http://hdl.handle.net/10027/1129 Thu, 23 May 2013 19:56:06 GMT 2013-05-23T19:56:06Z http://hdl.handle.net/10027/8751 A Simple Linear Response Closure Approximation for Slow Dynamics of A Multiscale System with Linear Coupling COUPLING∗ ABRAMOV, RAFAIL V. Many applications of contemporary science involve multiscale dynamics, which are typically characterized by the time and space scale separation of patterns of motion, with fewer slowly evolving variables and a much larger set of faster evolving variables. This time-space scale separation causes direct numerical simulation of the evolution of the dynamics to be computationally expensive due to both the large number of variables and the necessity to choose a small discretization time step in order to resolve the fast components of dynamics. In this work we propose a simple method of determining the closed model for slow variables alone, which requires only a single computation of appropriate statistics for the fast dynamics with a certain fixed state of the slow variables. The method is based on the first-order Taylor expansion of the averaged coupling term with respect to the slow variables, which can be computed using the linear fluctuation-dissipation theorem. We show that, with simple linear coupling in both slow and fast variables, this method produces quite comparable statistics to what is exhibited by a complete two-scale model. The main advantage of the method is that it applies even when the statistics of the full multiscale model cannot be simulated due to computational complexity, which makes it practical for real-world large scale applications. This is a copy of an article published in the Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal © 2012 Society for Industrial and Applied Mathematics Sun, 01 Jan 2012 06:00:00 GMT http://hdl.handle.net/10027/8751 2012-01-01T06:00:00Z http://hdl.handle.net/10027/8724 Geometric and Analytic Quasiconformality in Metric Measure Spaces Williams, Marshall We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism f : X → Y between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either space. When X and Y have locally Q-bounded geometry and Y is contained in an Alexandrov space of curvature bounded above, the sharpness of our results implies that, as in the classical case, the modular and pointwise outer dilatations of f are related by KO(f) = esssupHO(x, f). First published in Proceedings of the American Mathematical Society in volume 140 and issue 4, published by the American Mathematical Society Sun, 01 Apr 2012 05:00:00 GMT http://hdl.handle.net/10027/8724 2012-04-01T05:00:00Z http://hdl.handle.net/10027/8612 Selection of the number of clusters via the bootstrap method Fang, Yixin; Wang, Junhui Here the problem of selecting the number of clusters in cluster analysis is considered. Recently, the concept of clustering stability, which measures the robustness of any given clustering algorithm, has been utilized in Wang (2010) for selecting the number of clusters through cross validation. In this manuscript, an estimation scheme for clustering instability is developed based on the bootstrap, and then the number of clusters is selected so that the corresponding estimated clustering instability is minimized. The proposed selection criterion’s effectiveness is demonstrated on simulations and real examples. NOTICE: this is the author’s version of a work that was accepted for publication in Computational Statistics and Data Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computational Statistics and Data Analysis, Vol 56, Issue 3, (MAR 1 2012). DOI: 10.1016/j.csda.2011.09.003 Thu, 01 Mar 2012 06:00:00 GMT http://hdl.handle.net/10027/8612 2012-03-01T06:00:00Z http://hdl.handle.net/10027/8610 High Performance Multiple Sequence Alignment System for Pyrosequencing Reads from Multiple Reference Genomes Saeed, Fahad; Perez-Rathke, Alan; Gwarnicki, Jaroslaw; Berger-Wolf, Tanya; Khokhar, Ashfaq Genome resequencing with short reads generated from pyrosequencing generally relies on mapping the short reads against a single reference genome. However, mapping of reads from multiple reference genomes is not possible using a pairwise mapping algorithm. In order to align the reads w.r.t each other and the reference genomes, existing multiple sequence alignment(MSA) methods cannot be used because they do not take into account the position of these short reads with respect to the genome, and are highly inefficient for large number of sequences. In this paper, we develop a highly scalable parallel algorithm based on domain decomposition, referred to as PPyro- Align, to align such large number of reads from single or multiple reference genomes. The proposed alignment algorithm accurately aligns the erroneous reads, and has been implemented on a cluster of workstations using MPI library. Experimental results for different problem sizes are analyzed in terms of execution time, quality of the alignments, and the ability of the algorithm to handle reads from multiple haplotypes. We report high quality multiple alignment of up to 0.5 million reads. The algorithm is shown to be highly scalable and exhibits superlinear speedups with increasing number of processors. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Parallel and Distributed Computing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Parallel and Distributed Computing, Vol 72, Issue 1, (JAN 2012). DOI: 10.1016/j.jpdc.2011.08.001 Sun, 01 Jan 2012 06:00:00 GMT http://hdl.handle.net/10027/8610 2012-01-01T06:00:00Z