On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics

In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work is the development of an efficient direct numerical collocation method. The paper is completed with two examples taken from crack theory and acoustics: the study of a single crack in a linear isotropic elastic medium, and diffraction of a plane acoustic wave by a thin rigid screen.Comment: accepted by Acta Mechanica, 19 pages, 3 figure

Identifying Cis-Regulatory Sequences by Word Profile Similarity

Recognizing regulatory sequences in genomes is a continuing challenge, despite a wealth of available genomic data and a growing number of experimentally validated examples.We discuss here a simple approach to search for regulatory sequences based on the compositional similarity of genomic regions and known cis-regulatory sequences. This method, which is not limited to searching for predefined motifs, recovers sequences known to be under similar regulatory control. The words shared by the recovered sequences often correspond to known binding sites. Furthermore, we show that although local word profile clustering is predictive for the regulatory sequences involved in blastoderm segmentation, local dissimilarity is a more universal feature of known regulatory sequences in Drosophila.Our method leverages sequence motifs within a known regulatory sequence to identify co-regulated sequences without explicitly defining binding sites. We also show that regulatory sequences can be distinguished from surrounding sequences by local sequence dissimilarity, a novel feature in identifying regulatory sequences across a genome. Source code for WPH-finder is available for download at http://rana.lbl.gov/downloads/wph.tar.gz

Alignment and Prediction of cis-Regulatory Modules Based on a Probabilistic Model of Evolution

Cross-species comparison has emerged as a powerful paradigm for predicting cis-regulatory modules (CRMs) and understanding their evolution. The comparison requires reliable sequence alignment, which remains a challenging task for less conserved noncoding sequences. Furthermore, the existing models of DNA sequence evolution generally do not explicitly treat the special properties of CRM sequences. To address these limitations, we propose a model of CRM evolution that captures different modes of evolution of functional transcription factor binding sites (TFBSs) and the background sequences. A particularly novel aspect of our work is a probabilistic model of gains and losses of TFBSs, a process being recognized as an important part of regulatory sequence evolution. We present a computational framework that uses this model to solve the problems of CRM alignment and prediction. Our alignment method is similar to existing methods of statistical alignment but uses the conserved binding sites to improve alignment. Our CRM prediction method deals with the inherent uncertainties of binding site annotations and sequence alignment in a probabilistic framework. In simulated as well as real data, we demonstrate that our program is able to improve both alignment and prediction of CRM sequences over several state-of-the-art methods. Finally, we used alignments produced by our program to study binding site conservation in genome-wide binding data of key transcription factors in the Drosophila blastoderm, with two intriguing results: (i) the factor-bound sequences are under strong evolutionary constraints even if their neighboring genes are not expressed in the blastoderm and (ii) binding sites in distal bound sequences (relative to transcription start sites) tend to be more conserved than those in proximal regions. Our approach is implemented as software, EMMA (Evolutionary Model-based cis-regulatory Module Analysis), ready to be applied in a broad biological context

THE FINITE PART OF DIVERGENT INTEGRALS WITH LOGARITHMIC FACTORS

The concepts of the finite part (f.p.) and analytic finite part (a.f.p.) of divergent integrals are defined in the situation where the singular function in the integral has a logarithmic factor. The change of variables in f.p.- and a.f.p-integrals is examined