scholarly journals Dynamics of complex systems inferred from multivariate time series

2021 ◽  
Author(s):  
Els Weinans
Keyword(s):  
Time Series ◽  
Complex Systems ◽  
Multivariate Time Series

scholarly journals Evaluating the performance of multivariate indicators of resilience loss

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Els Weinans ◽  
Rick Quax ◽  
Egbert H. van Nes ◽  
Ingrid A. van de Leemput
Keyword(s):  
Time Series ◽  
Complex Systems ◽  
Multivariate Time Series ◽  
Tipping Points ◽  
Physical And Mental Health ◽  
One Dimensional ◽  
Slowing Down ◽  
The Past ◽  
Technological Developments ◽  
Resilience Indicators

AbstractVarious complex systems, such as the climate, ecosystems, and physical and mental health can show large shifts in response to small changes in their environment. These ‘tipping points’ are notoriously hard to predict based on trends. However, in the past 20 years several indicators pointing to a loss of resilience have been developed. These indicators use fluctuations in time series to detect critical slowing down preceding a tipping point. Most of the existing indicators are based on models of one-dimensional systems. However, complex systems generally consist of multiple interacting entities. Moreover, because of technological developments and wearables, multivariate time series are becoming increasingly available in different fields of science. In order to apply the framework of resilience indicators to multivariate time series, various extensions have been proposed. Not all multivariate indicators have been tested for the same types of systems and therefore a systematic comparison between the methods is lacking. Here, we evaluate the performance of the different multivariate indicators of resilience loss in different scenarios. We show that there is not one method outperforming the others. Instead, which method is best to use depends on the type of scenario the system is subject to. We propose a set of guidelines to help future users choose which multivariate indicator of resilience is best to use for their particular system.

scholarly journals Spectral Ranking of Causal Influence in Complex Systems

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 369
Author(s):  
Errol Zalmijn ◽  
Tom Heskes ◽  
Tom Claassen
Keyword(s):  
Time Series ◽  
Complex Systems ◽  
Information Transfer ◽  
Deviant Behavior ◽  
Interaction Analysis ◽  
Multivariate Time Series ◽  
Search Space ◽  
Eigenvector Centrality ◽  
Causal Influence ◽  
Weighted Directed Graph

Similar to natural complex systems, such as the Earth’s climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors measure relevant process variables at appropriate sampling rates, to provide time series as primary sources for system diagnostics. However, high-dimensionality, non-linearity and non-stationarity of the data are major challenges to efficiently, yet accurately, diagnose rare or new system issues by merely using model-based approaches. To reliably narrow down the causal search space, we validate a ranking algorithm that applies transfer entropy for bivariate interaction analysis of a system’s multivariate time series to obtain a weighted directed graph, and graph eigenvector centrality to identify the system’s most important sources of original information or causal influence. The results suggest that this approach robustly identifies the true drivers or causes of a complex system’s deviant behavior, even when its reconstructed information transfer network includes redundant edges.

scholarly journals Finding the direction of lowest resilience in multivariate complex systems

2019 ◽  
Vol 16 (159) ◽  
pp. 20190629 ◽  
Author(s):  
Els Weinans ◽  
J. Jelle Lever ◽  
Sebastian Bathiany ◽  
Rick Quax ◽  
Jordi Bascompte ◽  
...  
Keyword(s):  
Time Series ◽  
Complex Systems ◽  
Financial Markets ◽  
Multivariate Time Series ◽  
Network Systems ◽  
Short Time Series ◽  
Novel Approach ◽  
Data Resolution ◽  
Multivariate Systems ◽  
Short Time

The dynamics of complex systems, such as ecosystems, financial markets and the human brain, emerge from the interactions of numerous components. We often lack the knowledge to build reliable models for the behaviour of such network systems. This makes it difficult to predict potential instabilities. We show that one could use the natural fluctuations in multivariate time series to reveal network regions with particularly slow dynamics. The multidimensional slowness points to the direction of minimal resilience, in the sense that simultaneous perturbations on this set of nodes will take longest to recover. We compare an autocorrelation-based method with a variance-based method for different time-series lengths, data resolution and different noise regimes. We show that the autocorrelation-based method is less robust for short time series or time series with a low resolution but more robust for varying noise levels. This novel approach may help to identify unstable regions of multivariate systems or to distinguish safe from unsafe perturbations.

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