A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

An empirical study of business method patent applications filed in Australia 2000-2009

This article sets out the results of an empirical research study into the uses to which the Australian patent system is being put in the early 21st century. The focus of the study is business method patents, which are of interest because they are a controversial class of patent that are thought to differ significantly from the mechanical, chemical and industrial inventions that have traditionally been the mainstay of the patent system. The purpose of the study is to understand what sort of business method patent applications have been lodged in Australia in the first decade of this century and how the patent office is responding to those applications.

A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

Performance assessment of exponential Rosenbrock method for large systems of ODE

This paper studies time integration methods for large stiff systems of ordinary differential equations (ODEs) of the form u'(t) = g(u(t)). For such problems, implicit methods generally outperform explicit methods, since the time step is usually less restricted by stability constraints. Recently, however, explicit so-called exponential integrators have become popular for stiff problems due to their favourable stability properties. These methods use matrix-vector products involving exponential-like functions of the Jacobian matrix, which can be approximated using Krylov subspace methods that require only matrix-vector products with the Jacobian. In this paper, we implement exponential integrators of second, third and fourth order and demonstrate that they are competitive with well-established approaches based on the backward differentiation formulas and a preconditioned Newton-Krylov solution strategy.

Synthesis and characterisation of nanoscale magnesium oxide powders and their application in thick films of Bi2Sr2CaCu2O8

Nanoscale MgO powder was synthesized from magnesite ore by a wet chemical method. Acid dissolution was used to obtain a solution from which magnesium containing complexes were precipitated by either oxalic acid or ammonium hydroxide, The transformation of precipitates to the oxide was monitored by thermal analysis and XRD and the transformed powders were studied by electron microscopy. The MgO powders were added as dopants to Bi2SrCa2CuO8 powders and high temperature superconductor thick films were deposited on silver. Addition of suitable MgO powder resulted in increase of critical current density, J(c), from 8,900 Acm(-2) to 13,900 Acm(-2) measured at 77 K and 0 T. The effect of MgO addition was evaluated by XRD, electron microscopy and critical current density measurements. (C) 1998 Elsevier Science B.V.

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge-Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E coli, and conclude with a discussion on the significance of this work. (C) 2004 Elsevier Ltd. All rights reserved.

A hybrid smoothed finite element method (H-SFEM) to solid mechanics problems

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and Node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained by adjusting ; (2) there exists a preferable at which the H-SFEM can produce the ultrasonic accurate solution.

Effect of preparation method of palygorskite-supported Fe and Ni catalysts on catalytic cracking of biomass tar

In this study, the effect of catalyst preparation and additive precursors on the catalytic decomposition of biomass using palygorskite-supported Fe and Ni catalysts was investigated. The catalysts were characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM). It is concluded that the most active additive precursor was Fe(NO3)3·9H2O. As for the catalyst preparation method, co-precipitation had superiority over incipient wetness impregnation at low Fe loadings.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

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.

A hydrogen/methane sensor based on niobium tungsten oxide nanorods synthesised by hydrothermal method

An investigation on hydrogen and methane sensing performance of hydrothermally formed niobium tungsten oxide nanorods employed in a Schottky diode structure is presented herein. By implementing tungsten into the surface of the niobium lattice, we create Nb5+ and W5+ oxide states and an abundant number of surface traps, which can collect and hold the adsorbate charge to reinforce a greater bending of the energy bands at the metal/oxide interface. We show experimentally, that extremely large voltage shifts can be achieved by these nanorods under exposure to gas at both room and high temperatures and attribute this to the strong accumulation of the dipolar charges at the interface via the surface traps. Thus, our results demonstrate that niobium tungsten oxide nanorods can be implemented for gas sensing applications, showing ultra-high sensitivities.

Synthesis of an erodible biomimetic hydrogel for drug delivery using native chemical ligation

Hydrogels are hydrophilic, three dimensional polymers that imbibe large quantities of water while remaining insoluble in aqueous solutions due to chemical or physical cross-linking. The polymers swell in water or biological fluids, immobilizing the bioactive agent, leading to drug release in a well-defined specific manner. Thus the hydrogels’ elastic properties, swellability and biocompatibility make them excellent formulations for drug delivery. Currently, many drug potencies and therapeutic effects are limited or otherwise reduced because of the partial degradation that occurs before the administered drug reaches the desired site of action. On the other hand, sustained release medications release drugs continually, rather than providing relief of symptoms and protection solely when necessary. In fact, it would be much better if drugs could be administered in a manner that precisely matches physiological needs at desired times and at the desired site (site specific targeting). There is therefore an unmet need to develop controlled drug delivery systems especially for delivery of peptide and protein bound drugs. The purpose of this project is to produce hydrogels for structural drug delivery and time-dependent sustained release of drugs (bioactive agents). We use an innovative polymerisation strategy based on native chemical ligation (NCL) to covalently cross-link polymers to form hydrogels. When mixed in aqueous solution, four armed (polyethylene glycol) amine (PEG-4A) end functionalised with thioester and four branched Nterminal cysteine peptide dendrimers spontaneously conjugated to produce biomimetic hydrogels. These hydrogels showed superior resistance to shear stress compared to an equivalent PEG macromonomer system and were shown to be proteolytically degradable with concomitant release of a model payload molecule. This is the first report of a peptide dendrimers/PEG macromonomer approach to hydrogel production and opens up the prospect of facile hydrogel synthesis together with tailored payload release.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

Deformation with coupled chemical diffusion

The deformation of rocks is commonly intimately associated with metamorphic reactions. This paper is a step towards understanding the behaviour of fully coupled, deforming, chemically reacting systems by considering a simple example of the problem comprising a single layer system with elastic-power law viscous constitutive behaviour where the deformation is controlled by the diffusion of a single chemical component that is produced during a metamorphic reaction. Analysis of the problem using the principles of non-equilibrium thermodynamics allows the energy dissipated by the chemical reaction-diffusion processes to be coupled with the energy dissipated during deformation of the layers. This leads to strain-rate softening behaviour and the resultant development of localised deformation which in turn nucleates buckles in the layer. All such diffusion processes, in leading to Herring-Nabarro, Coble or “pressure solution” behaviour, are capable of producing mechanical weakening through the development of a “chemical viscosity”, with the potential for instability in the deformation. For geologically realistic strain rates these chemical feed-back instabilities occur at the centimetre to micron scales, and so produce structures at these scales, as opposed to thermal feed-back instabilities that become important at the 100–1000 m scales.

Understanding the enhancement in photoelectrochemical properties of photocatalytically prepared TiO2-reduced graphene oxide composite

Solution-phase photocatalytic reduction of graphene oxide to reduced graphene oxide (RGO) by titanium dioxide (TiO2) nanoparticles produces an RGO-TiO2 composite that possesses enhanced charge transport properties beyond those of pure TiO2 nanoparticle films. These composite films exhibit electron lifetimes up to four times longer than that of intrinsic TiO2 films due to RGO acting as a highly conducting intraparticle charge transport network within the film. The intrinsic UV-active charge generation (photocurrent) of pure TiO2 was enhanced by a factor of 10 by incorporating RGO; we attribute this to both the highly conductive nature of the RGO and to improved charge collection facilitated by the intimate contact between RGO and the TiO2, uniquely afforded by the solution-phase photocatalytic reduction method. Integrating RGO into nanoparticle films using this technique should improve the performance of photovoltaic devices that utilize nanoparticle films, such as dye-sensitized and quantum-dot-sensitized solar cells.