A data-driven test to compare two or multiple time series

2011 ◽  
Vol 55 (6) ◽  
pp. 2183-2196 ◽  
Author(s):  
Lei Jin
Keyword(s):  
Time Series ◽  
Data Driven ◽  
Multiple Time ◽  
Multiple Time Series ◽  
Data Driven Test

scholarly journals Contractibility of a persistence map preimage

2020 ◽  
Vol 4 (4) ◽  
pp. 509-523
Author(s):  
Jacek Cyranka ◽  
Konstantin Mischaikow ◽  
Charles Weibel
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Time Series ◽  
Data Driven ◽  
Dimensional System ◽  
Multiple Time ◽  
Multiple Time Series ◽  
Topological Features ◽  
Persistence Diagram ◽  
Persistence Diagrams

Abstract This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of snapshots of solutions, what conclusions can be drawn about solutions of the original dynamical system? We address this challenge in the context of an N dimensional system of ordinary differential equation defined in $${\mathbb {R}}^N$$ R N . To each point in $${\mathbb {R}}^N$$ R N (e.g. an initial condition) we associate a persistence diagram. The main result of this paper is that under this association the preimage of every persistence diagram is contractible. As an application we provide conditions under which multiple time series of persistence diagrams can be used to conclude the existence of a fixed point of the differential equation that generates the time series.

scholarly journals Inferring pairwise regulatory relationships from multiple time series datasets

2007 ◽  
Vol 23 (6) ◽  
pp. 755-763 ◽  
Author(s):  
Y. Shi ◽  
T. Mitchell ◽  
Z. Bar-Joseph
Keyword(s):  
Time Series ◽  
Multiple Time ◽  
Multiple Time Series
Sign in / Sign up

Export Citation Format

Share Document