Time intervals production in tapping and oscillatory motion

Complexity synchronization in living matter: a mini review

Fractal time series have been argued to be ubiquitous in human physiology and some of the implications of that ubiquity are quite remarkable. One consequence of the omnipresent fractality is complexity synchronization (CS) observed in the interactions among simultaneously recorded physiologic time series discussed herein. This new kind of synchronization has been revealed in the interaction triad of organ-networks (ONs) consisting of the mutually interacting time series generated by the brain (electroencephalograms, EEGs), heart (electrocardiograms, ECGs), and lungs (Respiration). The scaled time series from each member of the triad look nothing like one another and yet they bear a deeply recorded synchronization invisible to the naked eye. The theory of scaling statistics is used to explain the source of the CS observed in the information exchange among these multifractal time series. The multifractal dimension (MFD) of each time series is a measure of the time-dependent complexity of that time series, and it is the matching of the MFD time series that provides the synchronization referred to as CS. The CS is one manifestation of the hypothesis given by a "Law of Multifractal Dimension Synchronization" (LMFDS) which is supported by data. Therefore, the review aspects of this paper are chosen to make the extended range of the LMFDS hypothesis sufficiently reasonable to warrant further empirical testing.

Tenets and Methods of Fractal Analysis (1/f Noise)

This chapter deals with the methodical challenges confronting researchers of the fractal phenomenon known as pink or 1/f noise. This chapter introduces concepts and statistical techniques for identifying fractal patterns in empirical time series. It defines some basic statistical terms, describes two essential characteristics of pink noise (self-similarity and long memory), and outlines four parameters representing the theoretical properties of fractal processes: the Hurst coefficient (H), the scaling exponent (α), the power exponent (β), and the fractional differencing parameter (d) of the ARFIMA (autoregressive fractionally integrated moving average) method. Then, it compares and evaluates different approaches to estimating fractal parameters from observed data and outlines the advantages, disadvantages, and constraints of some popular estimators. The final section of this chapter answers the questions: Which strategy is appropriate for the identification of fractal noise in empirical settings and how can it be applied to the data?

Multifractal long-range dependence pattern of functional magnetic resonance imaging in the human brain at rest

Long-range dependence is a prevalent phenomenon in various biological systems that characterizes the long-memory effect of temporal fluctuations. While recent research suggests that functional magnetic resonance imaging signal has fractal property, it remains unknown about the multifractal long-range dependence pattern of resting-state functional magnetic resonance imaging signals. The current study adopted the multifractal detrended fluctuation analysis on highly sampled resting-state functional magnetic resonance imaging scans to investigate long-range dependence profile associated with the whole-brain voxels as specific functional networks. Our findings revealed the long-range dependence's multifractal properties. Moreover, long-term persistent fluctuations are found for all stations with stronger persistency in whole-brain regions. Subsets with large fluctuations contribute more to the multifractal spectrum in the whole brain. Additionally, we found that the preprocessing with band-pass filtering provided significantly higher reliability for estimating long-range dependence. Our validation analysis confirmed that the optimal pipeline of long-range dependence analysis should include band-pass filtering and removal of daily temporal dependence. Furthermore, multifractal long-range dependence characteristics in healthy control and schizophrenia are different significantly. This work has provided an analytical pipeline for the multifractal long-range dependence in the resting-state functional magnetic resonance imaging signal. The findings suggest differential long-memory effects in the intrinsic functional networks, which may offer a neural marker finding for understanding brain function and pathology.

Visual feedback modulates the 1/f structure of movement amplitude time series

In our prior studies, human participants were required to generate long sequences of targeted hand movement when task difficulty varied between conditions, and where full vision of the hand and target was always available. The movement amplitude-that is, the actual distance travelled-for each movement was measured; consecutive movement amplitude values were formed into time series; then, the time series were submitted to spectral analysis. As task difficulty increased, there was a pink-to-white-noise shift in movement amplitude time-series structure. Those changes could be attributed to a difficulty-induced increase in the need to engage visual feedback processes, which maintain accurate guidance of the hand to the target. The current study was designed to provide a more direct test of the hypothesis that difficulty-induced increases in visual feedback processing modulate movement amplitude time-series structure. To that end, we examined cyclical aiming performance under four unique conditions created from the crossing of two index of difficulty (2 and 5 bits) and two visual feedback (visual feedback and no-visual feedback) conditions. That allowed us to examine how variations in visual feedback quality might influence difficulty-induced changes in time-series structure. In the visual feedback condition, we predicted that the increase in difficulty should result in a pink-to-white-noise shift in time-series structure. If that expected shift resulted from increased engagement of visual feedback processing, then in the no-visual feedback condition-where visual feedback processing was disabled-we should observe a strengthened pink-noise time-series structure that does not change with the increase in difficulty. The current results confirmed those predictions. That provides further support for the hypothesis that engagement of closed-loop visual feedback processing modulates movement amplitude time-series structure.

Complexity Synchronization of Organ Networks

The transdisciplinary nature of science as a whole became evident as the necessity for the complex nature of phenomena to explain social and life science, along with the physical sciences, blossomed into complexity theory and most recently into complexitysynchronization. This science motif is based on the scaling arising from the 1/f-variability in complex dynamic networks and the need for a network of networks to exchange information internally during intra-network dynamics and externally during inter-network dynamics. The measure of complexity adopted herein is the multifractal dimension of the crucial event time series generated by an organ network, and the difference in the multifractal dimensions of two organ networks quantifies the relative complexity between interacting complex networks. Information flows from dynamic networks at a higher level of complexity to those at lower levels of complexity, as summarized in the 'complexity matching effect', and the flow is maximally efficient when the complexities are equal. Herein, we use the scaling of empirical datasets from the brain, cardiovascular and respiratory networks to support the hypothesis that complexity synchronization occurs between scaling indices or equivalently with the matching of the time dependencies of the networks' multifractal dimensions.

Temporal Structure in Sensorimotor Variability: A Stable Trait, But What For?

Human performance shows substantial endogenous variability over time, and this variability is a robust marker of individual differences. Of growing interest to psychologists is the realisation that variability is not fully random, but often exhibits temporal dependencies. However, their measurement and interpretation come with several controversies. Furthermore, their potential benefit for studying individual differences in healthy and clinical populations remains unclear. Here, we gather new and archival datasets featuring 11 sensorimotor and cognitive tasks across 526 participants, to examine individual differences in temporal structures. We first investigate intra-individual repeatability of the most common measures of temporal structures - to test their potential for capturing stable individual differences. Secondly, we examine inter-individual differences in these measures using: (1) task performance assessed from the same data, (2) meta-cognitive ratings of on-taskness from thought probes occasionally presented throughout the task, and (3) self-assessed attention-deficit related traits. Across all datasets, autocorrelation at lag 1 and Power Spectra Density slope showed high intra-individual repeatability across sessions and correlated with task performance. The Detrended Fluctuation Analysis slope showed the same pattern, but less reliably. The long-term component (d) of the ARFIMA(1,d,1) model showed poor repeatability and no correlation to performance. Overall, these measures failed to show external validity when correlated with either mean subjective attentional state or self-assessed traits between participants. Thus, some measures of serial dependencies may be stable individual traits, but their usefulness in capturing individual differences in other constructs typically associated with variability in performance seems limited. We conclude with comprehensive recommendations for researchers.

Supplementary Information

The online version contains supplementary material available at 10.1007/s42113-022-00162-1.

Rhythmic ability decline in aging individuals: The role of movement task complexity

Study aim: To investigate age-related changes in rhythmic reproduction ability in relation to the complexity of the adopted movement task.

Material and methods: A Stereophotogrammetric system was used to quantify individual rhythmic performances through motion analysis. Seventeen younger adult (age: 34.8 ± 4.2 yrs) and sixteen older adult (age: 69.9 ± 3.8 yrs) sedentary individuals volunteered for this study. Participants were administered a rhythmic test, which included three different rhythmic patterns to be reproduced by means of finger-tapping, foot-tapping and walking. Number of correct reproductions, time delays and rhythmic ratios were assessed and submitted to analysis of variance.

Results: For all rhythmic parameters, age-related differences emerged about rhythmic patterns and motor tasks. Older adults showed reduced accuracy as compared to their younger counterparts with a marked tendency to speed up beats reproduction (p < 0.05). Increased movement complexity negatively influenced rhythmic ability, with worst performances in the walking task (p < 0.05).

Conclusions: Complexity of the motor reproduction worsen rhythmic ability. Future research should focus on how specific rhythmic training with progressive movement task complexity could contrast this age-related decline.

Dynamic Systems Approach in Sensorimotor Synchronization: Adaptation to Tempo Step-Change

This paper presents a dynamic systems model of a sensorimotor synchronization (SMS) task. An SMS task typically gives temporally discrete human responses to some temporally discrete stimuli. Here, a dynamic systems modeling approach is applied after converting the discrete events to regularly sampled time signals. To collect data for model parameter fitting, a previously published pilot study was expanded. Three human participants took part in an experiment: to tap a finger on a keyboard, following a metronome which changed tempo in steps. System identification was used to estimate the transfer function that represented the relationship between the stimulus and the step response signals, assuming a separate linear, time-invariant system for each tempo step. Different versions of model complexity were investigated. As a minimum, a second-order linear system with delay, two poles, and one zero was needed to model the most important features of the tempo step response by humans, while an additional third pole could give a somewhat better fit to the response data. The modeling results revealed the behavior of the system in two distinct regimes: tempo steps below and above the conscious awareness of tempo change, i.e., around 12% of the base tempo. For the tempo steps above this value, model parameters were derived as linear functions of step size for the group of three participants. The results were interpreted in the light of known facts from other fields like SMS, psychoacoustics and behavioral neuroscience.

Attention Guides the Motor-Timing Strategies in Finger-Tapping Tasks When Moving Fast and Slow

Human beings adapt the spontaneous pace of their actions to interact with the environment. Yet, the nature of the mechanism enabling such adaptive behavior remains poorly understood. The aim of the present contribution was to examine the role of attention in motor timing using (a) time series analysis, and (b) a dual task paradigm. In a series of two studies, a finger-tapping task was used in sensorimotor synchronization with various tempi (from 300 to 1,100 ms) and motor complexity (one target vs. six targets). Time series analyzes indicated that two different timing strategies were used depending on the speed constraints. At slow tempi, tapping sequences were characterized by strong negative autocorrelations, suggesting the implication of cognitive predictive timing. When moving at fast and close-to-spontaneous tempi, tapping sequences were characterized by less negative autocorrelations, suggesting that timing properties emerged from body movement dynamics. The analysis of the dual-task reaction times confirmed that both the temporal and spatial constraints impacted the attentional resources allocated to the finger-tapping tasks. Overall, our work suggests that moving fast and slow involve distinct timing strategies that are characterized by contrasting attentional demands.

The influence of performing gesture type on interpersonal musical timing, and the role of visual contact and tempo

Bodily gestures play an important role in the communication of expressive intentions between humans. Music ensemble performance, as an outstanding example of nonverbal human communication, offers an exemplary context to study and understand the gestural control and communication of these expressive intentions. An important mechanism in music ensemble performance is the anticipation and control of interpersonal timing. When performing, musicians are involved in a complex system of mutual adaptation which is not completely understood so far. In this study, we investigated the role of performers' gestures in the mediation process of interpersonal timing in a dyad performance. Therefore, we designed an experiment in which we controlled for the use of hand and arm movements in a musical task, in which dyads were asked to synchronously tap out a melody. Next to their comfortable/natural way of tapping, we instructed participants to either perform pronounced expressive hand and arm gestures in between successive taps, or to restrict from any overt body movement. In addition, we looked at effects of visual contact (yes/no) and tempo (slow: 50 beats per minute; fast: 100 beats per minute). The results show that performers' gestures improve interpersonal musical timing, in terms of the consistency and accuracy of onset asynchronies, and of the variability of produced inter-onset intervals. Interestingly, we found that the use of expressive gestures, in regard to comfortable/natural movements, add to these positive timing effects, but only when there is visual contact and at the slow tempo. In addition, we found that the type of gestures employed by musicians may modulate leader-follower dynamics. Together, these findings are explained by human anticipation mechanisms facilitated by gesturing, shedding new light on the principles underlying human communication of expressive intentions, through music.

Load Magnitude and Locomotion Pattern Alter Locomotor System Function in Healthy Young Adult Women

Introduction

During cyclical steady state ambulation, such as walking, variability in stride intervals can indicate the state of the system. In order to define locomotor system function, observed variability in motor patterns, stride regulation and gait complexity must be assessed in the presence of a perturbation. Common perturbations, especially for military populations, are load carriage and an imposed locomotion pattern known as forced marching (FM). We examined the interactive effects of load magnitude and locomotion pattern on motor variability, stride regulation and gait complexity during bipedal ambulation in recruit-aged females.

Methods

Eleven healthy physically active females (18–30 years) completed 1-min trials of running and FM at three load conditions: no additional weight/bodyweight (BW), an additional 25% of BW (BW + 25%), and an additional 45% of BW (BW + 45%). A goal equivalent manifold (GEM) approach was used to assess motor variability yielding relative variability (RV; ratio of “good” to “bad” variability) and detrended fluctuation analysis (DFA) to determine gait complexity on stride length (SL) and stride time (ST) parameters. DFA was also used on GEM outcomes to calculate stride regulation.

Results

There was a main effect of load (p = 0.01) on RV; as load increased, RV decreased. There was a main effect of locomotion (p = 0.01), with FM exhibiting greater RV than running. Strides were regulated more tightly and corrected quicker at BW + 45% compared (p < 0.05) to BW. Stride regulation was greater for FM compared to running. There was a main effect of load for gait complexity (p = 0.002); as load increased gait complexity decreased, likewise FM had less (p = 0.02) gait complexity than running.

Discussion

This study is the first to employ a GEM approach and a complexity analysis to gait tasks under load carriage. Reduction in “good” variability as load increases potentially exposes anatomical structures to repetitive site-specific loading. Furthermore, load carriage magnitudes of BW + 45% potentially destabilize the system making individuals less adaptable to additional perturbations. This is further evidenced by the decrease in gait complexity, which all participants demonstrated values similarly observed in neurologically impaired populations during the BW + 45% load condition.

Interpersonal Synchronization Processes in Discrete and Continuous Tasks

Three frameworks have been proposed to account for interpersonal synchronization: The information processing approach argues that synchronization is achieved by mutual adaptation, the coordination dynamics perspective supposes a continuous coupling between systems, and complexity matching suggests a global, multi-scale interaction. We hypothesized that the relevancy of these models was related to the nature of the performed tasks. 10 dyads performed synchronized tapping and synchronized forearm oscillations, in two conditions: full (participants had full information about their partner), and digital (information was limited to discrete auditory signals). Results shows that whatever the task and the available information, synchronization was dominated by a discrete mutual adaptation. These results question the relevancy of the coordination dynamics perspective in interpersonal coordination.

Biases in the Simulation and Analysis of Fractal Processes

Fractal processes have recently received a growing interest, especially in the domain of rehabilitation. More precisely, the evolution of fractality with aging and disease, suggesting a loss of complexity, has inspired a number of studies that tried, for example, to entrain patients with fractal rhythms. This kind of study requires relevant methods for generating fractal signals and for assessing the fractality of the series produced by participants. In the present work, we engaged a cross validation of three methods of generation and three methods of analysis. We generated exact fractal series with the Davies–Harte (DH) algorithm, the spectral synthesis method (SSM), and the ARFIMA simulation method. The series were analyzed by detrended fluctuation analysis (DFA), power spectral density (PSD) method, and ARFIMA modeling. Results show that some methods of generation present systematic biases: DH presented a strong bias toward white noise in fBm series close to the 1/f boundary and SSM produced series with a larger variability around the expected exponent, as compared with other methods. In contrast, ARFIMA simulations provided quite accurate series, without major bias. Concerning the methods of analysis, DFA tended to systematically underestimate fBm series. In contrast, PSD yielded overestimates for fBm series. With DFA, the variability of estimates tended to increase for fGn series as they approached the 1/f boundary and reached unacceptable levels for fBm series. The highest levels of variability were produced by PSD. Finally, ARFIMA methods generated the best series and provided the most accurate and less variable estimates.

Fractal properties and short-term correlations in motor control in cycling: influence of a cognitive challenge

Fluctuations in cyclic tasks periods is a known characteristic of human motor control. Specifically, long-range fractal fluctuations have been evidenced in the temporal structure of these variations in human locomotion and thought to be the outcome of a multicomponent physiologic system in which control is distributed across intricate cortical, spinal and neuromuscular regulation loops. Combined with long-range correlation analyses, short-range autocorrelations have proven their use to describe control distribution across central and motor components. We used relevant tools to characterize long- and short-range correlations in revolution time series during cycling on an ergometer in 19 healthy young adults. We evaluated the impact of introducing a cognitive task (PASAT) to assess the role of central structures in control organization. Autocorrelation function and detrending fluctuation analysis (DFA) demonstrated the presence of fractal scaling. PSD in the short range revealed a singular behavior which cannot be explained by the usual models of even-based and emergent timing. The main outcomes are that (1) timing in cycling is a fractal process, (2) this long-range fractal behavior increases in persistence with dual-task condition, which has not been previously observed, (3) short-range behavior is highly persistent and unaffected by dual-task. Relying on the inertia of the oscillator may be a way to distribute more control to the periphery, thereby allocating less resources to central process and better managing additional cognitive demands. This original behavior in cycling may explain the high short-range persistence unaffected by dual-task, and the increase in long-range persistence with dual-task.

A neuromechanistic model for rhythmic beat generation

When listening to music, humans can easily identify and move to the beat. Numerous experimental studies have identified brain regions that may be involved with beat perception and representation. Several theoretical and algorithmic approaches have been proposed to account for this ability. Related to, but different from the issue of how we perceive a beat, is the question of how we learn to generate and hold a beat. In this paper, we introduce a neuronal framework for a beat generator that is capable of learning isochronous rhythms over a range of frequencies that are relevant to music and speech. Our approach combines ideas from error-correction and entrainment models to investigate the dynamics of how a biophysically-based neuronal network model synchronizes its period and phase to match that of an external stimulus. The model makes novel use of on-going faster gamma rhythms to form a set of discrete clocks that provide estimates, but not exact information, of how well the beat generator spike times match those of a stimulus sequence. The beat generator is endowed with plasticity allowing it to quickly learn and thereby adjust its spike times to achieve synchronization. Our model makes generalizable predictions about the existence of asymmetries in the synchronization process, as well as specific predictions about resynchronization times after changes in stimulus tempo or phase. Analysis of the model demonstrates that accurate rhythmic time keeping can be achieved over a range of frequencies relevant to music, in a manner that is robust to changes in parameters and to the presence of noise.

Do intentionality constraints shape the relationship between motor variability and performance?

The aim of this experiment was to assess if the previously supported relationship between the structure of motor variability and performance changes when the task or organismic constraints encourage individuals to adjust their movement to achieve a goal. Forty-two healthy volunteers (aged 26.05 ± 5.02 years) performed three sets of cyclic pointing movements, 600 cycles each. Every set was performed under different conditions: 1) without a target; 2) with a target; 3) with a target and a financial reward. The amount of performance variability was analysed using the standard deviation of the medial-lateral (ML) and anterior-posterior (AP) axes and the bivariate variable error. The structure of the variability was assessed by Detrended Fluctuation Analysis (DFA) of the following time series: the coordinate values of the endpoint in ML, AP axes and resultant distance (RD), the hand orientation and the movement time. The performance of the task constrained with a target, or a target and reward, required higher implication to adjust an individual’s movements to achieve the task goal, showing a decrease in dispersions and lower autocorrelation. Under the condition without a target, variability dispersion was positively related to autocorrelation of the movement values from ML axis and RD time series, and negatively related to the values from the hand orientation time series. There was a loss of the relationship between variability structure and performance when the task was constrained by the target and the reward. That could indicate different strategies of the participants to achieve the objective. Considering the results and previous studies, the relationship between variability structure and performance could depend on task constraints such as feedback, difficulty or the skill level of participants and it is mediated by individual constraints such as implication or intentionality.

Does dance training influence beat sensorimotor synchronization? Differences in finger-tapping sensorimotor synchronization between competitive ballroom dancers and nondancers

Sensorimotor synchronization is the coordination of rhythmic movement with an external beat. Dancers often synchronize each beat of their motion with an external rhythm. Compared with social dancing, competitive ballroom dancing requires a higher level of sensorimotor ability. Although previous studies have found that dance experience may facilitate sensorimotor synchronization, they did not examine this in competitive ballroom dancers. Thus, the present study compared sensorimotor synchronization in 41 nondancers and 41 skilled, competitive ballroom dancers as they performed a simple beat synchronization finger-tapping task. All participants finger-tapped freely at their preferred tempo before the formal experiments. Participants were then required to synchronize their finger-tapping with auditory, visual, or combined audiovisual signals in separate experiments and at varying tempos. To assess sensorimotor plasticity, the participants then repeated the free-tapping task after completing all three finger-tapping experiments. Compared with nondancers, dancers showed more accurate and stable beat synchronization. Dancers tapped before onset of all three types of sensorimotor stimulation, indicating a significant negative mean asynchrony and had a tendency to anticipate (predict) the stimuli. Dancers tended to auditory stimulation for beat sensorimotor synchronization, whereas nondancers tended to visual stimuli. Dancers had a faster tempo preference in the initial free-tapping task; however, the preferred tapping tempo increased in all participants in the second free-tapping task, suggesting that beat induction is affected by practice. Together these findings suggest that dance experience enhances sensorimotor synchronization and sensorimotor plasticity, with ballroom dancers tending to auditory stimulation for beat induction.

When Coordinating Finger Tapping to a Variable Beat the Variability Scaling Structure of the Movement and the Cortical BOLD Signal are Both Entrained to the Auditory Stimuli

Rhythmic actions are characterizable as a repeating invariant pattern of movement together with variability taking the form of cycle-to-cycle fluctuations. Variability in behavioral measures is atypically random, and often exhibits serial temporal dependencies and statistical self-similarity in the scaling of variability magnitudes across timescales. Self-similar (i.e. fractal) variability scaling is evident in measures of both brain and behavior. Variability scaling structure can be quantified via the scaling exponent (α) from detrended fluctuation analysis (DFA). Here we study the task of coordinating thumb-finger tapping to the beats of constructed auditory stimuli. We test the hypothesis that variability scaling evident in tap-to-tap intervals as well as in the fluctuations of cortical hemodynamics will become entrained to (i.e. drawn toward) manipulated changes in the variability scaling of a stimulus's beat-to-beat intervals. Consistent with this hypothesis, manipulated changes of the exponent α of the experimental stimuli produced corresponding changes in the exponent α of both tap-to-tap intervals and cortical hemodynamics. The changes in hemodynamics were observed in both motor and sensorimotor cortical areas in the contralateral hemisphere. These results were observed only for the longer timescales of the detrended fluctuation analysis used to measure the exponent α. These findings suggest that complex auditory stimuli engage both brain and behavior at the level of variability scaling structures.

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.

Paired Synchronous Rhythmic Finger Tapping without an External Timing Cue Shows Greater Speed Increases Relative to Those for Solo Tapping

In solo synchronization-continuation (SC) tasks, intertap intervals (ITI) are known to drift from the initial tempo. It has been demonstrated that people in paired and group contexts modulate their action timing unconsciously in various situations such as choice reaction tasks, rhythmic body sway, and hand clapping in concerts, which suggests the possibility that ITI drift is also affected by paired context. We conducted solo and paired SC tapping experiments with three tempos (75, 120, and 200 bpm) and examined whether tempo-keeping performance changed according to tempo and/or the number of players. Results indicated that those tapping in the paired conditions were faster, relative to those observed in the solo conditions, for all tempos. For the faster participants, the degree of ITI drift in the solo conditions was strongly correlated with that in the paired conditions. Regression analyses suggested that both faster and slower participants adapted their tap timing to that of their partners. A possible explanation for these results is that the participants reset the phase of their internal clocks according to the faster beat between their own tap and the partners' tap. Our results indicated that paired context could bias the direction of ITI drift toward decreasing.

Manual asymmetries in bimanual isochronous tapping tasks in children

Tapping tasks have been investigated throughout the years, with variations in features such as the complexity of the task, the use of one or both hands, the employ of auditory or visual stimuli, and the characteristics of the subjects. The evaluation of lateral asymmetries in tapping tasks in children offers an insight into the structure of rhythmic movements and handedness at early stages of development. The current study aims to investigate the ability of children (aged six and seven years-old) to maintain a rhythm, in a bimanual tapping task at two different target frequencies, as well as the manual asymmetries displayed while doing so. The analyzed data in this work are the series of the time intervals between successive taps. We suggest several profiles of behavior, regarding the overall performance of children in both tempo conditions. We also propose a new method of quantifying the variability of the performance and the asymmetry of the hands, based on ellipses placed on scatter plots of the non-dominant-dominant series versus the dominant-non-dominant series. We then use running correlations to identify changes of coordination tendencies over time. The main results show that variability is larger in the task with the longer target interval. Furthermore, most children evidence lateral asymmetries, but in general they show the capacity to maintain the mean of consecutive intertap intervals of both hands close to the target interval. Finally, we try to interpret our findings in the light of existing models and timing modes.

Synthesis of asymmetric movement trajectories in timed rhythmic behaviour by means of frequency modulation

Results from different empirical investigations on gestural aspects of timed rhythmic movements indicate that the production of asymmetric movement trajectories is a feature that seems to be a common characteristic of various performances of repetitive rhythmic patterns. The behavioural or neural origin of these asymmetrical trajectories is, however, not identified. In the present study we outline a theoretical model that is capable of producing syntheses of asymmetric movement trajectories documented in empirical investigations by Balasubramaniam et al. (2004). Characteristic qualities of the extension/flexion profiles in the observed asymmetric trajectories are reproduced, and we conduct an experiment similar to Balasubramaniam et al. (2004) to show that the empirically documented movement trajectories and our modelled approximations share the same spectral components. The model is based on an application of frequency modulated movements, and a theoretical interpretation offered by the model is to view paced rhythmic movements as a result of an unpaced movement being "stretched" and "compressed", caused by the presence of a metronome. We discuss our model construction within the framework of event-based and emergent timing, and argue that a change between these timing modes might be reflected by the strength of the modulation in our model.

Sensorimotor Grounding of Musical Embodiment and the Role of Prediction: A Review

In a previous article, we reviewed empirical evidence demonstrating action-based effects on music perception to substantiate the musical embodiment thesis (Maes et al., 2014). Evidence was largely based on studies demonstrating that music perception automatically engages motor processes, or that body states/movements influence music perception. Here, we argue that more rigorous evidence is needed before any decisive conclusion in favor of a “radical” musical embodiment thesis can be posited. In the current article, we provide a focused review of recent research to collect further evidence for the “radical” embodiment thesis that music perception is a dynamic process firmly rooted in the natural disposition of sounds and the human auditory and motor system. Though, we emphasize that, on top of these natural dispositions, long-term processes operate, rooted in repeated sensorimotor experiences and leading to learning, prediction, and error minimization. This approach sheds new light on the development of musical repertoires, and may refine our understanding of action-based effects on music perception as discussed in our previous article (Maes et al., 2014). Additionally, we discuss two of our recent empirical studies demonstrating that music performance relies on similar principles of sensorimotor dynamics and predictive processing.

The Musician Redefined: A Behavioral Assessment of Rhythm Perception in Professional Club DJs

Studies of musical training demonstrate functional advantages in rhythm tasks that result from enriched auditory experience. Anatomical correlates exist in brain areas involved in auditory perception, speech processing, motor control, attention, and emotion. However, these studies fail to include many classes of musicians that might undergo experience-related change. The current study examined rhythm processing in professional disc jockeys (DJs) who routinely engage in temporally-demanding tasks during practice and performance. In Experiment 1, DJs outperformed controls at detecting a deviation in a rhythmic pattern, and were no different than trained percussionists. In Experiment 2, participants receiving one week of DJ training trended toward outperforming untrained participants on this same measure. Across experiments, movement improved detection of rhythmic deviations, providing evidence of privileged auditory-motor connections, and underscoring the importance of motor areas to rhythm perception. It is clear that DJs show experience-dependent changes in perception that are comparable to more traditional musicians.

The impact of cognitive load on operatic singers' timing performance

In the present paper, we report the results of an empirical study on the effects of cognitive load on operatic singing. The main aim of the study was to investigate to what extent a working memory task affected the timing of operatic singers' performance. Thereby, we focused on singers' tendency to speed up, or slow down their performance of musical phrases and pauses. Twelve professional operatic singers were asked to perform an operatic aria three times; once without an additional working memory task, once with a concurrent working memory task (counting shapes on a computer screen), and once with a relatively more difficult working memory task (more shapes to be counted appearing one after another). The results show that, in general, singers speeded up their performance under heightened cognitive load. Interestingly, this effect was more pronounced in pauses—more in particular longer pauses—compared to musical phrases. We discuss the role of sensorimotor control and feedback processes in musical timing to explain these findings.

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.

Embodiment of intersubjective time: relational dynamics as attractors in the temporal coordination of interpersonal behaviors and experiences

This paper addresses the issue of “being together,” and more specifically the issue of “being together in time.” We provide with an integrative framework that is inspired by phenomenology, the enactive approach and dynamical systems theories. To do so, we first define embodiment as a living and lived phenomenon that emerges from agent-world coupling. We then show that embodiment is essentially dynamical and therefore we describe experiential, behavioral and brain dynamics. Both lived temporality and the temporality of the living appear to be complex, multiscale phenomena. Next we discuss embodied dynamics in the context of interpersonal interactions, and briefly review the empirical literature on between-persons temporal coordination. Overall, we propose that being together in time emerges from the relational dynamics of embodied interactions and their flexible co-regulation.

The role of working memory in the temporal control of discrete and continuous movements

Music performance requires precise control of limb movements in order to achieve temporal precision of performed tone onsets. Previous findings suggest that processes recruited for the temporal control of rhythmic body movements, such as those required in music performance, depend on the movement type (discrete vs. continuous) and the rate of the produced interonset intervals (sub-second vs. supra-second). Using a dual-task paradigm, the current study addressed these factors in the temporal control of cellists’ bowing movements. Cellists performed melodies in a synchronization-continuation timing task at a specified fast (intertone interval = 700 ms) or slow (intertone interval = 1,100 ms) tempo with either discrete (staccato) or continuous (legato) bowing movements. A secondary working memory task involved a concurrent digit-switch counting task. Analyses of the produced tone durations showed that the working memory load significantly impaired temporal regularity when the melodies were performed with discrete bowing movements at the slower tempo. In addition, discrete movements led to more errors on the working memory task. These findings suggest that continuous body movements provide temporal control information to performers under high cognitive load conditions.

A little elastic for a better performance: kinesiotaping of the motor effector modulates neural mechanisms for rhythmic movements

A rhythmic motor performance is brought about by an integration of timing information with movements. Investigations on the millisecond time scale distinguish two forms of time control, event-based timing and emergent timing. While event-based timing asserts the existence of a central internal timekeeper for the control of repetitive movements, the emergent timing perspective claims that timing emerges from dynamic control of nontemporal movements parameters. We have recently demonstrated that the precision of an isochronous performance, defined as performance of repeated movements having a uniform duration, was insensible to auditory stimuli of various characteristics (Bravi et al., 2014). Such finding has led us to investigate whether the application of an elastic therapeutic tape (Kinesio® Tex taping; KTT) used for treating athletic injuries and a variety of physical disorders, is able to reduce the timing variability of repetitive rhythmic movement. Young healthy subjects, tested with and without KTT, have participated in sessions in which sets of repeated isochronous wrist's flexion-extensions (IWFEs) were performed under various auditory conditions and during their recall. Kinematics was recorded and temporal parameters were extracted and analyzed. Our results show that the application of KTT decreases the variability of rhythmic movements by a 2-fold effect: on the one hand KTT provides extra proprioceptive information activating cutaneous mechanoreceptors, on the other KTT biases toward the emergent timing thus modulating the processes for rhythmic movements. Therefore, KTT appears able to render movements less audio dependent by relieving, at least partially, the central structures from time control and making available more resources for an augmented performance.

The impact of the perception of rhythmic music on self-paced oscillatory movements

Inspired by theories of perception-action coupling and embodied music cognition, we investigated how rhythmic music perception impacts self-paced oscillatory movements. In a pilot study, we examined the kinematic parameters of self-paced oscillatory movements, walking and finger tapping using optical motion capture. In accordance with biomechanical constraints accounts of motion, we found that movements followed a hierarchical organization depending on the proximal/distal characteristic of the limb used. Based on these findings, we were interested in knowing how and when the perception of rhythmic music could resonate with the motor system in the context of these constrained oscillatory movements. In order to test this, we conducted an experiment where participants performed four different effector-specific movements (lower leg, whole arm and forearm oscillation and finger tapping) while rhythmic music was playing in the background. Musical stimuli consisted of computer-generated MIDI musical pieces with a 4/4 metrical structure. The musical tempo of each song increased from 60 BPM to 120 BPM by 6 BPM increments. A specific tempo was maintained for 20 s before a 2 s transition to the higher tempo. The task of the participant was to maintain a comfortable pace for the four movements (self-paced) while not paying attention to the music. No instruction on whether to synchronize with the music was given. Results showed that participants were distinctively influenced by the background music depending on the movement used with the tapping task being consistently the most influenced. Furthermore, eight strategies put in place by participants to cope with the task were unveiled. Despite not instructed to do so, participants also occasionally synchronized with music. Results are discussed in terms of the link between perception and action (i.e., motor/perceptual resonance). In general, our results give support to the notion that rhythmic music is processed in a motoric fashion.

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.

Characteristics of stride behavior during treadmill walking and stationary stepping

Much has been learned about the characteristics of gait in overground and treadmill walking. However, there are many contexts in which overground or treadmill walking might not be possible, such as in home-based physical therapy. In those cases, a surrogate task to index gait behavior would be a valuable tool. Thus, the purpose of this study was to evaluate the stride behavior characteristics of stationary stepping compared with treadmill walking. Healthy young adults (N = 10) preformed two 15-minute tasks: (1) treadmill walking and (2) stationary stepping. Several stride behavior characteristics were recorded, including the number of strides taken, minimum and maximum knee angle, stride interval mean, stride interval standard deviation, and detrended fluctuation analysis (DFA) alpha of the stride interval time series. The results showed that stride behavior was similar between tasks when examined at the group level. However, when individual level analyses were used to examine the reliability of each metric between tasks, poor reliability was observed in most metrics, indicating that stationary stepping may not be an appropriate surrogate task for overground or treadmill walking. These results are discussed in the context of a gait dynamics framework, with attention to task constraints that may have influenced the findings.

The timing and temporal patterns of eye blinking are dynamically modulated by attention

A number of human behaviors and movements show self-similar temporal patterns in their occurrence over time. Human walking, finger tapping and heartbeat intervals have fluctuations that are statistically similar at multiple time scales. However, whether eye blinking, which is a unique human behavior that occurs spontaneously, embeds a similar temporal structure within other types of movements is largely unknown. In this study, we used attention-requiring tasks to assess how the temporal pattern of eye blinking is altered in both the second and sub-second time scales. Our results showed that eyeblink activity was more suppressed as the task difficulty level increased and was facilitated immediately after exposure to auditory stimuli, which were presented for 6 to 14s. Moreover, similar transient suppressive and facilitative patterns were observed in the response period, which lasted for less than one second. Furthermore, we found that spontaneous eye blinking intervals fluctuated according to an 1/f scaling property, which is widely observed in various human movements. These results suggest that the dynamics of eye blinking under specific cognitive tasks exhibit a similar temporal structure at multiple time scales.

Measuring fractality

WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent β of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators ([Formula: see text] power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series.

Event-based and emergent timing: dichotomy or continuum? A reply to Repp and Steinman (2010)

B. H. Repp and S. R. Steiman (2010) suggested that event-based and emergent timing, usually conceived as mutually exclusive modes of timing, could in fact coexist in a single activity. According to this point of view, rhythmic activities could exploit mixtures of control modes, in which the relative importance of event-based and emergent components could depend on task characteristics. This point of view, in the opinion of the authors of the present article, corresponds to a fundamental misunderstanding of the theoretical basis of the event-based and emergent distinction, and is not supported by any experimental evidence. However, they present some new results that could support new lines of reasoning for the future developments of research in this domain.

Effects of accuracy feedback on fractal characteristics of time estimation

The current experiment investigated the effect of visual accuracy feedback on the structure of variability of time interval estimates in the continuation tapping paradigm. Participants were asked to repeatedly estimate a 1-s interval for a prolonged period of time by tapping their index finger. In some conditions, participants received accuracy feedback after every estimate, whereas in other conditions, no feedback was given. Also, the likelihood of receiving visual feedback was manipulated by adjusting the tolerance band around the 1-s target interval so that feedback was displayed only if the temporal estimate deviated from the target interval by more than 50, 100, or 200 ms respectively. We analyzed the structure of variability of the inter-tap intervals with fractal and multifractal methods that allow for a quantification of complex long-range correlation patterns in the timing performance. Our results indicate that feedback changes the long-range correlation structure of time estimates: Increased amounts of feedback lead to a decrease in fractal long-range correlations, as well to a decrease in the magnitude of local fluctuations in the performance. The multifractal characteristics of the time estimates were not impacted by the presence of accuracy feedback. Nevertheless, most of the data sets show significant multifractal signatures. We interpret these findings as showing that feedback acts to constrain and possibly reorganize timing performance. Implications for mechanistic and complex systems-based theories of timing behavior are discussed.

Circle drawing does not exhibit auditory-motor synchronization

Differences in timing control processes between tapping and circle drawing have been extensively documented during continuation timing. Differences between event and emergent control processes have also been documented for synchronization timing using emergent tasks that have minimal event-related information. However, it is not known whether the original circle-drawing task also behaves differently than tapping during synchronization. In this experiment, 10 participants performed a table-tapping and a continuous circle-drawing task to an auditory metronome. Synchronization performance was assessed via the value and variability of asynchronies. Synchronization was substantially more difficult in circle drawing than in tapping. Participants drawing timed circles exhibited drift in synchronization error and did not maintain a consistent phase relationship with the metronome. An analysis of temporal anchoring revealed that timing to the timing target was not more accurate than timing to other locations on the circle trajectory. The authors conclude that participants were not able to synchronize movement with metronome tones in the circle-drawing task despite other findings that cyclical tasks do exhibit auditory motor synchronization, because the circle-drawing task is unique and absent of event and cycle position information.

Synchronization in repetitive smooth movement requires perceptible events

Accurate timing performance during auditory-motor synchronization has been well documented for finger tapping tasks. It is believed that information pertaining to an event in movement production aids in detecting and correcting for errors between movement cycle completion and the metronome tone. Tasks with minimal event-related information exhibit more variable synchronization and less rapid error correction. Recent work from our laboratory has indicated that a task purportedly lacking an event structure (circle drawing) did not exhibit accurate synchronization or error correction (Studenka & Zelaznik, in press). In the present paper we report on two experiments examining synchronization in tapping and circle drawing tasks. In Experiment 1, error correction processes of an event-timed tapping timing task and an emergently timed circle drawing timing task were examined. Rapid and complete error correction was seen for the tapping, but not for the circle drawing task. In Experiment 2, a perceptual event was added to delineate a cycle in circle drawing, and the perceptual event of table contact was removed from the tapping task. The inclusion of an event produced a marked improvement in synchronization error correction for circle drawing, and the removal of tactile feedback (taking away an event) slightly reduced the error correction response of tapping. Furthermore, the task kinematics of circle drawing remained smooth providing evidence that event structure can be kinematic or perceptual in nature. Thus, synchronization and error correction, characteristic of event timing (Ivry, Spencer, Zelaznik, & Diedrichsen, 2002; Repp, 2005), depends upon the presence of a distinguishable source of sensory information at the timing goal.

Comfortable synchronization of cyclic drawing movements with a metronome

Continuous circle drawing is considered a paragon of emergent timing, whereas the timing of finger tapping is said to be event-based. Synchronization with a metronome, however, must to some extent be event-based for both types of movement. Because the target events in the movement trajectory are more poorly defined in circle drawing than in tapping, circle drawing shows more variable asynchronies with a metronome than does tapping. One factor that may have contributed to high variability in past studies is that circle size, drawing direction, and target point were prescribed and perhaps outside the comfort range. In the present study, participants were free to choose most comfortable settings of these parameters for two continuously drawn shapes, circles and infinity signs, while synchronizing with a regular or intermittently perturbed metronome at four different tempi. Results showed that preferred circle sizes were generally smaller than in previous studies but tended to increase as tempo decreased. Synchronization results were similar for circles and infinity signs, and similar to earlier results for circles drawn within a fixed template (Repp & Steinman, 2010). Comparison with tapping data still showed drawing to exhibit much greater variability and persistence of asynchronies as well as slower phase correction in response to phase shifts in the metronome. With comfort level ruled out as a factor, these differences can now be attributed more confidently to differences in event definition and/or movement dynamics.