A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

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.

A probabilistic analysis of Clostridium perfringens growth during food service operations

The purpose of this study was threefold: first, the study was designed to illustrate the use of data and information collected in food safety surveys in a quantitative risk assessment. In this case, the focus was on the food service industry; however, similar data from other parts of the food chain could be similarly incorporated. The second objective was to quantitatively describe and better understand the role that the food service industry plays in the safety of food. The third objective was to illustrate the additional decision-making information that is available when uncertainty and variability are incorporated into the modelling of systems. (C) 2002 Elsevier Science B.V. All rights reserved.

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.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Bridging the gap between different statistical approaches: An integrated framework for modelling

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of 'good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions. The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches. This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.

Indirect evidence of density-dependent population regulation in Aponomma hydrosauri (Acari : Ixodidae), an ectoparasite of reptiles

The extent to which density-dependent processes regulate natural populations is the subject of an ongoing debate. We contribute evidence to this debate showing that density-dependent processes influence the population dynamics of the ectoparasite Aponomma hydrosauri (Acari: Ixodidae), a tick species that infests reptiles in Australia. The first piece of evidence comes from an unusually long-term dataset on the distribution of ticks among individual hosts. If density-dependent processes are influencing either host mortality or vital rates of the parasite population, and those distributions can be approximated with negative binomial distributions, then general host-parasite models predict that the aggregation coefficient of the parasite distribution will increase with the average intensity of infections. We fit negative binomial distributions to the frequency distributions of ticks on hosts, and find that the estimated aggregation coefficient k increases with increasing average tick density. This pattern indirectly implies that one or more vital rates of the tick population must be changing with increasing tick density, because mortality rates of the tick's main host, the sleepy lizard, Tiliqua rugosa, are unaffected by changes in tick burdens. Our second piece of evidence is a re-analysis of experimental data on the attachment success of individual ticks to lizard hosts using generalized linear modelling. The probability of successful engorgement decreases with increasing numbers of ticks attached to a host. This is direct evidence of a density-dependent process that could lead to an increase in the aggregation coefficient of tick distributions described earlier. The population-scale increase in the aggregation coefficient is indirect evidence of a density-dependent process or processes sufficiently strong to produce a population-wide pattern, and thus also likely to influence population regulation. The direct observation of a density-dependent process is evidence of at least part of the responsible mechanism.

The JK three-product cyclone - performance and potential applications

In spite of their wide application in comminution circuits, hydrocyclones have at least one significant disadvantage in that their operation inherently tends to return the fine denser liberated minerals to the grinding mill. This results in unnecessary overgrinding which adds to the milling cost and can adversely affect the efficiency of downstream processes. In an attempt to solve this problem, a three-product cyclone has been developed at the Julius Kruttschnitt Mineral Research Centre (JKMRC) to generate a second overflow in which the fine dense liberated minerals can be selectively concentrated for further treatment. In this paper, the design and operation of the three-product cyclone are described. The influence of the length of the second vortex finder on the performance of a 150-mm unit treating a mixture of magnetite and silica is investigated. Conventional cyclone tests were also conducted under similar conditions. Using the operational performance data of the three-product and conventional cyclones, it is shown that by optimising the length of the second vortex finder, the amount of fine dense mineral particles that reports to the three-product cyclone underflow can be reduced. In addition, the three-product cyclone can be used to generate middlings stream that may be more suitable for flash flotation than the conventional cyclone underflow, or alternatively, could be classified with a microscreen to separate the valuables from the gangue. At the same time, a fines stream having similar properties to those of the conventional overflow can be obtained. Hence, if the middlings stream was used as feed for flash flotation or microscreening, the fines stream could be used in lieu of the conventional overflow without compromising the feed requirements for the conventional flotation circuit. Some of the other potential applications of the new cyclone are described. (C) 2003 Elsevier Science B.V. 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.

An EM-based Semi-Parametric Mixture Model Approach to the Regression Analysis of Competing-Risks Data

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright (C) 2003 John Wiley Sons, Ltd.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

But what if I don't want to wait forever?

We present an abstract model of the leader election protocol used in the IEEE 1394 High Performance Serial Bus standard. The model is expressed in the probabilistic Guarded Command Language. By formal reasoning based on this description, we establish the probability of the root contention part of the protocol successfully terminating in terms of the number of attempts to do so. Some simple calculations then allow us to establish an upper bound on the time taken for those attempts.

Development of a more efficient classifying cyclone

A more efficient classifying cyclone (CC) for fine particle classification has been developed in recent years at the JKMRC. The novel CC, known as the JKCC, has modified profiles of the cyclone body, vortex finder, and spigot when compared to conventional hydrocyclones. The novel design increases the centrifugal force inside the cyclone and mitigates the short circuiting flow that exists in all current cyclones. It also decreases the probability of particle contamination in the place near the cyclone spigot. Consequently the cyclone efficiency is improved while the unit maintains a simple structure. An international patent has been granted for this novel cyclone design. In the first development stage-a feasibility study-a 100 mm JKCC was tested and compared with two 100 min commercial units. Very encouraging results were achieved, indicating good potential for the novel design. In the second development stage-a scale-up stage-the JKCC was scaled up to 200 mm in diameter, and its geometry was optimized through numerous tests. The performance of the JKCC was compared with a 150 nun commercial unit and exhibited sharper separation, finer separation size, and lower flow ratios. The JKCC is now being scaled up into a fill-size (480 mm) hydrocyclone in the third development stage-an industrial study. The 480 mm diameter unit will be tested in an Australian coal preparation plant, and directly compared with a commercial CC operating under the same conditions. Classifying cyclone performance for fine coal could be further improved if the unit is installed in an inclined position. The study using the 200 mm JKCC has revealed that sharpness of separation improved and the flow ratio to underflow was decreased by 43% as the cyclone inclination was varied from the vertical position (0degrees) to the horizontal position (90degrees). The separation size was not affected, although the feed rate was slightly decreased. To ensure self-emptying upon shutdown, it is recommended that the JKCC be installed at an inclination of 75-80degrees. At this angle the cyclone performance is very similar to that at a horizontal position. Similar findings have been derived from the testing of a conventional hydrocyclone. This may be of benefit to operations that require improved performance from their classifying cyclones in terms of sharpness of separation and flow ratio, while tolerating slightly reduced feed rate.