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.

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.

Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the EM algorithm could improve its rate of convergence. In this paper, we show how this modified EM algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the EM algorithm for segmenting MR images of the human brain. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

Methods for prediction of peptide binding to MHC molecules: A comparative study

Background: A variety of methods for prediction of peptide binding to major histocompatibility complex (MHC) have been proposed. These methods are based on binding motifs, binding matrices, hidden Markov models (HMM), or artificial neural networks (ANN). There has been little prior work on the comparative analysis of these methods. Materials and Methods: We performed a comparison of the performance of six methods applied to the prediction of two human MHC class I molecules, including binding matrices and motifs, ANNs, and HMMs. Results: The selection of the optimal prediction method depends on the amount of available data (the number of peptides of known binding affinity to the MHC molecule of interest), the biases in the data set and the intended purpose of the prediction (screening of a single protein versus mass screening). When little or no peptide data are available, binding motifs are the most useful alternative to random guessing or use of a complete overlapping set of peptides for selection of candidate binders. As the number of known peptide binders increases, binding matrices and HMM become more useful predictors. ANN and HMM are the predictive methods of choice for MHC alleles with more than 100 known binding peptides. Conclusion: The ability of bioinformatic methods to reliably predict MHC binding peptides, and thereby potential T-cell epitopes, has major implications for clinical immunology, particularly in the area of vaccine design.

A two-dimensional fuzzy random model of soil pore structure

A new conceptual model for soil pore-solid structure is formalized. Soil pore-solid structure is proposed to comprise spatially abutting elements each with a value which is its membership to the fuzzy set ''pore,'' termed porosity. These values have a range between zero (all solid) and unity (all pore). Images are used to represent structures in which the elements are pixels and the value of each is a porosity. Two-dimensional random fields are generated by allocating each pixel a porosity by independently sampling a statistical distribution. These random fields are reorganized into other pore-solid structural types by selecting parent points which have a specified local region of influence. Pixels of larger or smaller porosity are aggregated about the parent points and within the region of interest by controlled swapping of pixels in the image. This creates local regions of homogeneity within the random field. This is similar to the process known as simulated annealing. The resulting structures are characterized using one-and two-dimensional variograms and functions describing their connectivity. A variety of examples of structures created by the model is presented and compared. Extension to three dimensions presents no theoretical difficulties and is currently under development.

Elastic moduli of model random three-dimensional closed-cell cellular solids

Most cellular solids are random materials, while practically all theoretical structure-property results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic properties of solids with a closed-cell cellular structure. We have computed the density (rho) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law E infinity rho (n) (1<n<2), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Review of recent results on excursion set models

Many images consist of two or more 'phases', where a phase is a collection of homogeneous zones. For example, the phases may represent the presence of different sulphides in an ore sample. Frequently, these phases exhibit very little structure, though all connected components of a given phase may be similar in some sense. As a consequence, random set models are commonly used to model such images. The Boolean model and models derived from the Boolean model are often chosen. An alternative approach to modelling such images is to use the excursion sets of random fields to model each phase. In this paper, the properties of excursion sets will be firstly discussed in terms of modelling binary images. Ways of extending these models to multi-phase images will then be explored. A desirable feature of any model is to be able to fit it to data reasonably well. Different methods for fitting random set models based on excursion sets will be presented and some of the difficulties with these methods will be discussed.

Prediction of promiscuous peptides that bind HLA class I molecules

Promiscuous T-cell epitopes make ideal targets for vaccine development. We report here a computational system, multipred, for the prediction of peptide binding to the HLA-A2 supertype. It combines a novel representation of peptide/MHC interactions with a hidden Markov model as the prediction algorithm. multipred is both sensitive and specific, and demonstrates high accuracy of peptide-binding predictions for HLA-A*0201, *0204, and *0205 alleles, good accuracy for *0206 allele, and marginal accuracy for *0203 allele. multipred replaces earlier requirements for individual prediction models for each HLA allelic variant and simplifies computational aspects of peptide-binding prediction. Preliminary testing indicates that multipred can predict peptide binding to HLA-A2 supertype molecules with high accuracy, including those allelic variants for which no experimental binding data are currently available.

Computational methods for prediction of T-cell epitopes - a framework for modelling, testing, and applications

Computational models complement laboratory experimentation for efficient identification of MHC-binding peptides and T-cell epitopes. Methods for prediction of MHC-binding peptides include binding motifs, quantitative matrices, artificial neural networks, hidden Markov models, and molecular modelling. Models derived by these methods have been successfully used for prediction of T-cell epitopes in cancer, autoimmunity, infectious disease, and allergy. For maximum benefit, the use of computer models must be treated as experiments analogous to standard laboratory procedures and performed according to strict standards. This requires careful selection of data for model building, and adequate testing and validation. A range of web-based databases and MHC-binding prediction programs are available. Although some available prediction programs for particular MHC alleles have reasonable accuracy, there is no guarantee that all models produce good quality predictions. In this article, we present and discuss a framework for modelling, testing, and applications of computational methods used in predictions of T-cell epitopes. (C) 2004 Elsevier Inc. All rights reserved.

Identification and analysis of chromodomain-containing proteins encoded in the mouse transcriptome

The chromodomain is 40-50 amino acids in length and is conserved in a wide range of chromatic and regulatory proteins involved in chromatin remodeling. Chromodomain-containing proteins can be classified into families based on their broader characteristics, in particular the presence of other types of domains, and which correlate with different subclasses of the chromodomains themselves. Hidden Markov model (HMM)-generated profiles of different subclasses of chromodomains were used here to identify sequences encoding chromodomain-containing proteins in the mouse transcriptome and genome. A total of 36 different loci encoding proteins containing chromodomains, including 17 novel loci, were identified. Six of these loci (including three apparent pseudogenes, a novel HP1 ortholog, and two novel Msl-3 transcription factor-like proteins) are not present in the human genome, whereas the human genome contains four loci (two CDY orthologs and two apparent CDY pseuclogenes) that are not present in mouse. A number of these loci exhibit alternative splicing to produce different isoforms, including 43 novel variants, some of which lack the chromodomain. The likely functions of these proteins are discussed in relation to the known functions of other chromodomain-containing proteins within the same family.

Genetic algorithm optimization of adaptive multi-scale GLCM features

We introduce a new second-order method of texture analysis called Adaptive Multi-Scale Grey Level Co-occurrence Matrix (AMSGLCM), based on the well-known Grey Level Co-occurrence Matrix (GLCM) method. The method deviates significantly from GLCM in that features are extracted, not via a fixed 2D weighting function of co-occurrence matrix elements, but by a variable summation of matrix elements in 3D localized neighborhoods. We subsequently present a new methodology for extracting optimized, highly discriminant features from these localized areas using adaptive Gaussian weighting functions. Genetic Algorithm (GA) optimization is used to produce a set of features whose classification worth is evaluated by discriminatory power and feature correlation considerations. We critically appraised the performance of our method and GLCM in pairwise classification of images from visually similar texture classes, captured from Markov Random Field (MRF) synthesized, natural, and biological origins. In these cross-validated classification trials, our method demonstrated significant benefits over GLCM, including increased feature discriminatory power, automatic feature adaptability, and significantly improved classification performance.

Wurst: a protein threading server with a structural scoring function, sequence profiles and optimized substitution matrices

Wurst is a protein threading program with an emphasis on high quality sequence to structure alignments (http://www.zbh.uni-hamburg.de/wurst). Submitted sequences are aligned to each of about 3000 templates with a conventional dynamic programming algorithm, but using a score function with sophisticated structure and sequence terms. The structure terms are a log-odds probability of sequence to structure fragment compatibility, obtained from a Bayesian classification procedure. A simplex optimization was used to optimize the sequence-based terms for the goal of alignment and model quality and to balance the sequence and structural contributions against each other. Both sequence and structural terms operate with sequence profiles.

Predictive vaccinology: Optimisation of predictions using support vector machine classifiers

Promiscuous human leukocyte antigen (HLA) binding peptides are ideal targets for vaccine development. Existing computational models for prediction of promiscuous peptides used hidden Markov models and artificial neural networks as prediction algorithms. We report a system based on support vector machines that outperforms previously published methods. Preliminary testing showed that it can predict peptides binding to HLA-A2 and -A3 super-type molecules with excellent accuracy, even for molecules where no binding data are currently available.