A mixture model-based approach to the clustering of microarray expression data

Motivation: This paper introduces the software EMMIX-GENE that has been developed for the specific purpose of a model-based approach to the clustering of microarray expression data, in particular, of tissue samples on a very large number of genes. The latter is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. A feasible approach is provided by first selecting a subset of the genes relevant for the clustering of the tissue samples by fitting mixtures of t distributions to rank the genes in order of increasing size of the likelihood ratio statistic for the test of one versus two components in the mixture model. The imposition of a threshold on the likelihood ratio statistic used in conjunction with a threshold on the size of a cluster allows the selection of a relevant set of genes. However, even this reduced set of genes will usually be too large for a normal mixture model to be fitted directly to the tissues, and so the use of mixtures of factor analyzers is exploited to reduce effectively the dimension of the feature space of genes. Results: The usefulness of the EMMIX-GENE approach for the clustering of tissue samples is demonstrated on two well-known data sets on colon and leukaemia tissues. For both data sets, relevant subsets of the genes are able to be selected that reveal interesting clusterings of the tissues that are either consistent with the external classification of the tissues or with background and biological knowledge of these sets.

Read-only-memory-based quantum computation: Experimental explorations using nuclear magnetic resonance and future prospects

Read-only-memory-based (ROM-based) quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less magical, and being more suited to implementing space-efficient computation (i.e., computation using the minimum number of writable qubits). Here we consider a number of small (one- and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using nuclear magnetic resonance ensemble QC. The average fidelities for the implementation were in the ranges 0.9-0.97 for the one-qubit algorithms, and 0.84-0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature real-world problem relating to the lengths of paths in a network.

Comparisons between bone and cementum compositions and the possible basis for their layered appearances

In humans, age estimation from the adult skeleton represents an attempt to determine chronological age based on growth and maturational events. In teeth, such events can be characterized by appositional growth layers in midroot cementum. The purpose of this study was to determine the underlying cause of the layered microstructure of human midroot cementum. Whether cementum growth layers are caused by changes in relative mineralization, collagen packing and/or orientation, or by variations in organic matrix apposition was investigated by subjecting midroot sections of human canine teeth to analysis using polarized light and scanning electron microscopy (SEM). Polarized light was used to examine transverse midroot sections in both mineralized and demineralized states. Mineralized sections were also reexamined following subsequent decollagenization. Polarized light was additionally used in the examination of mineralized sections taken transversely, longitudinally, and obliquely from the same tooth root. From the birefringence patterns it was concluded that collagen orientation does not change with varying section plane. Instead, the mineral phase was most responsible for the birefringence of the cementum. SEM studies suggested that neither collagen packing nor collagen orientation change across the width of the cementum, confirming and validating the results of the polarized light examination. Also, SEM analysis using electron backscatter and the electron probe suggested no changes in the mean atomic number density, calcium, phosphate, and sulfur levels across the width of the cementum. Therefore, we conclude that crystalline orientation and/or size is responsible for the layered appearance of cementum. (Bone 30:386-392; 2002) (C) 2002 by Elsevier Science Inc. All rights reserved.

Close packed transitions in slit-shaped pores: Density functional theory study of methane adsorption capacity in carbon

An important feature of improving lattice gas models and classical isotherms is the incorporation of a pore size dependent capacity, which has hitherto been overlooked. In this paper, we develop a model for predicting the temperature dependent variation in capacity with pore size. The model is based on the analysis of a lattice gas model using a density functional theory approach at the close packed limit. Fluid-fluid and solid-fluid interactions are modeled by the Lennard-Jones 12-6 potential and Steele's 10-4-3, potential respectively. The capacity of methane in a slit-shaped carbon pore is calculated from the characteristic parameters of the unit cell, which are extracted by minimizing the grand potential of the unit cell. The capacities predicted by the proposed model are in good agreement with those obtained from grand canonical Monte Carlo simulation, for pores that can accommodate up to three adsorbed layers. Single particle and pair distributions exhibit characteristic features that correspond to the sequence of buckling and rhombic transitions that occur as the slit pore width is increased. The model provides a useful tool to model continuous variation in the microstructure of an adsorbed phase, namely buckling and rhombic transitions, with increasing pore width. (C) 2002 American Institute of Physics.

MR image-based measurement of rates of change in volumes of brain structures. Part 1: Method and validation

A detailed analysis procedure is described for evaluating rates of volumetric change in brain structures based on structural magnetic resonance (MR) images. In this procedure, a series of image processing tools have been employed to address the problems encountered in measuring rates of change based on structural MR images. These tools include an algorithm for intensity non-uniforniity correction, a robust algorithm for three-dimensional image registration with sub-voxel precision and an algorithm for brain tissue segmentation. However, a unique feature in the procedure is the use of a fractional volume model that has been developed to provide a quantitative measure for the partial volume effect. With this model, the fractional constituent tissue volumes are evaluated for voxels at the tissue boundary that manifest partial volume effect, thus allowing tissue boundaries be defined at a sub-voxel level and in an automated fashion. Validation studies are presented on key algorithms including segmentation and registration. An overall assessment of the method is provided through the evaluation of the rates of brain atrophy in a group of normal elderly subjects for which the rate of brain atrophy due to normal aging is predictably small. An application of the method is given in Part 11 where the rates of brain atrophy in various brain regions are studied in relation to normal aging and Alzheimer's disease. (C) 2002 Elsevier Science Inc. All rights reserved.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Modeling of gas adsorption equilibrium over a wide range of pressure: A thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R I in the temperature range from 25 to 70 C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

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.

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.

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.

The modeling of turbulent reactive flows based on multiple mapping conditioning

A new modeling approach-multiple mapping conditioning (MMC)-is introduced to treat mixing and reaction in turbulent flows. The model combines the advantages of the probability density function and the conditional moment closure methods and is based on a certain generalization of the mapping closure concept. An equivalent stochastic formulation of the MMC model is given. The validity of the closuring hypothesis of the model is demonstrated by a comparison with direct numerical simulation results for the three-stream mixing problem. (C) 2003 American Institute of Physics.

The tree cut and merge algorithm for estimation of network reliability

This article presents Monte Carlo techniques for estimating network reliability. For highly reliable networks, techniques based on graph evolution models provide very good performance. However, they are known to have significant simulation cost. An existing hybrid scheme (based on partitioning the time space) is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme. To overcome these difficulties, a new hybrid scheme (based on partitioning the edge set) is proposed in this article. The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network. It also provides reliability bounds with little overhead.

Knowledge-based system on optimum design of liquid retaining structures with genetic algorithms

This paper delineates the development of a prototype hybrid knowledge-based system for the optimum design of liquid retaining structures by coupling the blackboard architecture, an expert system shell VISUAL RULE STUDIO and genetic algorithm (GA). Through custom-built interactive graphical user interfaces under a user-friendly environment, the user is directed throughout the design process, which includes preliminary design, load specification, model generation, finite element analysis, code compliance checking, and member sizing optimization. For structural optimization, GA is applied to the minimum cost design of structural systems with discrete reinforced concrete sections. The design of a typical example of the liquid retaining structure is illustrated. The results demonstrate extraordinarily converging speed as near-optimal solutions are acquired after merely exploration of a small portion of the search space. This system can act as a consultant to assist novice designers in the design of liquid retaining structures.

Use of confocal scanning laser microscopy to measure the concentrations of aerial and penetrative hyphae during growth of Rhizopus oligosporus on a solid surface

In order to develop a method for use in investigations of spatial biomass distribution in solid-state fermentation systems, confocal scanning laser microscopy was used to determine the concentrations of aerial and penetrative biomass against height and depth above and below the substrate surface, during growth of Rhizopus oligosporus on potato dextrose agar. Penetrative hyphae had penetrated to a depth of 0.445 cm by 64 h and showed rhizoid morphology, in which the maximum biomass concentration, of 4.45 mg dry wt cm(-3), occurred at a depth of 0.075 cm. For aerial biomass the maximum density of 39.54 mg dry wt(-3) occurred at the substrate surface. For both aerial and penetrative biomass, there were two distinct regions in which the biomass concentration decayed exponentially with distance from the surface. For aerial biomass, the first exponential decay region was up to 0.1 cm height. The second region above the height of 0.1 cm corresponded to that in which sporangiophores dominated. This work lays the foundation for deeper studies into what controls the growth of fungal hyphae above and below the surfaces of solid substrates. (C) Wiley Periodicals, Inc.

Conformational changes in SP-B as a function of surface pressure

X-ray reflectivity of bovine and sheep surfactant-associated protein B (SP-B) monolayers is used in conjunction with pressure-area isotherms and protein models to suggest that the protein undergoes changes in its tertiary structure at the air/water interface under the influence of surface pressure, indicating the likely importance of such changes to the phenomena of protein squeeze out as well as lipid exchange between the air-water interface and subphase structures. We describe an algorithm based on the well-established box- or layer-models that greatly assists the fitting of such unknown scattering-length density profiles, and which takes the available instrumental resolution into account. Scattering-length density profiles from neutron reflectivity of bovine SP-B monolayers on aqueous subphases are shown to be consistent with the exchange of a large number of labile protons as well as the inclusion of a significant amount of water, which is partly squeezed out of the protein monolayer at elevated surface pressures.