Windowed detrended cross-correlation analysis of synchronization processes

Roume, Clément; Almurad, Zainy M.H.; Scotti, M.; Ezzina, Samar; Blain, Hubert; Delignières, Didier

doi:10.1016/j.physa.2018.08.074

Cited by 20 publications

(37 citation statements)

References 43 publications

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“…The standard deviation and α-scaling were determined for SSDyn time series. In addition, and to further understand the nature of the synchronization, we have determined the Windowed Detrended Cross Correlation function (WDCC) according to Roume et al [35]. WDCC was calculated from lag −10 to lag +10, between ASYN and ST time series for each stimuli condition.…”

Section: Discussionmentioning

confidence: 99%

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Synchronization dynamics modulates stride-to-stride fluctuations when walking to an invariant but not to a fractal-like stimulus

Vaz

Groff

Rowen

et al. 2019

Neuroscience Letters

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Walking with different types of cueing/stimulus (i.e. auditory, visual) has shown to alter gait variability, thus emerging as an innovative therapeutical tool to restore abnormal gait variability in clinical populations. However, the majority of the research in this area has focused on auditory stimulus, while visual stimulus is an understudied alternative that needs more attention, particularly due to the natural dependence on vision during walking. Furthermore, the time differences between the occurrences of the walking steps and the sensory cues, also known as asynchronies, have also received minimal attention even though how well will synchronize with different stimuli is of great importance. This study investigated how synchronizing to visual stimulus that is presented with different temporal structures could affect gait variability and their respected asynchronies. Participants performed four 15-minute walking trials around an indoor track while wearing insole footswitches for the following conditions: a) self-paced walking, and b) walking with glasses that instructed the subjects to step in sync with a virtual moving bar. The stepping occurences of the moving bar were presented in three different ways b1) non-variable, b2) variable and b3) random. Stride times and asynchronies were determined, and the mean values along with the fractal scaling (an indicator of the complexity) in their time series, were calculated. The fractal scaling of the stride times was unaltered when participants walked with the variable stimulus as compared to the self-paced walking condition; while significantly decreased during the non-variable and random conditions indicating a loss of complexity for these two conditions. Regarding the asynchronies, no differences were observed in the means or the fractal scaling of the asynchronies. The correlation analysis between stride times and asynchronies revealed a strong relationship for the non-variable condition but a weak one for both variable and random conditions. Taken together, the present study results supports the idea of an existing internal timekeeper that exhibits complexity. We have shown that this complex pattern is similar regardless of the stimulus condition, suggesting that the system's complexity is likely to be expressed at the task performance level-asyncrhonies-when walking to a stimulus. Thus, future research in Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Section: Discussionmentioning

confidence: 99%

“…the short-term processes. As recently proposed [35] the WDCC function should be considered as a pattern. Here we observed an overall identical pattern between conditions suggesting similar local dynamics regardless of the stimulus temporal structure.…”

Section: Compensatory Strategies Are Not Driven By the Structure Of Tmentioning

confidence: 99%

Synchronization dynamics modulates stride-to-stride fluctuations when walking to an invariant but not to a fractal-like stimulus

Vaz

Groff

Rowen

et al. 2019

Neuroscience Letters

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“…Almurad et al (2017) and Roume et al (2018) proposed another method, the Windowed detrended cross-correlation analysis (WDCC), based on the analysis of cross-correlations between the series produced by the two systems. In this method, the series is divided into short intervals of 15 data points, detrended within each interval, and the cross-correlation function, from lag −10 to lag 10, is computed within each interval.…”

Section: Introductionmentioning

confidence: 99%

“…Windowed detrended cross-correlation analysis allows distinguishing complexity matching from synchronization processes based on discrete asynchronies corrections: in the first case the cross-correlation function presents a positive peak at lag 0, whereas in the second case one obtains positive peaks at lags −1 and 1, and a negative peak at lag 0 (Konvalinka et al, 2010; Almurad et al, 2017; Roume et al, 2018). Additionally, complexity matching seems characterized by quite moderate levels of lag 0 cross-correlation, in contrast with those expected in continuous coupling models (Delignières and Marmelat, 2014; Coey et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Complexity Matching: Restoring the Complexity of Locomotion in Older People Through Arm-in-Arm Walking

et al. 2018

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The complexity matching effect refers to a maximization of information exchange, when interacting systems share similar complexities. Additionally, interacting systems tend to attune their complexities in order to enhance their coordination. This effect has been observed in a number of synchronization experiments, and interpreted as a transfer of multifractality between systems. Finally, it has been shown that when two systems of different complexity levels interact, this transfer of multifractality operates from the most complex system to the less complex, yielding an increase of complexity in the latter. This theoretical framework inspired the present experiment that tested the possible restoration of complexity in older people. In young and healthy participants, walking is known to present 1/f fluctuations, reflecting the complexity of the locomotion system, providing walkers with both stability and adaptability. In contrast walking tends to present a more disordered dynamics in older people, and this whitening was shown to correlate with fall propensity. We hypothesized that if an aged participant walked in close synchrony with a young companion, the complexity matching effect should result in the restoration of complexity in the former. Older participants were involved in a prolonged training program of synchronized walking, with a young experimenter. Synchronization within the dyads was dominated by complexity matching. We observed a restoration of complexity in participants after 3 weeks, and this effect was persistent 2 weeks after the end of the training session. This work presents the first demonstration of a restoration of complexity in deficient systems.

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“…In contrast to these two theories, our model, inspired by the strong anticipation hypothesis, offers a different explanation based on a dynamical systems approach where the properties of the model and its interaction with the external stimulus and surrounding active systems are mathematically described as constrained by universal physical laws [27]. Stephen and Dixon [55] have described that strong anticipation can happen at local and global temporal scales, where local strong anticipation occurs between systems continuously coupled and global strong anticipation is more complex, involving multi-scale interactions (see [56–57] for a thorough discussion of global vs local strong anticipation). The SAPPA model is a clear example of local strong anticipation.…”

Section: Discussionmentioning

confidence: 99%

Delayed feedback embedded in perception-action coordination cycles results in anticipation behavior during synchronized rhythmic action: A dynamical systems approach

et al. 2019

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Dancing and playing music require people to coordinate actions with auditory rhythms. In laboratory perception-action coordination tasks, people are asked to synchronize taps with a metronome. When synchronizing with a metronome, people tend to anticipate stimulus onsets, tapping slightly before the stimulus. The anticipation tendency increases with longer stimulus periods of up to 3500ms, but is less pronounced in trained individuals like musicians compared to non-musicians. Furthermore, external factors influence the timing of tapping. These factors include the presence of auditory feedback from one’s own taps, the presence of a partner performing coordinated joint tapping, and transmission latencies (TLs) between coordinating partners. Phenomena like the anticipation tendency can be explained by delay-coupled systems, which may be inherent to the sensorimotor system during perception-action coordination. Here we tested whether a dynamical systems model based on this hypothesis reproduces observed patterns of human synchronization. We simulated behavior with a model consisting of an oscillator receiving its own delayed activity as input. Three simulation experiments were conducted using previously-published behavioral data from 1) simple tapping, 2) two-person alternating beat-tapping, and 3) two-person alternating rhythm-clapping in the presence of a range of constant auditory TLs. In Experiment 1, our model replicated the larger anticipation observed for longer stimulus intervals and adjusting the amplitude of the delayed feedback reproduced the difference between musicians and non-musicians. In Experiment 2, by connecting two models we replicated the smaller anticipation observed in human joint tapping with bi-directional auditory feedback compared to joint tapping without feedback. In Experiment 3, we varied TLs between two models alternately receiving signals from one another. Results showed reciprocal lags at points of alternation, consistent with behavioral patterns. Overall, our model explains various anticipatory behaviors, and has potential to inform theories of adaptive human synchronization.

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Windowed detrended cross-correlation analysis of synchronization processes

Cited by 20 publications

References 43 publications

Synchronization dynamics modulates stride-to-stride fluctuations when walking to an invariant but not to a fractal-like stimulus

Synchronization dynamics modulates stride-to-stride fluctuations when walking to an invariant but not to a fractal-like stimulus

Complexity Matching: Restoring the Complexity of Locomotion in Older People Through Arm-in-Arm Walking

Delayed feedback embedded in perception-action coordination cycles results in anticipation behavior during synchronized rhythmic action: A dynamical systems approach

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