengers per square metre have been developed to define optimum or crowded rail passenger density. Whilst such metrics are important to operational procedures, service evaluation and reporting, they fail to fully capture and convey the ways in which passengers experience crowded situations. This paper reports findings from a two year study of rail passenger crowding in five Australian capital cities which involved a novel mixed-methodology including ethnography, focus groups and an online stated preference choice experiment. The resulting data address the following four fundamental research questions: 1) to what extent are Australian rail passengers concerned by crowding, 2) what conditions exacerbate feelings of crowdedness, 3) what conditions mitigate feelings of crowdedness, and 4) how can we usefully understand passengers’ experiences of crowdedness? It concludes with some observations on the significance and implications of these findings for customer service provision. The findings outlined in this paper demonstrate that the experience of crowdedness (including its tolerance) cannot be understood in isolation from other customer services issues such as interior design, quality of environment, safety and public health concerns. It is hypothesised that tolerance of crowding will increase alongside improvements to overall customer service. This was the first comprehensive study of crowding in the Australian rail industry.

Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.