Finding the direction of lowest resilience in multivariate complex systems

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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Estimation and classification of temporal trends to support integrated ecosystem assessment

ICES Journal of Marine Science ◽

10.1093/icesjms/fsaa111 ◽

2020 ◽

Author(s):

Hiroko Kato Solvang ◽

Benjamin Planque

Keyword(s):

Time Series ◽

Barents Sea ◽

Multivariate Time Series ◽

Marine Ecosystem ◽

Temporal Trends ◽

Dynamic Factor ◽

Short Time Series ◽

Common Trends ◽

Common Trend ◽

Short Time

Abstract We propose a trend estimation and classification (TREC) approach to estimating dominant common trends among multivariate time series observations. Our methods are based on two statistical procedures that includes trend modelling and discriminant analysis for classifying similar trend (common trend) classes. We use simulations to evaluate the proposed approach and compare it with a relevant dynamic factor analysis in the time domain, which was recently proposed to estimate common trends in fisheries time series. We apply the TREC approach to the multivariate short time series datasets investigated by the ICES integrated assessment working groups for the Norwegian Sea and the Barents Sea. The proposed approach is robust for application to short time series, and it directly identifies and classifies the dominant trends underlying observations. Based on the classified trend classes, we suggest that communication among stakeholders like marine managers, industry representatives, non-governmental organizations, and governmental agencies can be enhanced by finding the common tendency between a biological community in a marine ecosystem and the environmental factors, as well as by the icons produced by generalizing common trend patterns.

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Deep learning for clustering of multivariate clinical patient trajectories with missing values

GigaScience ◽

10.1093/gigascience/giz134 ◽

2019 ◽

Vol 8 (11) ◽

Cited By ~ 5

Author(s):

Johann de Jong ◽

Mohammad Asif Emon ◽

Ping Wu ◽

Reagon Karki ◽

Meemansa Sood ◽

...

Keyword(s):

Time Series ◽

Deep Learning ◽

Alzheimer Disease ◽

Parkinson Disease ◽

Disease Progression ◽

Missing Values ◽

Multivariate Time Series ◽

Short Time Series ◽

Deep Embedding ◽

Short Time

Abstract Background Precision medicine requires a stratification of patients by disease presentation that is sufficiently informative to allow for selecting treatments on a per-patient basis. For many diseases, such as neurological disorders, this stratification problem translates into a complex problem of clustering multivariate and relatively short time series because (i) these diseases are multifactorial and not well described by single clinical outcome variables and (ii) disease progression needs to be monitored over time. Additionally, clinical data often additionally are hindered by the presence of many missing values, further complicating any clustering attempts. Findings The problem of clustering multivariate short time series with many missing values is generally not well addressed in the literature. In this work, we propose a deep learning–based method to address this issue, variational deep embedding with recurrence (VaDER). VaDER relies on a Gaussian mixture variational autoencoder framework, which is further extended to (i) model multivariate time series and (ii) directly deal with missing values. We validated VaDER by accurately recovering clusters from simulated and benchmark data with known ground truth clustering, while varying the degree of missingness. We then used VaDER to successfully stratify patients with Alzheimer disease and patients with Parkinson disease into subgroups characterized by clinically divergent disease progression profiles. Additional analyses demonstrated that these clinical differences reflected known underlying aspects of Alzheimer disease and Parkinson disease. Conclusions We believe our results show that VaDER can be of great value for future efforts in patient stratification, and multivariate time-series clustering in general.

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Tropical forest dynamics correspond to fair games in economic theory of financial markets

10.1101/2021.11.09.467956 ◽

2021 ◽

Author(s):

Yue Lin ◽

James Rosindell ◽

Uta Berger ◽

Helge Bruelheide ◽

Jens Kattge ◽

...

Keyword(s):

Time Series ◽

Complex Systems ◽

Time Series Data ◽

Dominant Role ◽

Series Data ◽

Market Theory ◽

Efficient Market ◽

Short Time Series ◽

Efficient Market Theory ◽

Short Time

Ecological and economic systems both comprise of autonomous adaptive agents. It is thus possible that similar mechanisms determine the organization of both these complex systems. Indeed several economic theories have already been successfully applied in an ecological context. Here we show that 'efficient market theory' in economics, where future earnings are distributed between competitors by a 'fair game', corresponds to fitness-equalizing mechanisms of coexistence in ecology. In contrast to stabilizing mechanisms, which promote coexistence by giving each species an equilibrium abundance that is resilient to perturbations, equalizing mechanisms promote coexistence without such resilience by minimizing the net fitness differences between species. However, identifying stabilizing and equalizing mechanisms from the short time-series data that are typically available in ecology is challenging. We used techniques from economics that are applied to collections of short time-series from a system. We found that observed species abundance dynamics in a neotropical forest are generally in agreement with efficient market theory implying a dominant role of equalizing mechanisms, which finding quantifies and supports what was generally believed about that specific forest system. Our study highlights that complex systems from ecology and economics share common features suggesting the possibility of further synergy between ecology and economics in future.

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A strategy for meta-analysis of short time series microarray datasets

Frontiers in Bioscience ◽

10.2741/3512 ◽

2009 ◽

Vol Volume (14) ◽

pp. 4058 ◽

Cited By ~ 2

Author(s):

Ruping Sun

Keyword(s):

Time Series ◽

Meta Analysis ◽

Short Time Series ◽

Microarray Datasets ◽

Short Time ◽

Time Series Microarray

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Finder: A novel approach of change point detection for multivariate time series

Applied Intelligence ◽

10.1007/s10489-021-02532-x ◽

2021 ◽

Author(s):

Haizhou Du ◽

Ziyi Duan

Keyword(s):

Time Series ◽

Change Point ◽

Multivariate Time Series ◽

Change Point Detection ◽

Novel Approach ◽

Point Detection

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Identifying bidirectional total and non-linear information flow in functional corticomuscular coupling during a dorsiflexion task: a pilot study

Journal of NeuroEngineering and Rehabilitation ◽

10.1186/s12984-021-00872-w ◽

2021 ◽

Vol 18 (1) ◽

Author(s):

Tie Liang ◽

Qingyu Zhang ◽

Xiaoguang Liu ◽

Bin Dong ◽

Xiuling Liu ◽

...

Keyword(s):

Time Series ◽

Information Flow ◽

Gamma Band ◽

Motor Dysfunction ◽

Beta Band ◽

Short Time Series ◽

Information Interaction ◽

Stroke Group ◽

Short Time ◽

Maximal Information Coefficient

Abstract Background The key challenge to constructing functional corticomuscular coupling (FCMC) is to accurately identify the direction and strength of the information flow between scalp electroencephalography (EEG) and surface electromyography (SEMG). Traditional TE and TDMI methods have difficulty in identifying the information interaction for short time series as they tend to rely on long and stable data, so we propose a time-delayed maximal information coefficient (TDMIC) method. With this method, we aim to investigate the directional specificity of bidirectional total and nonlinear information flow on FCMC, and to explore the neural mechanisms underlying motor dysfunction in stroke patients. Methods We introduced a time-delayed parameter in the maximal information coefficient to capture the direction of information interaction between two time series. We employed the linear and non-linear system model based on short data to verify the validity of our algorithm. We then used the TDMIC method to study the characteristics of total and nonlinear information flow in FCMC during a dorsiflexion task for healthy controls and stroke patients. Results The simulation results showed that the TDMIC method can better detect the direction of information interaction compared with TE and TDMI methods. For healthy controls, the beta band (14–30 Hz) had higher information flow in FCMC than the gamma band (31–45 Hz). Furthermore, the beta-band total and nonlinear information flow in the descending direction (EEG to EMG) was significantly higher than that in the ascending direction (EMG to EEG), whereas in the gamma band the ascending direction had significantly higher information flow than the descending direction. Additionally, we found that the strong bidirectional information flow mainly acted on Cz, C3, CP3, P3 and CPz. Compared to controls, both the beta-and gamma-band bidirectional total and nonlinear information flows of the stroke group were significantly weaker. There is no significant difference in the direction of beta- and gamma-band information flow in stroke group. Conclusions The proposed method could effectively identify the information interaction between short time series. According to our experiment, the beta band mainly passes downward motor control information while the gamma band features upward sensory feedback information delivery. Our observation demonstrate that the center and contralateral sensorimotor cortex play a major role in lower limb motor control. The study further demonstrates that brain damage caused by stroke disrupts the bidirectional information interaction between cortex and effector muscles in the sensorimotor system, leading to motor dysfunction.

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Evaluating the performance of multivariate indicators of resilience loss

Scientific Reports ◽

10.1038/s41598-021-87839-y ◽

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.

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Improved Lempel-Ziv Algorithm Based on Complexity Measurement of Short Time Series

Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007) ◽

10.1109/fskd.2007.357 ◽

2007 ◽

Cited By ~ 4

Author(s):

Feng-tao Liu ◽

Yong Tang

Keyword(s):

Time Series ◽

Short Time Series ◽

Complexity Measurement ◽

Short Time

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Uncertainty quantification of the effects of biotic interactions on community dynamics from nonlinear time-series data

Journal of The Royal Society Interface ◽

10.1098/rsif.2018.0695 ◽

2018 ◽

Vol 15 (147) ◽

pp. 20180695 ◽

Cited By ~ 7

Author(s):

Simone Cenci ◽

Serguei Saavedra

Keyword(s):

Time Series ◽

Community Dynamics ◽

Time Series Data ◽

Multivariate Time Series ◽

Model Averaging ◽

Biotic Interactions ◽

Series Data ◽

Time Intervals ◽

Novel Approach ◽

Data Generating Process

Biotic interactions are expected to play a major role in shaping the dynamics of ecological systems. Yet, quantifying the effects of biotic interactions has been challenging due to a lack of appropriate methods to extract accurate measurements of interaction parameters from experimental data. One of the main limitations of existing methods is that the parameters inferred from noisy, sparsely sampled, nonlinear data are seldom uniquely identifiable. That is, many different parameters can be compatible with the same dataset and can generalize to independent data equally well. Hence, it is difficult to justify conclusive assertions about the effect of biotic interactions without information about their associated uncertainty. Here, we develop an ensemble method based on model averaging to quantify the uncertainty associated with the effect of biotic interactions on community dynamics from non-equilibrium ecological time-series data. Our method is able to detect the most informative time intervals for each biotic interaction within a multivariate time series and can be easily adapted to different regression schemes. Overall, this novel approach can be used to associate a time-dependent uncertainty with the effect of biotic interactions. Moreover, because we quantify uncertainty with minimal assumptions about the data-generating process, our approach can be applied to any data for which interactions among variables strongly affect the overall dynamics of the system.

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