当前位置: X-MOL 学术J. Math. Biol. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Using extremal events to characterize noisy time series.
Journal of Mathematical Biology ( IF 2.2 ) Pub Date : 2020-02-01 , DOI: 10.1007/s00285-020-01471-4
Eric Berry 1 , Bree Cummins 1 , Robert R Nerem 1 , Lauren M Smith 2 , Steven B Haase 2 , Tomas Gedeon 1
Affiliation  

Experimental time series provide an informative window into the underlying dynamical system, and the timing of the extrema of a time series (or its derivative) contains information about its structure. However, the time series often contain significant measurement errors. We describe a method for characterizing a time series for any assumed level of measurement error [Formula: see text] by a sequence of intervals, each of which is guaranteed to contain an extremum for any function that [Formula: see text]-approximates the time series. Based on the merge tree of a continuous function, we define a new object called the normalized branch decomposition, which allows us to compute intervals for any level [Formula: see text]. We show that there is a well-defined total order on these intervals for a single time series, and that it is naturally extended to a partial order across a collection of time series comprising a dataset. We use the order of the extracted intervals in two applications. First, the partial order describing a single dataset can be used to pattern match against switching model output (Cummins et al. in SIAM J Appl Dyn Syst 17(2):1589-1616, 2018), which allows the rejection of a network model. Second, the comparison between graph distances of the partial orders of different datasets can be used to quantify similarity between biological replicates.

中文翻译:

使用极端事件来表征嘈杂的时间序列。

实验时间序列为深入了解动力学系统提供了信息窗口,时间序列(或其导数)的极值时序包含有关其结构的信息。但是,时间序列通常包含重大的测量误差。我们描述了一种通过一系列间隔来表征任何假定的测量误差水平[公式:参见文本]的时间序列的方法,其中每个间隔都保证包含对[公式]近似的任何函数的极值。时间序列。基于连续函数的合并树,我们定义了一个称为标准化分支分解的新对象,该对象使我们能够计算任何级别的间隔[公式:请参见文本]。我们表明,对于单个时间序列,这些间隔上有明确定义的总顺序,并且自然地将其扩展到包含数据集的时间序列集合中的部分顺序。我们在两个应用程序中使用提取间隔的顺序。首先,可以使用描述单个数据集的偏序来针对切换模型输出进行模式匹配(Cummins等人,SIAM J Appl Dyn Syst 17(2):1589-1616,2018),这允许拒绝网络模型。其次,不同数据集的部分顺序的图形距离之间的比较可用于量化生物学重复之间的相似性。1589-1616,2018),它允许拒绝网络模型。其次,不同数据集的部分顺序的图形距离之间的比较可用于量化生物学重复之间的相似性。1589-1616,2018),它允许拒绝网络模型。第二,不同数据集的部分顺序的图形距离之间的比较可用于量化生物学重复之间的相似性。
更新日期:2020-04-16
down
wechat
bug