Abstract:
:Many processes in science and engineering develop multiscale temporal and spatial patterns, with complex underlying dynamics and time-dependent external forcings. Because of the importance in understanding and predicting these phenomena, extracting the salient modes of variability empirically from incomplete observations is a problem of wide contemporary interest. Here, we present a technique for analyzing high-dimensional, complex time series that exploits the geometrical relationships between the observed data points to recover features characteristic of strongly nonlinear dynamics (such as intermittency and rare events), which are not accessible to classical singular spectrum analysis. The method employs Laplacian eigenmaps, evaluated after suitable time-lagged embedding, to produce a reduced representation of the observed samples, where standard tools of matrix algebra can be used to perform truncated singular-value decomposition despite the nonlinear geometrical structure of the dataset. We illustrate the utility of the technique in capturing intermittent modes associated with the Kuroshio current in the North Pacific sector of a general circulation model and dimensional reduction of a low-order atmospheric model featuring chaotic intermittent regime transitions, where classical singular spectrum analysis is already known to fail dramatically.
journal_name
Proc Natl Acad Sci U S Aauthors
Giannakis D,Majda AJdoi
10.1073/pnas.1118984109subject
Has Abstractpub_date
2012-02-14 00:00:00pages
2222-7issue
7eissn
0027-8424issn
1091-6490pii
1118984109journal_volume
109pub_type
杂志文章abstract::In yeast, the mRNA encoded by the MAT alpha 1 gene is unstable (t1/2 = 5 min) and the mRNAs encoded by the ACT1 gene (t1/2 = 30 min) and the PGK1 gene (t1/2 = 45 min) are stable. To understand the RNA structural features that dictate mRNA decay rates in yeast, we have constructed PGK1/MAT alpha 1 and ACT1/MAT alpha 1 ...
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abstract::In this article, we address the problem of modeling generic features of structurally but not textually related DNA motifs, that is, motifs whose consensus sequences are entirely different but nevertheless share "metasequence features" reflecting similarities in the DNA-binding domains of their associated protein recog...
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更新日期:2015-02-17 00:00:00