Long-range correlation in synchronization and syncopation tapping: a linear phase correction model

How the Complexity of Psychological Processes Reframes the Issue of Reproducibility in Psychological Science

In the past decade, various recommendations have been published to enhance the methodological rigor and publication standards in psychological science. However, adhering to these recommendations may have limited impact on the reproducibility of causal effects as long as psychological phenomena continue to be viewed as decomposable into separate and additive statistical structures of causal relationships. In this article, we show that (a) psychological phenomena are patterns emerging from nondecomposable and nonisolable complex processes that obey idiosyncratic nonlinear dynamics, (b) these processual features jeopardize the chances of standard reproducibility of statistical results, and (c) these features call on researchers to reconsider what can and should be reproduced, that is, the psychological processes per se, and the signatures of their complexity and dynamics. Accordingly, we argue for a greater consideration of process causality of psychological phenomena reflected by key properties of complex dynamical systems (CDSs). This implies developing and testing formal models of psychological dynamics, which can be implemented by computer simulation. The scope of the CDS paradigm and its convergences with other paradigms are discussed regarding the reproducibility issue. Ironically, the CDS approach could account for both reproducibility and nonreproducibility of the statistical effects usually sought in mainstream psychological science.

Multiple levels of contextual influence on action-based timing behavior and cortical activation

Procedures used to elicit both behavioral and neurophysiological data to address a particular cognitive question can impact the nature of the data collected. We used functional near-infrared spectroscopy (fNIRS) to assess performance of a modified finger tapping task in which participants performed synchronized or syncopated tapping relative to a metronomic tone. Both versions of the tapping task included a pacing phase (tapping with the tone) followed by a continuation phase (tapping without the tone). Both behavioral and brain-based findings revealed two distinct timing mechanisms underlying the two forms of tapping. Here we investigate the impact of an additional-and extremely subtle-manipulation of the study's experimental design. We measured responses in 23 healthy adults as they performed the two versions of the finger-tapping tasks either blocked by tapping type or alternating from one to the other type during the course of the experiment. As in our previous study, behavioral tapping indices and cortical hemodynamics were monitored, allowing us to compare results across the two study designs. Consistent with previous findings, results reflected distinct, context-dependent parameters of the tapping. Moreover, our results demonstrated a significant impact of study design on rhythmic entrainment in the presence/absence of auditory stimuli. Tapping accuracy and hemodynamic responsivity collectively indicate that the block design context is preferable for studying action-based timing behavior.

Exploring complexity matching and asynchrony dynamics in synchronized and syncopated task performances

When two people synchronize their rhythmic behaviors (e.g., finger tapping; walking) they match one another not only at a local scale of beat-to-beat intervals, but also at a global scale of the complex (fractal) patterns of variation in their interval series. This "complexity matching" had been demonstrated in a variety of timing behaviors, but the current study was designed to address two important gaps in previous research. First, very little was known about complexity matching outside of synchronization tasks. This was important because different modes are associated with differences in the strength of coordination and the fractal scaling of the task performance. Second, very little was known about the dynamics of the asynchrony series. This was important because asynchrony is a variable directly quantifying the coordination between the two timing behaviors and the task goal. So, the current study explored complexity matching in both synchronized and syncopated finger tapping tasks, and included analyses of the fractal scaling of the asynchrony series. Participants completed an interpersonal finger tapping task, in both synchronization and syncopation conditions. The magnitude of variation and the exact power law scaling of the tapping intervals were manipulated by having one participant tap in time with a metronome. Complexity matching was most stable when there was sufficient variation in the task behavior and when a persistent scaling dynamic was presented. There were, however, several interesting differences between the two coordination modes, in terms of the heterogeneity of the complexity matching effect and the scaling of the asynchronies. These findings raised a number of important points concerning how to approach and understand the interaction of inherently complex systems.

Trajectory formation during sensorimotor synchronization and syncopation to auditory and visual metronomes

Previous work on sensorimotor synchronization has investigated the dynamics of finger tapping and how individual movement trajectories contribute to timing accuracy via asymmetry in movement velocities. The present study investigated sensorimotor synchronization (in-phase) and syncopation (anti-phase) to both an auditory metronome and a visual flashing light at multiple frequencies to understand how individual movement phases contribute to the variability of timekeeping and error correction in different sensory modalities and with different task constraints. Results demonstrate that the proportional time spent in both the upward phase of movement and the holding phase of movement (time spent on the surface of the table) remain relatively invariant across both stimulus modalities and across tapping styles (syncopation and synchronization), but changes with interval duration, increasing as interval duration increases. The time spent in the downward phase of movement did significantly differ across stimulus modality and tapping style, increasing during both visuomotor timing and syncopation, accompanied by a significant decrease in flexion velocity during syncopation. Extension velocity and flexion time were found to be the main contributors to differences between visual and auditory timing, while flexion velocity and flexion time were found to be the main contributors to differences between synchronization and syncopation. No correlations were found between asynchrony and the upward, downward, or holding phases of movement, suggesting the existence of multiple error correction strategies.

Correlated microtiming deviations in jazz and rock music

Musical rhythms performed by humans typically show temporal fluctuations. While they have been characterized in simple rhythmic tasks, it is an open question what is the nature of temporal fluctuations, when several musicians perform music jointly in all its natural complexity. To study such fluctuations in over 100 original jazz and rock/pop recordings played with and without metronome we developed a semi-automated workflow allowing the extraction of cymbal beat onsets with millisecond precision. Analyzing the inter-beat interval (IBI) time series revealed evidence for two long-range correlated processes characterized by power laws in the IBI power spectral densities. One process dominates on short timescales (t < 8 beats) and reflects microtiming variability in the generation of single beats. The other dominates on longer timescales and reflects slow tempo variations. Whereas the latter did not show differences between musical genres (jazz vs. rock/pop), the process on short timescales showed higher variability for jazz recordings, indicating that jazz makes stronger use of microtiming fluctuations within a measure than rock/pop. Our results elucidate principles of rhythmic performance and can inspire algorithms for artificial music generation. By studying microtiming fluctuations in original music recordings, we bridge the gap between minimalistic tapping paradigms and expressive rhythmic performances.

Complexity matching effects in bimanual and interpersonal syncopated finger tapping

The current study was designed to investigate complexity matching during syncopated behavioral coordination. Participants either tapped in (bimanual) syncopation using their two hands, or tapped in (interpersonal) syncopation with a partner, with each participant using one of their hands. The time series of inter-tap intervals (ITI) from each hand were submitted to fractal analysis, as well as to short-term and multi-timescale cross-correlation analyses. The results demonstrated that the fractal scaling of one hand's ITI was strongly correlated to that of the other hand, and this complexity matching effect was stronger in the bimanual condition than in the interpersonal condition. Moreover, the degree of complexity matching was predicted by the strength of short-term cross-correlation and the stability of the asynchrony between the two tapping series. These results suggest that complexity matching is not specific to the inphase synchronization tasks used in past research, but is a general result of coordination between complex systems.

Interaction between intention and environmental constraints on the fractal dynamics of human performance

The current study investigated whether the influence of available task constraints on power-law scaling might be moderated by a participant's task intention. Participants performed a simple rhythmic movement task with the intention of controlling either movement period or amplitude, either with or without an experimental stimulus designed to constrain period. In the absence of the stimulus, differences in intention did not produce any changes in power-law scaling. When the stimulus was present, however, a shift toward more random fluctuations occurred in the corresponding task dimension, regardless of participants' intentions. More importantly, participants' intentions interacted with available task constraints to produce an even greater shift toward random variation when the task dimension constrained by the stimulus was also the dimension the participant intended to control. Together, the results suggest that intentions serve to more tightly constrain behavior to existing environmental constraints, evidenced by changes in the fractal scaling of task performance.

Long-range correlation properties in timing of skilled piano performance: the influence of auditory feedback and deep brain stimulation

Unintentional timing deviations during musical performance can be conceived of as timing errors. However, recent research on humanizing computer-generated music has demonstrated that timing fluctuations that exhibit long-range temporal correlations (LRTC) are preferred by human listeners. This preference can be accounted for by the ubiquitous presence of LRTC in human tapping and rhythmic performances. Interestingly, the manifestation of LRTC in tapping behavior seems to be driven in a subject-specific manner by the LRTC properties of resting-state background cortical oscillatory activity. In this framework, the current study aimed to investigate whether propagation of timing deviations during the skilled, memorized piano performance (without metronome) of 17 professional pianists exhibits LRTC and whether the structure of the correlations is influenced by the presence or absence of auditory feedback. As an additional goal, we set out to investigate the influence of altering the dynamics along the cortico-basal-ganglia-thalamo-cortical network via deep brain stimulation (DBS) on the LRTC properties of musical performance. Specifically, we investigated temporal deviations during the skilled piano performance of a non-professional pianist who was treated with subthalamic-deep brain stimulation (STN-DBS) due to severe Parkinson's disease, with predominant tremor affecting his right upper extremity. In the tremor-affected right hand, the timing fluctuations of the performance exhibited random correlations with DBS OFF. By contrast, DBS restored long-range dependency in the temporal fluctuations, corresponding with the general motor improvement on DBS. Overall, the present investigations demonstrate the presence of LRTC in skilled piano performances, indicating that unintentional temporal deviations are correlated over a wide range of time scales. This phenomenon is stable after removal of the auditory feedback, but is altered by STN-DBS, which suggests that cortico-basal ganglia-thalamocortical circuits play a role in the modulation of the serial correlations of timing fluctuations exhibited in skilled musical performance.

Auditory-motor synchronization with temporally fluctuating sequences is dependent on fractal structure but not musical expertise

Fractal structure is a ubiquitous property found in nature and biology, and has been observed in processes at different levels of organization, including rhythmic behavior and musical structure. A temporal process is characterized as fractal when serial long-term correlations and statistical self-similarity (scaling) are present. Previous studies of sensorimotor synchronization using isochronous (non-fractal) stimuli show that participants' errors exhibit persistent structure (positive long-term correlations), while their inter-tap intervals (ITIs) exhibit anti-persistent structure (negative long-term correlations). Auditory-motor synchronization has not been investigated with anti-persistent stimuli. In the current study, we systematically investigated whether the fractal structure of auditory rhythms was reflected in the responses of participants who were asked to coordinate their taps with each event. We asked musicians and non-musicians to tap with 12 different rhythms that ranged from anti-persistent to persistent. The scaling exponents of the ITIs were strongly correlated with the scaling exponents of the stimuli, showing that the long-term structure of the participants' taps scaled with the long-term structure of the stimuli. Surprisingly, the performance of the musicians was not significantly better than that of the non-musicians. Our results imply that humans are able to readily adapt (rather than simply react) to the overall statistical structure of temporally fluctuating stimuli, regardless of musical skill.

Dynamic structure of joint-action stimulus-response activity

The mere presence of a co-actor can influence an individual’s response behavior. For instance, a social Simon effect has been observed when two individuals perform a Go/No-Go response to one of two stimuli in the presence of each other, but not when they perform the same task alone. Such effects are argued to provide evidence that individuals co-represent the task goals and the to-be-performed actions of a co-actor. Motivated by the complex-systems approach, the present study was designed to investigate an alternative hypothesis — that such joint-action effects are due to a dynamical (time-evolving) interpersonal coupling that operates to perturb the behavior of socially situated actors. To investigate this possibility, participants performed a standard Go/No-Go Simon task in joint and individual conditions. The dynamic structure of recorded reaction times was examined using fractal statistics and instantaneous cross-correlation. Consistent with our hypothesis that participants responding in a shared space would become behaviorally coupled, the analyses revealed that reaction times in the joint condition displayed decreased fractal structure (indicative of interpersonal perturbation processes modulating ongoing participant behavior) compared to the individual condition, and were more correlated across a range of time-scales compared to the reaction times of pseudo-pair controls. Collectively, the findings imply that dynamic processes might underlie social stimulus-response compatibility effects and shape joint cognitive processes in general.

Sensorimotor synchronization: a review of recent research (2006-2012)

Sensorimotor synchronization (SMS) is the coordination of rhythmic movement with an external rhythm, ranging from finger tapping in time with a metronome to musical ensemble performance. An earlier review (Repp, 2005) covered tapping studies; two additional reviews (Repp, 2006a, b) focused on music performance and on rate limits of SMS, respectively. The present article supplements and extends these earlier reviews by surveying more recent research in what appears to be a burgeoning field. The article comprises four parts, dealing with (1) conventional tapping studies, (2) other forms of moving in synchrony with external rhythms (including dance and nonhuman animals' synchronization abilities), (3) interpersonal synchronization (including musical ensemble performance), and (4) the neuroscience of SMS. It is evident that much new knowledge about SMS has been acquired in the last 7 years.

Connected text reading and differences in text reading fluency in adult readers

The process of connected text reading has received very little attention in contemporary cognitive psychology. This lack of attention is in parts due to a research tradition that emphasizes the role of basic lexical constituents, which can be studied in isolated words or sentences. However, this lack of attention is in parts also due to the lack of statistical analysis techniques, which accommodate interdependent time series. In this study, we investigate text reading performance with traditional and nonlinear analysis techniques and show how outcomes from multiple analyses can used to create a more detailed picture of the process of text reading. Specifically, we investigate reading performance of groups of literate adult readers that differ in reading fluency during a self-paced text reading task. Our results indicate that classical metrics of reading (such as word frequency) do not capture text reading very well, and that classical measures of reading fluency (such as average reading time) distinguish relatively poorly between participant groups. Nonlinear analyses of distribution tails and reading time fluctuations provide more fine-grained information about the reading process and reading fluency.

Quantifying phase correction in sensorimotor synchronization: empirical comparison of three paradigms

Tapping in synchrony with a metronome requires phase error correction, a process often described by a single-parameter autoregressive model. The parameter (α) is a measure of sensorimotor coupling strength. This study compares α estimates obtained from three experimental paradigms: synchronization with (1) a perfectly regular metronome (RM), (2) a perturbed metronome containing phase shifts (PS), and (3) an "adaptively timed" metronome (AT). Musically trained participants performed in each paradigm at four tempi, with baseline interval durations ranging from 400 to 1300 ms. Two estimation methods were applied to each data set. Results showed that all α estimates increased with interval duration. However, the PS paradigm yielded much larger α values than did the AT paradigm, with those from the RM paradigm falling in between. Positional analysis of the PS data revealed that α increased immediately following a phase shift and then decreased sharply. Unexpectedly, all PS α estimates were uncorrelated with the RM and AT estimates, which were strongly correlated. These results suggest that abruptly perturbed sequences engage a different mechanism of phase correction than do regular or continuously modulated sequences.

Motor imagery may incorporate trial-to-trial error

The authors tested for 1/f noise in motor imagery (MI). Participants pointed and imagined pointing to a single target (Experiment 1), to targets of varied size (Experiment 2), and switched between pointing and grasping (Experiment 3). Experiment 1 showed comparable patterns of serial correlation in actual and imagined movement. Experiment 2 suggested increased correlation for MI and performance with increased task difficulty, perhaps reflecting adaptation to a more complex environment. Experiment 3 suggested a parallel decrease in correlation with task switching, perhaps reflecting discontinuity of mental set. Although present results do not conclusively reveal 1/f fluctuation, the emergent patterns suggest that MI could incorporate trial-to-trial error across a range of constraints.