Unraveling the finding of 1/<Emphasis Type="Italic">f</Emphasis><Superscript><Emphasis Type="Italic">β</Emphasis></Superscript> noise in self-paced and synchronized tapping: a unifying mechanistic model

1/f ( beta ) noise has been revealed in both self-paced and synchronized tapping sequences, without being consistently taken into consideration for the modeling of underlying timing mechanisms. In this study we characterize variability, short-range, and long-range correlation properties of asynchronies and inter-tap intervals collected in a synchronization tapping experiment, attesting statistically the presence of 1/f ( beta ) noise in asynchronies. We verify that the linear phase correction model of synchronization tapping in its original formulation cannot account for the empirical long-range correlation properties. On the basis of previous accounts of 1/f ( beta ) noise in the literature on self-paced tapping, we propose an extension of the original synchronization model by modeling the timekeeping process as a source of 1/f ( beta ) fluctuations. Simulations show that this '1/f-AR synchronization model' accounts for the statistical properties of empirical series, including long-range correlations, and provides an unifying mechanistic account of 1/f ( beta ) noise in self-paced and synchronization tapping. This account opens the original synchronization framework to further investigations of timing mechanisms with regard to the serial correlation properties in performed time intervals.     

Visuomotor synchronization: Analysis of the initiation and stable synchronization phases

The initiation phase of visuomotor synchronization and the phase of stable synchronization were studied in an experiment where eight adult subjects synchronized their motor responses with an isochronous sequence of visual stimuli. The period of the sequence varied in a wide range (from 500 to 2200 ms). Analysis of the statistical characteristics of synchronization errors (asynchronies) showed that the phase of stable visuomotor synchronization fit the model of current phase correction of a central timer; as in the case of audiomotor synchronization, the variability of the intervals of the central timer and the phase correction coefficient increased with increasing period of the stimulus sequence. The initiation phase of visuomotor synchronization was characterized by a considerable inter-and intraindividual variability of the form (exponential, linear, or step) and duration (from one to ten responses) of the transition from reacting to a sensory signal to synchronization. The shape and duration of the transitional region depend on the phase correction coefficient and the possibility of using an estimate of the sequence period stored in memory. The obtained data indicate that the initiation stage is not automatic throughout the studied range of periods of the visual stimulus sequence; in particular, working memory plays a substantial role in its organization.     

Multiple synchronization strategies in rhythmic sensorimotor tasks: phase vs period correction

To characterize synchronisation strategies in the tracking of auditory rhythm with rhythmic finger tapping, the adaptation process after unexpected step changes of an interstimulus interval (ISI) of 500 ms was investigated. Step changes of 2% (10 ms), 4% (20 ms), and 10% (50 ms) of ISI were applied to the stimulus sequence. Synchronisation patterns of 5 subjects were analyzed based on synchronisation error (SE) and interresponse intervals (IRI). A strategy shift contigent upon the size of the introduced step change was detected. After small ISI changes, rapid IRI matching to the new ISI was accompanied by temporarily enlarged SE values, which slowly returned to preferred SE values before the step change. Large ISI changes showed quick SE adaptations accompanied by a temporary overcorrection of IRI. Response asymmetry between ISI decreases and increases emerged, showing a stronger adaptation during ISI increases. A two-dimensional difference equation was formulated to simulate the time series of intertap intervals and explain the control process during IRI and SE adjustments. The system constants were optimized to minimalize the deviations between the computed and the observed response trajectories, consisting of the time series of SE and IRI. It was shown that a successful model fit using a linear two-dimensional difference equation was based on the size and direction of the ISI changes. MANOVA procedures showed that differences in equation parameters during small and large step changes were statistically significant (P<0.05). It is therefore suggested that a uniform model accounting for synchronization responses to all step changes would require the introduction of nonlinear system properties. Received: 20 August 1997/Accepted in revised form: 9 June 1998     

Visuo-motor synchronization in children of 7-8 years old

The group of 22 children of 7-8 years old and the group of 17 adults participated in the experiment in which they were asked to synchronize their movements (pressing a button) with an isochronous sequence of visual stimuli. The period of the sequence was varied between 500 to 2000 ms with the 300 ms step. Two successive phases of visuo-motor synchronization were studied: the synchronization phase and the initiation phase which corresponds to the process of transition between reacting to a visual stimulus and the stable synchronization. The initiation phase was characterized by the shape and duration of the asynchrony time course (relaxation curve). The statistical properties of asynchrony were analyzed in the framework of the phase correction of the central timer. It is shown that (1) the range of successful visuo-motor synchronization is narrower in children of 7-8 than in adults and it spans from 600-700 ms to approx. 1700 Mc; (2) The initiation phase lasts about the same time in children of 7-8 and adults and typical shapes of individual relaxation curves are similar in both adults and children. (3) Although the statistical properties of asynchrony are comparable in children and adults, the mechanism of phase correction of the central timer operates with a lower value of the correction gain factor in children than in adults. In children, the phase correction process is also characterized by a substantially higher level of the central and motor noise which leads to a higher asynchrony variability and more frequent and longer lasting synchronization losses.     

Visuomotor synchronization in adults and seven- to eight-year-old children

A group of 22 seven- to eight-year-old children and a group of 17 adults participated in the experiment in which they synchronized their movements (pressing a button) with an isochronous sequence of visual stimuli. The period of the sequence was varied between 500 to 2000 ms at a step of 300 ms. Two consecutive phases of visuomotor synchronization were studied: the initiation phase, which corresponds to the process of transition between responding to a visual stimulus to stable synchronization with them, and the synchronization phase. The initiation phase was characterized by the shape and duration of the asynchrony time course (relaxation curve). The statistical properties of asynchrony were analyzed in terms of the phase correction of the central timer. It was shown that (1) the range of successful visuomotor synchronization was narrower in seven- to eight-year-old children than in adults (from 600–700 ms to ∼1700 ms); (2) the initiation phase duration was about the same in seven- to eight-year-old children and adults, and typical shapes of individual relaxation curves were similar in both adults and children; (3) although the statistical properties of asynchrony were comparable in children and adults, the mechanism of phase correction of the central timer operated at a lower correction gain factor in children than in adults. In children, the phase correction process was also characterized by a substantially higher level of the central and motor noise, which leads to higher asynchrony variability and more frequent and longer synchronization losses.     

MEG responses during rhythmic finger tapping in humans to phasic stimulation and their interpretation based on neural mechanisms

 The phase-resetting experiment was applied to human periodic finger tapping to understand how its rhythm is controlled by the internal neural clock that is assumed to exist. In the experiment, the right periodic tapping movement was disturbed transiently by a series of left finger taps in response to impulsive auditory cues presented randomly at various phases within the tapping cycle. After each left finger tap, the original periodic tapping was reestablished within several tapping cycles. Influences of the disturbance on the periodic right finger tapping varied depending on the phase of the periodic right finger tapping at which each left finger tap was made. It was confirmed that the periodic tapping was disturbed not by the auditory cues but by the left finger taps. Based on this fact, in this paper each single left tap was considered as the stimulus, and the phase of the periodic tapping of the right index finger when the left tap was executed as the phase of the stimulus. Responses of the neural activities (magnetoencephalography, MEG), the tapping movement, and the corresponding muscle activities (electromyography) were simultaneously measured. Phase-resetting curves (PRCs) representing the degree of phase reset as a function of the phase of the stimulus were obtained both for the left sensorimotor cortex MEG response and for the right index finger tapping response. The shapes of both PRCs were similar, suggesting that the phase reset of the left sensorimotor cortex activities and that of the finger tapping rhythm were the same. Four out of eight subjects showed type-0 reset in Winfree's definition, and the others showed type-1 reset. For general limit-cycle oscillators, type-0 reset is obtained for relatively strong perturbations and type 1 for weak perturbations. It was shown that the transient response of MEG to the single left tap stimuli in type-0 subjects, where the phase was progressively reset, were different from those in type-1 subjects. Based on detailed analysis of the differences, a neural network model for the phase reset of the tapping rhythm is proposed. Received: 10 February 2000 / Accepted in revised form: 15 January 2002     

Outbreaking forest insect drives phase synchrony among sympatric folivores: Exploring potential mechanisms

We explore a common feature of insect population dynamics, interspecific synchrony, which refers to synchrony in population dynamics among sympatric populations of different species. Such synchrony can arise via several possible mechanisms, including shared environmental effects and shared trophic interactions, but distinguishing the relative importance among different mechanisms can be challenging. We analyze interannual time series of population densities of the larch budmoth, Zeiraphera griseana (Lepidoptera: Tortricidae), along with six sympatric larch-feeding folivores from a site in the European Alps 1952–1979. These species include five lepidopterans, Exapate duratella, Ptycholomoides aeriferana, Spilonota laricana, Epirrita autumnata and Teleiodes saltuum, and one hymenopteran sawfly Pristiphora laricis. We document that the highly regular oscillatory behavior (period 9–10 years) of Z. griseana populations is similarly evident in the dynamics of most of the sympatric folivores. We also find that all of the sympatric species are phase synchronized with Z. griseana populations with half of the sympatric species exhibiting nonlagged phase synchrony and three of the species exhibiting 2–5 year lags behind Z. griseana populations. We adapt a previously developed tritrophic model of Z. griseana dynamics to explore possible mechanisms responsible for observed phase synchronization. Results suggest that either shared stochastic influences (e.g., weather) or shared parasitoid impacts are likely causes of nonlagged phase synchronization. The model further indicates that observed patterns of lagged phase synchronization are most likely caused by either shared delayed induced host plant defenses or direct density-dependent effects shared with Z. griseana.     

Switching Dynamics in an Interpersonal Competition Brings about “Deadlock” Synchronization of Players

In competitive sport game behavior, certain interpersonal patterns of movement coordination evolve even though each individual player only intends to exert their own strategy to win. To investigate this interpersonal pattern formation process, we asked pairs of naïve participants to engage in a play-tag game in which they had to remove a tag fastened to their partner''s hip. Relative phase analysis of the players'' step towards-away velocities indicated that anti-phase synchronization evolved across 10 repetitions of the game. We clarified evolution of this synchronization process using a dynamical model with an attractor (at relative phase) and a repeller (at relative phase) and discuss the self-organized nature of model and its ability to embody general solution for martial art interpersonal coordination.     

Beat Synchronization across the Lifespan: Intersection of Development and Musical Experience

Rhythmic entrainment, or beat synchronization, provides an opportunity to understand how multiple systems operate together to integrate sensory-motor information. Also, synchronization is an essential component of musical performance that may be enhanced through musical training. Investigations of rhythmic entrainment have revealed a developmental trajectory across the lifespan, showing synchronization improves with age and musical experience. Here, we explore the development and maintenance of synchronization in childhood through older adulthood in a large cohort of participants (N = 145), and also ask how it may be altered by musical experience. We employed a uniform assessment of beat synchronization for all participants and compared performance developmentally and between individuals with and without musical experience. We show that the ability to consistently tap along to a beat improves with age into adulthood, yet in older adulthood tapping performance becomes more variable. Also, from childhood into young adulthood, individuals are able to tap increasingly close to the beat (i.e., asynchronies decline with age), however, this trend reverses from younger into older adulthood. There is a positive association between proportion of life spent playing music and tapping performance, which suggests a link between musical experience and auditory-motor integration. These results are broadly consistent with previous investigations into the development of beat synchronization across the lifespan, and thus complement existing studies and present new insights offered by a different, large cross-sectional sample.     

Spatial coupling in cyclic population dynamics: models and data

We use a dynamic random field to model a spatial collection of coupled oscillators with discrete time stochastic dynamics. At each time step the phase of each cyclic local population is subject to random noise, incremented by a common dynamic, and pulled by a coupling force in the direction of some collective mean phase. We define asynchrony and derive expressions for its measurement in this model. We describe robust methods for phase estimation of cyclic population time series, for estimating strength of coupling between local populations, and for measuring variance of locally acting noise from field data. Proposed methods allow intermittently acting phase synchronizing events operating over large spatial scales to be distinguished from more continuous and possibly locally acting coupling, both of which could result in elevated levels of phase synchronization. We demonstrate the utility of this approach by applying it to classical spatial time series data of Canadian lynx. Analysis confirms findings of previous studies and reveals evidence to suggest that interpopulation coupling was weaker over the 20th century than for the 1800s. Analysis supports the notion that synchrony in these populations is maintained by a continuous and locally acting coupling between adjacent regions with large phase adjustments occurring only infrequently. When this coupling is absent, asynchrony develops between populations.     

Deriving theoretical phase locking values of a coupled cortico-thalamic neural mass model using center manifold reduction

Cognitive functions such as sensory processing and memory processes lead to phase synchronization in the electroencephalogram or local field potential between different brain regions. There are a lot of computational researches deriving phase locking values (PLVs), which are an index of phase synchronization intensity, from neural models. However, these researches derive PLVs numerically. To the best of our knowledge, there have been no reports on the derivation of a theoretical PLV. In this study, we propose an analytical method for deriving theoretical PLVs from a cortico-thalamic neural mass model described by a delay differential equation. First, the model for generating neural signals is transformed into a normal form of the Hopf bifurcation using center manifold reduction. Second, the normal form is transformed into a phase model that is suitable for analyzing synchronization phenomena. Third, the Fokker–Planck equation of the phase model is derived and the phase difference distribution is obtained. Finally, the PLVs are calculated from the stationary distribution of the phase difference. The validity of the proposed method is confirmed via numerical simulations. Furthermore, we apply the proposed method to a working memory process, and discuss the neurophysiological basis behind the phase synchronization phenomenon. The results demonstrate the importance of decreasing the intensity of independent noise during the working memory process. The proposed method will be of great use in various experimental studies and simulations relevant to phase synchronization, because it enables the effect of neurophysiological changes on PLVs to be analyzed from a mathematical perspective.     

Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation

 Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are difficult to detect in electrode recordings. We present a framework and a model for the identification of such network states and of their dynamics in a specific experimental situation. Our approach operationalizes the notion of neuronal groups forming assemblies via synchronization based on experimentally obtained spike trains. The dynamics of such groups is reflected in the sequence of synchronized states, which we describe as a renewal dynamics. We furthermore introduce a rate function which is dependent on the internal network phase that quantifies the activity of neurons contributing to the observed spike train. This constitutes a hidden state model which is formally equivalent to a hidden Markov model, and all its parameters can be accurately determined from the experimental time series using the Baum-Welch algorithm. We apply our method to recordings from the cat visual cortex which exhibit oscillations and synchronizations. The parameters obtained for the hidden state model uncover characteristic properties of the system including synchronization, oscillation, switching, background activity and correlations. In applications involving multielectrode recordings, the extracted models quantify the extent of assembly formation and can be used for a temporally precise localization of system states underlying a specific spike train. Received: 30 March 1993/Accepted in revised form: 16 April 1994     

Improved measures of phase-coupling between spikes and the Local Field Potential

An important tool to study rhythmic neuronal synchronization is provided by relating spiking activity to the Local Field Potential (LFP). Two types of interdependent spike-LFP measures exist. The first approach is to directly quantify the consistency of single spike-LFP phases across spikes, referred to here as point-field phase synchronization measures. We show that conventional point-field phase synchronization measures are sensitive not only to the consistency of spike-LFP phases, but are also affected by statistical dependencies between spike-LFP phases, caused by e.g. non-Poissonian history-effects within spike trains such as bursting and refractoriness. To solve this problem, we develop a new pairwise measure that is not biased by the number of spikes and not affected by statistical dependencies between spike-LFP phases. The second approach is to quantify, similar to EEG-EEG coherence, the consistency of the relative phase between spike train and LFP signals across trials instead of across spikes, referred to here as spike train to field phase synchronization measures. We demonstrate an analytical relationship between point-field and spike train to field phase synchronization measures. Based on this relationship, we prove that the spike train to field pairwise phase consistency (PPC), a quantity closely related to the squared spike-field coherence, is a monotonically increasing function of the number of spikes per trial. This derived relationship is exact and analytic, and takes a linear form for weak phase-coupling. To solve this problem, we introduce a corrected version of the spike train to field PPC that is independent of the number of spikes per trial. Finally, we address the problem that dependencies between spike-LFP phase and the number of spikes per trial can cause spike-LFP phase synchronization measures to be biased by the number of trials. We show how to modify the developed point-field and spike train to field phase synchronization measures in order to make them unbiased by the number of trials.     

Two coupled oscillators as a model for the coordinated finger tapping by both hands

Recently, it was found that rhythmic movements (e.g. locomotion, swimmeret beating) are controlled by mutually coupled endogeneous neural oscillators (Kennedy and Davis, 1977; Pearson and Iles, 1973; Stein, 1974; Shik and Orlovsky, 1976; Grillner and Zangger, 1979). Meanwhile, it has been found out that the phase resetting experiment is useful to investigate the interaction of neural oscillators (Perkel et al., 1963; Stein, 1974). In the preceding paper (Yamanishi et al., 1979), we studied the functional interaction between the neural oscillator which is assumed to control finger tapping and the neural networks which control some tasks. The tasks were imposed on the subject as the perturbation of the phase resetting experiment. In this paper, we investigate the control mechanism of the coordinated finger tapping by both hands. First, the subjects were instructed to coordinate the finger tapping by both hands so as to keep the phase difference between two hands constant. The performance was evaluated by a systematic error and a standard deviation of phase differences. Second, we propose two coupled neural oscillators as a model for the coordinated finger tapping. Dynamical behavior of the model system is analyzed by using phase transition curves which were measured on one hand finger tapping in the previous experiment (Yamanishi et al., 1979). Prediction by the model is in good agreement with the results of the experiments. Therefore, it is suggested that the neural mechanism which controls the coordinated finger tapping may be composed of a coupled system of two neural oscillators each of which controls the right and the left finger tapping respectively.     

Unusual synchronization of Red Sea fish energy expenditures

The highly gregarious goat fish Parupeneus forskalii found in the Red Sea at Eilat, Israel exhibit highly synchronous swimming and feeding activity. Five fish were studied under controlled conditions and highly resolved time‐series of their energy expenditures were measured. All fish demonstrated strong phase synchronization in that their activity levels, although erratic in time and intensity, were collectively coordinated and peaked simultaneously together. The synchronization of these wildly varying, and possibly chaotic signals of energy expenditures, were quantified using phase analysis. We suggest that, ecologically, this collective synchronization is a strategy that increases food‐catch.     

Modeling inter-human movement coordination: synchronization governs joint task dynamics

Human interaction partners tend to synchronize their movements during repetitive actions such as walking. Research of inter-human coordination in purely rhythmic action tasks reveals that the observed patterns of interaction are dominated by synchronization effects. Initiated by our finding that human dyads synchronize their arm movements even in a goal-directed action task, we present a step-wise approach to a model of inter-human movement coordination. In an experiment, the hand trajectories of ten human dyads are recorded. Governed by a dynamical process of phase synchronization, the participants establish in-phase as well as anti-phase relations. The emerging relations are successfully reproduced by the attractor dynamics of coupled phase oscillators inspired by the Kuramoto model. Three different methods on transforming the motion trajectories into instantaneous phases are investigated and their influence on the model fit to the experimental data is evaluated. System identification technique allows us to estimate the model parameters, which are the coupling strength and the frequency detuning among the dyad. The stability properties of the identified model match the relations observed in the experimental data. In short, our model predicts the dynamics of inter-human movement coordination. It can directly be implemented to enrich human-robot interaction.     

A simple nonlinear model of electrical activity in the intestine

We have simulated electrical activity of the intestine in a computer model that describes the coupled layers of longitudinal muscle (LM) and interstitial cells of Cajal (ICC). The model suggests that pacemaker activity is due to the ICC layer, while the pulse propagation involves the LM layer that is in the excitatory state. The model describes well the experimentally observed phenomena: frequency change along the intestine, synchronization along short distances and desynchronization for long distances, and the decrease of propagation distance and propagation time along the intestine. We have observed the occurrence of phase interruptions or breaks, which are responsible for the limited values of propagation distance and time.     

Finger joint impedance during tapping on a computer keyswitch

We studied the dynamic behavior of finger joints during the contact period of tapping on a computer keyswitch, to characterize and parameterize joint function with a lumped-parameter impedance model. We tested the hypothesis that the metacarpophalangeal (MCP) and interphalangeal (IP) joints act similarly in terms of kinematics, torque, and energy production when tapping. Fifteen human subjects tapped with the index finger of the right hand on a computer keyswitch mounted on a two-axis force sensor, which measured forces in the vertical and sagittal planes. Miniature fiber-optic goniometers mounted across the dorsal side of each joint measured joint kinematics. Joint torques were calculated from endpoint forces and joint kinematics using an inverse dynamic algorithm. For each joint, a linear spring and damper model was fitted to joint torque, position, and velocity during the contact period of each tap (22 per subject on average). The spring-damper model could account for over 90% of the variance in torque when loading and unloading portions of the contact were separated, with model parameters comparable to those previously measured during isometric loading of the finger. The finger joints functioned differently, as illustrated by energy production during the contact period. During the loading phase of contact the MCP joint flexed and produced energy, whereas the proximal and distal IP joints extended and absorbed energy. These results suggest that the MCP joint does work on the interphalangeal joints as well as on the keyswitch.     

Optimal Information Transfer in the Cortex through Synchronization

In recent experimental work it has been shown that neuronal interactions are modulated by neuronal synchronization and that this modulation depends on phase shifts in neuronal oscillations. This result suggests that connections in a network can be shaped through synchronization. Here, we test and expand this hypothesis using a model network. We use transfer entropy, an information theoretical measure, to quantify the exchanged information. We show that transferred information depends on the phase relation of the signal, that the amount of exchanged information increases as a function of oscillations in the signal and that the speed of the information transfer increases as a function of synchronization. This implies that synchronization makes information transport more efficient. In summary, our results reinforce the hypothesis that synchronization modulates neuronal interactions and provide further evidence that gamma band synchronization has behavioral relevance.