Levene tests of homogeneity of variance for general block and treatment designs

This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F-distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plot.

Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

Identification of research to improve the efficiency of breeding strategies for white clover in Australia - a review

A major challenge faced by today's white clover breeder is how to manage resources within a breeding program. It is essential to utilise these resources with sufficient flexibility to build on past progress from conventional breeding strategies, but also take advantage of emerging opportunities from molecular breeding tools such as molecular markers and transformation. It is timely to review white clover breeding strategies. This background can then be used as a foundation for considering how to continue conventional plant improvement activities and complement them with molecular breeding opportunities. In this review, conventional white clover breeding strategies relevant to the Australian dryland target population environments are considered. Attention is given to: (i) availability of genetic variation, (ii) characterisation of germplasm collections, (iii) quantitative models for estimation of heritability, (iv) the role of multi-environment trials to accommodate genotype-by-environment interactions, (v) interdisciplinary research to understand adaptation to dryland environments, (vi) breeding and selection strategies, and (vii) cultivar structure. Current achievements in biotechnology with specific reference to white clover breeding in Australia are considered, and computer modelling of breeding programs is discussed as a useful integrative tool for the joint evaluation of conventional and molecular breeding strategies and optimisation of resource use in breeding programs. Four areas are identified as future research priorities: (i) capturing the potential genetic diversity among introduced accessions and ecotypes that are adapted to key constraints such as summer moisture stress and the use of molecular markers to assess the genetic diversity, (ii) understanding the underlying physiological/morphological root and shoot mechanisms involved in water use efficiency of white clover, with the objective of identifying appropriate selection criteria, (iii) estimation of quantitative genetic parameters of important morphological/physiological attributes to enable prediction of response to selection in target environments, and (iv) modelling white clover breeding strategies to evaluate the opportunities for integration of molecular breeding strategies with conventional breeding programs.

Australian empirical study into genetic discrimination

This paper outlines a major empirical study that is being undertaken by an interdisciplinary team into genetic discrimination in Australia. The 3-year study will examine the nature and extent of this newly emerging phenomenon across the perspectives of consumers, third parties, and the legal system and will analyze its social and legal dimensions. Although the project is confined to Australia, it is expected that the outcomes will have significance for the wider research community as this is the most substantial study of its kind to be undertaken to date into genetic discrimination.

Prediction of Golgi Type II membrane proteins based on their transmembrane domains

Motivation: A major issue in cell biology today is how distinct intracellular regions of the cell, like the Golgi Apparatus, maintain their unique composition of proteins and lipids. The cell differentially separates Golgi resident proteins from proteins that move through the organelle to other subcellular destinations. We set out to determine if we could distinguish these two types of transmembrane proteins using computational approaches. Results: A new method has been developed to predict Golgi membrane proteins based on their transmembrane domains. To establish the prediction procedure, we took the hydrophobicity values and frequencies of different residues within the transmembrane domains into consideration. A simple linear discriminant function was developed with a small number of parameters derived from a dataset of Type II transmembrane proteins of known localization. This can discriminate between proteins destined for Golgi apparatus or other locations (post-Golgi) with a success rate of 89.3% or 85.2%, respectively on our redundancy-reduced data sets.

Modelling High-Dimensional Data by Mixtures of Factor Analyzers

We focus on mixtures of factor analyzers from the perspective of a method for model-based density estimation from high-dimensional data, and hence for the clustering of such data. This approach enables a normal mixture model to be fitted to a sample of n data points of dimension p, where p is large relative to n. The number of free parameters is controlled through the dimension of the latent factor space. By working in this reduced space, it allows a model for each component-covariance matrix with complexity lying between that of the isotropic and full covariance structure models. We shall illustrate the use of mixtures of factor analyzers in a practical example that considers the clustering of cell lines on the basis of gene expressions from microarray experiments. (C) 2002 Elsevier Science B.V. All rights reserved.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

Principles versus artifacts in computer science curriculum design

Computer Science is a subject which has difficulty in marketing itself. Further, pinning down a standard curriculum is difficult-there are many preferences which are hard to accommodate. This paper argues the case that part of the problem is the fact that, unlike more established disciplines, the subject does not clearly distinguish the study of principles from the study of artifacts. This point was raised in Curriculum 2001 discussions, and debate needs to start in good time for the next curriculum standard. This paper provides a starting point for debate, by outlining a process by which principles and artifacts may be separated, and presents a sample curriculum to illustrate the possibilities. This sample curriculum has some positive points, though these positive points are incidental to the need to start debating the issue. Other models, with a less rigorous ordering of principles before artifacts, would still gain from making it clearer whether a specific concept was fundamental, or a property of a specific technology. (C) 2003 Elsevier Ltd. All rights reserved.

A new method for analysing the equilibrium and time-dependent behaviour of Markovian models

Many large-scale stochastic systems, such as telecommunications networks, can be modelled using a continuous-time Markov chain. However, it is frequently the case that a satisfactory analysis of their time-dependent, or even equilibrium, behaviour is impossible. In this paper, we propose a new method of analyzing Markovian models, whereby the existing transition structure is replaced by a more amenable one. Using rates of transition given by the equilibrium expected rates of the corresponding transitions of the original chain, we are able to approximate its behaviour. We present two formulations of the idea of expected rates. The first provides a method for analysing time-dependent behaviour, while the second provides a highly accurate means of analysing equilibrium behaviour. We shall illustrate our approach with reference to a variety of models, giving particular attention to queueing and loss networks. (C) 2003 Elsevier Ltd. All rights reserved.

Product form approximations for highly linear loss networks with trunk reservation

Admission controls, such as trunk reservation, are often used in loss networks to optimise their performance. Since the numerical evaluation of performance measures is complex, much attention has been given to finding approximation methods. The Erlang Fixed-Point (EFP) approximation, which is based on an independent blocking assumption, has been used for networks both with and without controls. Several more elaborate approximation methods which account for dependencies in blocking behaviour have been developed for the uncontrolled setting. This paper is an exploratory investigation of extensions and synthesis of these methods to systems with controls, in particular, trunk reservation. In order to isolate the dependency factor, we restrict our attention to a highly linear network. We will compare the performance of the resulting approximations against the benchmark of the EFP approximation extended to the trunk reservation setting. By doing this, we seek to gain insight into the critical factors in constructing an effective approximation. (C) 2003 Elsevier Ltd. All rights reserved.

A high definition, finite difference time domain method

A high definition, finite difference time domain (HD-FDTD) method is presented in this paper. This new method allows the FDTD method to be efficiently applied over a very large frequency range including low frequencies, which are problematic for conventional FDTD methods. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and has been verified against analytical solutions within the frequency range 50 Hz-1 GHz. As an example of the lower frequency range, the method has been applied to the problem of induced eddy currents in the human body resulting from the pulsed magnetic field gradients of an MRI system. The new method only requires approximately 0.3% of the source period to obtain an accurate solution. (C) 2003 Elsevier Science Inc. All rights reserved.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

Quasiequilibrium problem in H-spaces

In the present paper, we study the quasiequilibrium problem and generalized quasiequilibrium problem of generalized quasi-variational inequality in H-spaces by a new method. Some new equilibrium existence theorems are given. Our results are different from corresponding given results or contain some recent results as their special cases. (C) 2003 Elsevier Science Ltd. All rights reserved.

Explicit/implicit partitioning and a new explicit form of the generalized alpha method

Most finite element packages use the Newmark algorithm for time integration of structural dynamics. Various algorithms have been proposed to better optimize the high frequency dissipation of this algorithm. Hulbert and Chung proposed both implicit and explicit forms of the generalized alpha method. The algorithms optimize high frequency dissipation effectively, and despite recent work on algorithms that possess momentum conserving/energy dissipative properties in a non-linear context, the generalized alpha method remains an efficient way to solve many problems, especially with adaptive timestep control. However, the implicit and explicit algorithms use incompatible parameter sets and cannot be used together in a spatial partition, whereas this can be done for the Newmark algorithm, as Hughes and Liu demonstrated, and for the HHT-alpha algorithm developed from it. The present paper shows that the explicit generalized alpha method can be rewritten so that it becomes compatible with the implicit form. All four algorithmic parameters can be matched between the explicit and implicit forms. An element interface between implicit and explicit partitions can then be used, analogous to that devised by Hughes and Liu to extend the Newmark method. The stability of the explicit/implicit algorithm is examined in a linear context and found to exceed that of the explicit partition. The element partition is significantly less dissipative of intermediate frequencies than one using the HHT-alpha method. The explicit algorithm can also be rewritten so that the discrete equation of motion evaluates forces from displacements and velocities found at the predicted mid-point of a cycle. Copyright (C) 2003 John Wiley Sons, Ltd.

A partial velocity approach to subcycling structural dynamics

Subcycling, or the use of different timesteps at different nodes, can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions. The method that has been most widely adopted uses a nodal partition. extending the central difference method, in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes. This approach leads to narrow bands of unstable timesteps or statistical stability. It also can be in error due to lack of momentum conservation on the timestep interface. The author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability. However, these sacrifice accuracy to achieve stability. An approach to conserve momentum on an element interface by adding partial velocities is considered here. Applied to extend the central difference method. this approach is simple. and has accuracy advantages. The method can be programmed by summing impulses of internal forces, evaluated using local element timesteps, in order to predict a velocity change at a node. However, it is still only statistically stable, so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary. By replacing the central difference method with the explicit generalized alpha method. it is possible to gain stability by dissipating the high frequency response that leads to stability problems. However. coding the algorithm is less elegant, as the response depends on previous partial accelerations. Extension to implicit integration, is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface. (C) 2002 Elsevier Science B.V. All rights reserved.