On decomposition of sub-linearised polynomials

We give a detailed exposition of the theory of decompositions of linearised polynomials, using a well-known connection with skew-polynomial rings with zero derivative. It is known that there is a one-to-one correspondence between decompositions of linearised polynomials and sub-linearised polynomials. This correspondence leads to a formula for the number of indecomposable sub-linearised polynomials of given degree over a finite field. We also show how to extend existing factorisation algorithms over skew-polynomial rings to decompose sub-linearised polynomials without asymptotic cost.

Quantification and prevalence of Salmonella in beef cattle presenting at slaughter

Aims: A survey to determine the prevalence and numbers of Salmonella in beef cattle presented for slaughter at abattoirs across Australia was conducted between September 2002 and January 2003. Methods and Results: Automated immunomagnetic separation (AIMS) was used for detection and isolation of Salmonella enriched from cattle faeces. Salmonella were enumerated from positive samples using a combination of the Most Probable Number (MPN) technique and AIMS. A total of 310 faecal samples were tested, 155 were from lot-fed cattle and 155 from grass-fed cattle. Salmonella spp. were isolated from 21 (6.8%) of the cattle and the prevalence amongst grass-fed cattle (4.5%) was not significantly different to that found in lot-fed cattle (9%). Counts of Salmonella in positive faeces varied from

Polymorphisms in glutathione S-transferases and non-melanoma skin cancer risk in Australian renal transplant recipients

Caucasian renal transplant recipients from Queensland, Australia have the highest non-melanoma skin cancer (NMSC) risk worldwide. Although ultraviolet light (UVR) exposure is critical, genetic factors also appear important. We and others have shown that polymorphism in the glutathione S-transferases (GST) is associated with NMSC in UK recipients. However, the effect of high UVR exposure and differences in immunosuppressive regimen on these associations is unknown. In this study, we examined allelism in GSTM1, GSTM3, GSTT1 and GSTP1 in 361 Queensland renal transplant recipients. Data on squamous (SCC) and basal cell carcinoma (BCC), UVR/tobacco exposure and genotype were obtained. Associations with both NMSC risk and numbers were examined using logistic and negative binomial regression, respectively. In the total group, GSTM1 AB [P = 0.049, rate ratio (RR) = 0.23] and GSTM3 AA (P = 0.015, RR = 0.50) were associated with fewer SCC. Recipients were then stratified by prednisolone dose (less than or equal to7 versus >7 mg/day). In the low-dose group, GSTT1 null (P = 0.006, RR = 0.20) and GSTP1 Val/Val (P = 0.021, RR = 0.20) were associated with SCC numbers. In contrast, in the high-dose group, GSTM1 AB (P = 0.009, RR = 0.05), GSTM3 AB (P = 0.042, RR = 2.29) and BB (P = 0.014, RR = 5.31) and GSTP1 Val/Val (P = 0.036, RR = 2.98) were associated with SCC numbers. GSTM1 AB (P = 0.016) and GSTP1 Val/Val (P = 0.046) were also associated with fewer BCC in this group. GSTP1 associations were strongest in recipients with lower UVR/tobacco exposure. The data confirm our UK findings, suggesting that protection against UVR-induced oxidative stress is important in NMSC development in recipients, but that this effect depends on the immunosuppressant regimen.

Network topology and the evolution of dynamics in an artificial genetic regulatory network model created by whole genome duplication and divergence

Topological measures of large-scale complex networks are applied to a specific artificial regulatory network model created through a whole genome duplication and divergence mechanism. This class of networks share topological features with natural transcriptional regulatory networks. Specifically, these networks display scale-free and small-world topology and possess subgraph distributions similar to those of natural networks. Thus, the topologies inherent in natural networks may be in part due to their method of creation rather than being exclusively shaped by subsequent evolution under selection. The evolvability of the dynamics of these networks is also examined by evolving networks in simulation to obtain three simple types of output dynamics. The networks obtained from this process show a wide variety of topologies and numbers of genes indicating that it is relatively easy to evolve these classes of dynamics in this model. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

Stochastic modelling and simulations for solute transport in porous media

A stochastic model for solute transport in aquifers is studied based on the concepts of stochastic velocity and stochastic diffusivity. By applying finite difference techniques to the spatial variables of the stochastic governing equation, a system of stiff stochastic ordinary differential equations is obtained. Both the semi-implicit Euler method and the balanced implicit method are used for solving this stochastic system. Based on the Karhunen-Loeve expansion, stochastic processes in time and space are calculated by means of a spatial correlation matrix. Four types of spatial correlation matrices are presented based on the hydraulic properties of physical parameters. Simulations with two types of correlation matrices are presented.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.