Boundary integral equation methods for the elastic and thermoelastic waves in three dimensions

In this paper, we consider the boundary integral equation (BIE) method for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the Fredholm integral equations of the first kind. The innovative contribution of this work lies in the proposal of the new regularized formulations for the hyper-singular boundary integral operators (BIO) associated with the time-harmonic elastic and thermoelastic wave equations. With the help of the new regularized formulations, we only need to compute the integrals with weak singularities at most in the corresponding variational forms of the boundary integral equations. The accuracy of the regularized formulations is demonstrated through numerical examples using the Galerkin boundary element method (BEM).Comment: 24 pages, 6 figure

Reliable Data Processing Enabled By Program Analysis

Errors pose a serious threat to the output validity of modern data processing, which is often performed by computer programs. In scientific computation, data are collected through instruments or sensors that may be exposed to rough environmental conditions, leading to errors. Furthermore, during the computation process data may not be precisely represented due to the limited precision of the underlying machine, leading to representation errors. Computational processing of these data may hence produce unreliable output results or even faulty conclusions. We call them reliability problems. ^ We consider the reliability problems that are caused by two kinds of errors. The first kind of errors includes input and parameter errors, which originate from the external physical environment. We call these external errors. The other kind of errors is due to the limited representation of floating-point values. They occur when values cannot be precisely represented by machines. We call them internal representation errors, or internal errors. They are usually at a much smaller scale compared to external errors. Nonetheless, such tiny errors may still lead to unreliable results and serious problems. ^ In this dissertation, we develop program analysis techniques to enable reliable data processing. For external errors, we propose techniques to improve the sampling efficiency of Monte Carlo methods, namely execution coalescing and white-box sampling. For internal errors, we develop efficient monitoring techniques to detect instability problems at runtime in floating point program executions

SEED: efficient clustering of next-generation sequences.

MotivationSimilarity clustering of next-generation sequences (NGS) is an important computational problem to study the population sizes of DNA/RNA molecules and to reduce the redundancies in NGS data. Currently, most sequence clustering algorithms are limited by their speed and scalability, and thus cannot handle data with tens of millions of reads.ResultsHere, we introduce SEED-an efficient algorithm for clustering very large NGS sets. It joins sequences into clusters that can differ by up to three mismatches and three overhanging residues from their virtual center. It is based on a modified spaced seed method, called block spaced seeds. Its clustering component operates on the hash tables by first identifying virtual center sequences and then finding all their neighboring sequences that meet the similarity parameters. SEED can cluster 100 million short read sequences in <4 h with a linear time and memory performance. When using SEED as a preprocessing tool on genome/transcriptome assembly data, it was able to reduce the time and memory requirements of the Velvet/Oasis assembler for the datasets used in this study by 60-85% and 21-41%, respectively. In addition, the assemblies contained longer contigs than non-preprocessed data as indicated by 12-27% larger N50 values. Compared with other clustering tools, SEED showed the best performance in generating clusters of NGS data similar to true cluster results with a 2- to 10-fold better time performance. While most of SEED's utilities fall into the preprocessing area of NGS data, our tests also demonstrate its efficiency as stand-alone tool for discovering clusters of small RNA sequences in NGS data from unsequenced organisms.AvailabilityThe SEED software can be downloaded for free from this site: http://manuals.bioinformatics.ucr.edu/home/[email protected] informationSupplementary data are available at Bioinformatics online