Convergence Acceleration Techniques

This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the acceleration of slowly convergent and the summation of divergent series that are ubiquitous in relevant applications. The computing time is reduced in many cases by orders of magnitude.Comment: 6 pages, LaTeX; provides an easy-to-understand introduction to the field of convergence acceleratio

Learning short multivariate time series models through evolutionary and sparse matrix computation

Multivariate time series (MTS) data are widely available in different fields including medicine, finance, bioinformatics, science and engineering. Modelling MTS data accurately is important for many decision making activities. One area that has been largely overlooked so far is the particular type of time series where the data set consists of a large number of variables but with a small number of observations. In this paper we describe the development of a novel computational method based on Natural Computation and sparse matrices that bypasses the size restrictions of traditional statistical MTS methods, makes no distribution assumptions, and also locates the associated parameters. Extensive results are presented, where the proposed method is compared with both traditional statistical and heuristic search techniques and evaluated on a number of criteria. The results have implications for a wide range of applications involving the learning of short MTS models

Towards Novel Nonparametric Statistical Methods and Bioinformatics Tools for Clinical and Translational Sciences

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics. Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal systems, we often need to integrate information from several of these sources. Thus, as the field of clinical research moves toward complex diseases, the demand for modern data base systems and advanced statistical methods increases. The traditional statistical methods implemented in most of the bioinformatics tools currently used in the novel field of genetics and functional genomics are based on the linear model and, thus, have shortcomings when applied to nonlinear biological systems. The previous work on partially ordered data (Wittkowski 1988; 1992), when combined with theoretical results (Hoeffding 1948) and computational strategies (Deuchler 1914) has opened a new field of nonparametric statistics. With grid technology, new tools are now feasible when screening for interactions between genetics (Wittkowski, Liu 2002) and functional genomics (Wittkowski, Lee 2004). Having more complex study designs and more specific methods available increases the demand for decision support when selecting appropriate bioinformatics tools. With the advent of rapid prototyping systems for Web based database application, we have recently begun to complement previous work on knowledge based systems with graphical Web-based tools for acquisition of DESIGN and MODEL knowledge.Biostatistics Bioinformatics NIH NCRR ROADMAP

Sequence-specific sequence comparison using pairwise statistical significance

Sequence comparison is one of the most fundamental computational problems in bioinformatics for which many approaches have been and are still being developed. In particular, pairwise sequence alignment forms the crux of both DNA and protein sequence comparison techniques, which in turn forms the basis of many other applications in bioinformatics. Pairwise sequence alignment methods align two sequences using a substitution matrix consisting of pairwise scores of aligning different residues with each other (like BLOSUM62), and give an alignment score for the given sequence-pair. The biologists routinely use such pairwise alignment programs to identify similar, or more specifically, related sequences (having common ancestor). It is widely accepted that the relatedness of two sequences is better judged by statistical significance of the alignment score rather than by the alignment score alone. This research addresses the problem of accurately estimating statistical significance of pairwise alignment for the purpose of identifying related sequences, by making the sequence comparison process more sequence-specific. The major contributions of this research work are as follows. Firstly, using sequence-specific strategies for pairwise sequence alignment in conjunction with sequence-specific strategies for statistical significance estimation, wherein accurate methods for pairwise statistical significance estimation using standard, sequence-specific, and position-specific substitution matrices are developed. Secondly, using pairwise statistical significance to improve the performance of the most popular database search program PSI-BLAST. Thirdly, design and implementation of heuristics to speed-up pairwise statistical significance estimation by an factor of more than 200. The implementation of all the methods developed in this work is freely available online. With the all-pervasive application of sequence alignment methods in bioinformatics using the ever-increasing sequence data, this work is expected to offer useful contributions to the research community

Efficient Feature Selection and Classification of Protein Sequence Data in Bioinformatics

Bioinformatics has been an emerging area of research for the last three decades. The ultimate aims of bioinformatics were to store and manage the biological data, and develop and analyze computational tools to enhance their understanding. The size of data accumulated under various sequencing projects is increasing exponentially, which presents difficulties for the experimental methods. To reduce the gap between newly sequenced protein and proteins with known functions, many computational techniques involving classification and clustering algorithms were proposed in the past. The classification of protein sequences into existing superfamilies is helpful in predicting the structure and function of large amount of newly discovered proteins. The existing classification results are unsatisfactory due to a huge size of features obtained through various feature encoding methods. In this work, a statistical metric-based feature selection technique has been proposed in order to reduce the size of the extracted feature vector. The proposed method of protein classification shows significant improvement in terms of performance measure metrics: accuracy, sensitivity, specificity, recall, F-measure, and so forth

Statistical methods in ecological data analysis

Although analytical methods in statistics have all along been generic and evolutionary in the first half of past century, the developments happening in the field of computational statistics in the past couple of decades are more need based and custom tuned. A lot of effort is being put in by researchers in bundling methods, theory and procedures in classical statistical literature on their common applicability to a targeted exploration. It is common place to collate various univariate, multivariate, parametric, non-parametric, frequentist and non-frequentist methods, which have applications in different domains like ecology, clinical trials, bioinformatics etc. and tag them as per the domain subject matter. Thus the generic and specific procedures which are of relevance in exploratory and confirmatory analyses in the field of ecological studies of communities have been grouped under a common pivot. During the course of this discussion a couple of such statistical methods used in community structure studies would be dwelled upon