Model-based clustering in gene expression microarrays: An application to breast cancer data

In microarray studies, the application of clustering techniques is often used to derive meaningful insights into the data. In the past, hierarchical methods have been the primary clustering tool employed to perform this task. The hierarchical algorithms have been mainly applied heuristically to these cluster analysis problems. Further, a major limitation of these methods is their inability to determine the number of clusters. Thus there is a need for a model-based approach to these. clustering problems. To this end, McLachlan et al. [7] developed a mixture model-based algorithm (EMMIX-GENE) for the clustering of tissue samples. To further investigate the EMMIX-GENE procedure as a model-based -approach, we present a case study involving the application of EMMIX-GENE to the breast cancer data as studied recently in van 't Veer et al. [10]. Our analysis considers the problem of clustering the tissue samples on the basis of the genes which is a non-standard problem because the number of genes greatly exceed the number of tissue samples. We demonstrate how EMMIX-GENE can be useful in reducing the initial set of genes down to a more computationally manageable size. The results from this analysis also emphasise the difficulty associated with the task of separating two tissue groups on the basis of a particular subset of genes. These results also shed light on why supervised methods have such a high misallocation error rate for the breast cancer data.

A mechanistic model for carbon dioxide corrosion of mild steel in the presence of protective iron carbonate films - Part 3: Film growth model

A model of iron carbonate (FeCO3) film growth is proposed, which is an extension of the recent mechanistic model of carbon dioxide (CO2) corrosion by Nesic, et al. In the present model, the film growth occurs by precipitation of iron carbonate once saturation is exceeded. The kinetics of precipitation is dependent on temperature and local species concentrations that are calculated by solving the coupled species transport equations. Precipitation tends to build up a layer of FeCO3 on the surface of the steel and reduce the corrosion rate. On the other hand, the corrosion process induces voids under the precipitated film, thus increasing the porosity and leading to a higher corrosion rate. Depending on the environmental parameters such as temperature, pH, CO2 partial pressure, velocity, etc., the balance of the two processes can lead to a variety of outcomes. Very protective films and low corrosion rates are predicted at high pH, temperature, CO2 partial pressure, and Fe2+ ion concentration due to formation of dense protective films as expected. The model has been successfully calibrated against limited experimental data. Parametric testing of the model has been done to gain insight into the effect of various environmental parameters on iron carbonate film formation. The trends shown in the predictions agreed well with the general understanding of the CO2 corrosion process in the presence of iron carbonate films. The present model confirms that the concept of scaling tendency is a good tool for predicting the likelihood of protective iron carbonate film formation.

An energy-based model for swing hammer mills

An energy-based swing hammer mill model has been developed for coke oven feed preparation. it comprises a mechanistic power model to determine the dynamic internal recirculation and a perfect mixing mill model with a dual-classification function to mimic the operations of crusher and screen. The model parameters were calibrated using a pilot-scale swing hammer mill at various operating conditions. The effects of the underscreen configurations and the feed sizes on hammer mill operations were demonstrated through the fitted model parameters. Relationships between the model parameters and the machine configurations were established. The model was validated using the independent experimental data of single lithotype coal tests with the same BJD pilot-scale hammer mill and full operation audit data of an industrial hammer mill. The outcome of the energy-based swing hammer mill model is the capability to simulate the impact of changing blends of coal or mill configurations and operating conditions on product size distribution. Alternatively, the model can be used to select the machine settings required to achieve a desired product. (C) 2003 Elsevier Science B.V. All rights reserved.

A unified model of flames as gasdynamic discontinuities

Viewed on a hydrodynamic scale, flames in experiments are often thin so that they may be described as gasdynamic discontinuities separating the dense cold fresh mixture from the light hot burned products. The original model of a flame as a gasdynamic discontinuity was due to Darrieus and to Landau. In addition to the fluid dynamical equations, the model consists of a flame speed relation describing the evolution of the discontinuity surface, and jump conditions across the surface which relate the fluid variables on the two sides of the surface. The Darrieus-Landau model predicts, in contrast to observations, that a uniformly propagating planar flame is absolutely unstable and that the strength of the instability grows with increasing perturbation wavenumber so that there is no high-wavenumber cutoff of the instability. The model was modified by Markstein to exhibit a high-wavenumber cutoff if a phenomenological constant in the model has an appropriate sign. Both models are postulated, rather than derived from first principles, and both ignore the flame structure, which depends on chemical kinetics and transport processes within the flame. At present, there are two models which have been derived, rather than postulated, and which are valid in two non-overlapping regions of parameter space. Sivashinsky derived a generalization of the Darrieus-Landau model which is valid for Lewis numbers (ratio of thermal diffusivity to mass diffusivity of the deficient reaction component) bounded away from unity. Matalon & Matkowsky derived a model valid for Lewis numbers close to unity. Each model has its own advantages and disadvantages. Under appropriate conditions the Matalon-Matkowsky model exhibits a high-wavenumber cutoff of the Darrieus-Landau instability. However, since the Lewis numbers considered lie too close to unity, the Matalon-Matkowsky model does not capture the pulsating instability. The Sivashinsky model does capture the pulsating instability, but does not exhibit its high-wavenumber cutoff. In this paper, we derive a model consisting of a new flame speed relation and new jump conditions, which is valid for arbitrary Lewis numbers. It captures the pulsating instability and exhibits the high-wavenumber cutoff of all instabilities. The flame speed relation includes the effect of short wavelengths, not previously considered, which leads to stabilizing transverse surface diffusion terms.

A unit cell waveguide model of a reflectarray formed by microstrip patches and slots

An equivalent unit cell waveguide approach (WGA) is described to obtain reflection coefficient phase curves for designing a microstrip patch reflectarray supported by a ground plane with periodic apertures or slots. Based on the presented theory, a computer algorithm for determining the reflection coefficient of a plane wave normally incident on a multi-layer structure of patches and apertures is developed. The validity of the developed algorithm is verified by comparing the obtained results with those published in the literature and the ones generated by Agilent High Frequency Structure Simulator (HFSS). A good agreement in all the presented examples is obtained, proving that the developed theory and computer algorithm can be an effective tool for designing multi-layer microstrip reflectarrays with a periodically perforated ground plane. (C) 2003 Wiley Periodicals, Inc.

Study of n-fold Weibull competing risk model

This paper deals with an n-fold Weibull competing risk model. A characterisation of the WPP plot is given along with estimation of model parameters when modelling a given data set. These are illustrated through two examples. A study of the different possible shapes for the density and failure rate functions is also presented. (C) 2003 Elsevier Ltd. All rights reserved.

A model to investigate hepatic extraction of oxygen during anaesthesia in the dog

Measurement of hepatic oxygen extraction was performed on six healthy Greyhound dogs over a two hour period. The Greyhounds were anaesthetised and a right subcostal surgical incision performed. Ultrasonic flow transducers were used to measure flow rate in the hepatic artery and the portal vein. The blood oxygen tensions in arterial blood and in the portal and hepatic veins were also measured. Hepatic oxygen extraction remained stable throughout the study, despite a steady decline in arterial blood pressure. The methodology described in this study provides a direct measure of oxygen uptake by the liver in the dog and could readily be used to investigate hepatic uptake of drugs. (C) 2003 Elsevier Ltd. All rights reserved.

A comparison of model laws as a starting point for the development of an enforceable international consumer protection regime

This article is concerned primarily with an examination and comparison of select aspects of the model international consumer protection laws proposed by the United Nations (UN), the European Union (EU), and the Organisation for Economic Co-operation and Development (OECD), using the Trade Practices Act 1974 (Australia) as a basis for examination and comparison. As a secondary consideration, it also broadly examines the content of, and differences between, the model laws. The motive for this article is that any future enforceable international consumer protection regime (possibly in the form of an international treaty or convention) would need to take into account the UN, EU and OECD guidelines. A cross-comparison of those model laws, and a comparison of them with the consumer protection provisions of a well established national consumer protection law, should provide a useful starting point for the development of such a regime. The 'select aspects' of the model laws in question are the various provisions of those laws which could relate to situations involving the wrong delivery or non-delivery of goods.

Biaxial failure model for fiber reinforced concrete

Steel fiber reinforced concrete (SFRC) is widely applied in the construction industry. Numerical elastoplastic analysis of the macroscopic behavior is complex. This typically involves a piecewise linear failure curve including corner singularities. This paper presents a single smooth biaxial failure curve for SFRC based on a semianalytical approximation. Convexity of the proposed model is guaranteed so that numerical problems are avoided. The model has sufficient flexibility to closely match experimental results. The failure curve is also suitable for modeling plain concrete under biaxial loading. Since this model is capable of simulating the failure states in all stress regimes with a single envelope, the elastoplastic formulation is very concise and simple. The finite element implementation is developed to demonstrate the conciseness and the effectiveness of the model. The computed results display good agreement with published experimental data.

Model-based analysis of anaerobic acetate uptake by a mixed culture of polyphosphate-accumulating and glycogen-accumulating organisms

An increasing number of studies shows that the glycogen-accumulating organisms (GAOs) can survive and may indeed proliferate under the alternating anaerobic/aerobic conditions found in EBPR systems, thus forming a strong competitor of the polyphosphate-accumulating organisms (PAOs). Understanding their behaviors in a mixed PAO and GAO culture under various operational conditions is essential for developing operating strategies that disadvantage the growth of this group of unwanted organisms. A model-based data analysis method is developed in this paper for the study of the anaerobic PAO and GAO activities in a mixed PAO and GAO culture. The method primarily makes use of the hydrogen ion production rate and the carbon dioxide transfer rate resulting from the acetate uptake processes by PAOs and GAOs, measured with a recently developed titration and off-gas analysis (TOGA) sensor. The method is demonstrated using the data from a laboratory-scale sequencing batch reactor (SBR) operated under alternating anaerobic and aerobic conditions. The data analysis using the proposed method strongly indicates a coexistence of PAOs and GAOs in the system, which was independently confirmed by fluorescent in situ hybridization (FISH) measurement. The model-based analysis also allowed the identification of the respective acetate uptake rates by PAOs and GAOs, along with a number of kinetic and stoichiometric parameters involved in the PAO and GAO models. The excellent fit between the model predictions and the experimental data not involved in parameter identification shows that the parameter values found are reliable and accurate. It also demonstrates that the current anaerobic PAO and GAO models are able to accurately characterize the PAO/GAO mixed culture obtained in this study. This is of major importance as no pure culture of either PAOs or GAOs has been reported to date, and hence the current PAO and GAO models were developed for the interpretation of experimental results of mixed cultures. The proposed method is readily applicable for detailed investigations of the competition between PAOs and GAOs in enriched cultures. However, the fermentation of organic substrates carried out by ordinary heterotrophs needs to be accounted for when the method is applied to the study of PAO and GAO competition in full-scale sludges. (C) 2003 Wiley Periodicals, Inc.

Metabolic model for glycogen-accumulating organisms in anaerobic/aerobic activated sludge systems

Glycogen-accumulating organisms (GAO) have the potential to directly compete with polyphosphate-accumulating organisms (PAO) in EBPR systems as both are able to take up VFA anaerobically and grow on the intracellular storage products aerobically. Under anaerobic conditions GAO hydrolyse glycogen to gain energy and reducing equivalents to take up VFA and to synthesise polyhydroxyalkanoate (PHA). In the subsequent aerobic stage, PHA is being oxidised to gain energy for glycogen replenishment (from PHA) and for cell growth. This article describes a complete anaerobic and aerobic model for GAO based on the understanding of their metabolic pathways. The anaerobic model has been developed and reported previously, while the aerobic metabolic model was developed in this study. It is based on the assumption that acetyl-CoA and propionyl-CoA go through the catabolic and anabolic processes independently. Experimental validation shows that the integrated model can predict the anaerobic and aerobic results very well. It was found in this study that at pH 7 the maximum acetate uptake rate of GAO was slower than that reported for PAO in the anaerobic stage. On the other hand, the net biomass production per C-mol acetate added is about 9% higher for GAO than for PAO. This would indicate that PAO and GAO each have certain competitive advantages during different parts of the anaerobic/aerobic process cycle. (C) 2002 Wiley Periodicals, Inc.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 1. Methodology for residual generation

For dynamic simulations to be credible, verification of the computer code must be an integral part of the modelling process. This two-part paper describes a novel approach to verification through program testing and debugging. In Part 1, a methodology is presented for detecting and isolating coding errors using back-to-back testing. Residuals are generated by comparing the output of two independent implementations, in response to identical inputs. The key feature of the methodology is that a specially modified observer is created using one of the implementations, so as to impose an error-dependent structure on these residuals. Each error can be associated with a fixed and known subspace, permitting errors to be isolated to specific equations in the code. It is shown that the geometric properties extend to multiple errors in either one of the two implementations. Copyright (C) 2003 John Wiley Sons, Ltd.