Abstract
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.
Highlights
IntroductionBy collecting simultaneous time series measuring different components of a dynamical system, we can infer potentially causal relationships between components [2, 3, 4, 5]
Time series data provide a discrete measurement of a dynamical system
This approach, named DSGRN (Dynamic Signatures Generated by Regulatory Networks) [17], leverages the fact that the switching system admits a finite decomposition of phase space into domains, and each variable of the dynamical system can be assigned one of the finite number of states representing these domains
Summary
By collecting simultaneous time series measuring different components of a dynamical system, we can infer potentially causal relationships between components [2, 3, 4, 5]. These relationships are represented in the form of a regulatory network, deduced from data experimentally or via network learning [5, 6, 7, 8, 9, 10, 11]. In [12], we introduced a method to describe the global dynamics of a regulatory network for all parameterizations of the switching system. DSGRN provides a complete combinatorialization of dynamics in both phase space and parameter space
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
