The Haken-Kelso-Bunz (HKB) model: from matter to movement to mind

Bridging the gap of brain and experience - Converging Neurophenomenology with Spatiotemporal Neuroscience

Neuroscience faces the challenge of connecting brain and mind, with the mind manifesting in first-person experience while the brain's neural activity can only be investigated in third-person perspective. To connect neural and mental states, Neurophenomenology provides a methodological toolkit for systematically linking first-person subjective experience with third-person objective observations of the brain's neural activity. However, beyond providing a systematic methodological strategy ('disciplined circularity'), it leaves open how neural activity and subjective experience are related among themselves, independent of our methodological strategy. The recently introduced Spatiotemporal Neuroscience suggests that neural activity and subjective experience share a commonly underlying feature as their "common currency", notably analogous spatiotemporal dynamics. Can Spatiotemporal Neuroscience inform Neurophenomenology to allow for a deeper and more substantiative connection of first-person experience and third-person neural activity? The goal of our paper is to show how Spatiotemporal Neuroscience and Neurophenomenology can be converged and integrated with each other to gain better understanding of the brain-mind connection. We describe their convergence on theoretical grounds which, subsequently, is illustrated by empirical examples like self, meditation, and depression. In conclusion, we propose that the integration of Neurophenomenology and Spatiotemporal Neuroscience can provide complementary insights, enrich both fields, allows for deeper understanding of brain-mind connection, and opens the door for developing novel methodological approaches in their empirical investigation.

The effect of running experience and speed on local dynamic stability in running

Introduction

As a coach or health care professional working with physically active people, it can be difficult to guide runners towards safe and effective progression, because making changes to single aspects of running technique may not lead to the desired result. Alternatively, it has been proposed to consider the human body as one complex system when assessing and improving human movement. From this perspective, it appears that the movement variability and local dynamic stability, expressed as the maximum Lyapunov exponent (LyEmax), may be of particular interest. This study investigated the difference in LyEmax of the lower extremities' main joints (ankle, knee, hip) between experienced and novice runners at different running speeds.

Methods

Thirty-six participants were recruited, with 18 experienced runners and 18 novice runners. Participants ran at three different speeds on a treadmill for 10 minutes in each of the following conditions: preferred running speed, 10% slower, and 10% faster. Twenty-six participants were included in the analysis. The LyEmax was calculated from joint kinematics and a two-way ANOVA with repeated measures was applied.

Results

The results showed that there is a strong effect of running experience on the LyEmax with the experienced runners having more local dynamic stability. The effect of running speed was statistically significant only for the hip joint, where higher running speeds resulted in more local dynamic stability in both groups.

Discussion and conclusion

The results should be interpreted with caution, particularly due to the low running speeds chosen by the novice runners. Nevertheless, the study's findings support the emerging view that movement variability is a parameter on which it is important to focus, and that local dynamic stability should be improved in novice runners as well as with athletes or patients who are in a return-to-sport phase of a rehabilitation.

Inter-limb and inter-agent coordination in an original joint-action game: exploring novel approaches for clinical practice

After identifying a need to develop rehabilitation practices inspired from a systems perspective, we designed a joint-action game that involves both inter-limb and inter-agent coordination. The main specificity of our joint-action game lies in the informational and mechanical couplings that exist between the system elements-i.e., between lower limbs at one scale, and between agents at another scale. The present paper aims to investigate whether our joint-action game can foster the emergence of new coordination patterns at both scales, and discuss whether such patterns, if any, could be clinically relevant. Twelve dyads were asked to stand up on an unstable surface (BOSU) and to jointly manipulate a board on which a ball had to roll along a circular path containing target doors. Ball trajectory as well as lower limb and hand kinematics were obtained using an 8-camera motion capture system. Coordination between left and right knee joint angles was assessed through relative-phase and PCA analyses. Inter-agent coordination was evaluated using UCM analyses. The effects of amount of practice and performance on coordination were investigated. At both scales, significant coordination differences were found over practice and across levels of performance. More specifically, left and right knees were constrained to act as a single unit, while interpersonal synergies were observed in trials with better performance. We discussed how the exploration of coordinative solutions, as well as the dimensional reduction and reciprocal compensation among degrees of freedom that our game supports could be beneficially exploited in rehabilitation.

Modeling dynamics on the dance floor with directional swarmalators

Understanding collective behavior in both biological and social contexts, such as human interactions on dance floors, is a growing field of interest. Spatiotemporal dynamics of collective behavior have previously been modeled, for instance, with swarmalators, which are dynamical units that exhibit both swarming behavior and synchronization, combining spatial movement and entrainment. In our current study, we have expanded the swarmalator concept to encompass gaze direction as a representation of visual attention. We employ the newly developed directional swarmalator model for simulating the complex spatiotemporal dynamics observed on dance floors. Our model aims to reflect the complex dynamics of collective movement, as well as rhythmic synchronization and gaze alignment. It establishes a quantitative framework to dissect how individuals on dance floors self-organize and generate emergent patterns in response to both musical stimuli and visual perception of other dancers. The inclusion of gaze direction allows for the simulation of realistic scenarios on dance floors, mirroring the dynamic interplay of human movement in rhythm-driven environments. The model is initially tested against motion capture recordings of two groups dancing in a silent disco, however, it is theoretically adaptable to a variety of scenarios, including varying group sizes, adjustable degrees of auditory and visual coupling, as well as modifiable interaction ranges, making it a generic tool for exploring collective behavior in musical settings. The development of the directional swarmalator model contributes to understanding social dynamics in shared music and dance experiences.

Information Entropy in Chimera States of Human Dynamics

In human dynamics, functioning relies on intricate coordination patterns. Networks of synchronized oscillators in various biological and semiotic fields shape these dynamics. We have observed stability, instability, and transitions at multiple levels, indicating that coordination happens on all scales. We have examined coordination models for simplified and complex dynamics. In empirical research, we can frequently observe chimera states as the coexistence of coherence and incoherence, even in homogeneous networks. They are more evident in the heterogenous networks' standard in human dynamics, where oscillators and nodes are mixed as different types. This paper proposes a simplified and overarching model for mixed chimeras. We discuss the information dynamics in these types of networks and their pattern transitions.

Minds and markets as complex systems: an emerging approach to cognitive economics

Cognitive economics is an emerging interdisciplinary field that uses the tools of cognitive science to study economic and social decision-making. Although most strains of cognitive economics share commitments to bridging levels of analysis (cognitive, behavioral, and systems) and embracing interdisciplinary approaches, we review a newer strand of cognitive economic thinking with a further commitment: conceptualizing minds and markets each as complex adaptive systems. We describe three ongoing research programs that strive toward these goals: (i) studying narratives as a cognitive and social representation used to guide decision-making; (ii) building cognitively informed agent-based models; and (iii) understanding markets as an extended mind - the Market Mind Hypothesis - analyzed using the concepts, methods, and tools of Coordination Dynamics.

Dance of two brains: Interval subdivision in alternated condition enhances resistance to interference by others

The accomplishment of interpersonal sensorimotor synchronization is a challenging endeavor because it requires the achievement of a balance between accurate temporal control within individuals and smooth communication between them. This raises a critical question: How does the brain comprehend and process the perceptual information of others to guarantee accurate temporal control of action goals in a social context? A joint synchronization - continuation tapping task was conducted together with varying relative phases (0°/180°) and intervals of tempos (400 ms/800 ms/1600 ms) while neural data was collected using fNIRS (functional near-infrared spectroscopy). Individuals showed better behavioral performance and greater interpersonal brain synchronization(IBS) in the left dorsolateral prefrontal cortex at alternated condition (180° relative phase) compared to symmetric condition (0° relative phase), suggesting that the individual can better maintain behavioral performance and show improved IBS when the partner taps between the individual's gaps. Meanwhile, in most levels of alternated condition, IBS is inversely proportional to interference from partner, implying the counteraction of IBS against interference from others. In addition, when the interval of tempo was 1600 ms, behavioral performance showed a sharp decline, accompanied by a decrease in IBS, reflecting that IBS in SMS reflects effective information exchange between individuals rather than ineffective interference with each other. This study provides insight into the mechanisms underlying sensorimotor synchronization between individuals.

Pink noise promotes sooner state transitions during bimanual coordination

The seemingly straightforward task of tying one's shoes requires a sophisticated interplay of joints, muscles, and neural pathways, posing a formidable challenge for researchers studying the intricacies of coordination. A widely accepted framework for measuring coordinated behavior is the Haken-Kelso-Bunz (HKB) model. However, a significant limitation of this model is its lack of accounting for the diverse variability structures inherent in the coordinated systems it frequently models. Variability is a pervasive phenomenon across various biological and physical systems, and it changes in healthy adults, older adults, and pathological populations. Here, we show, both empirically and with simulations, that manipulating the variability in coordinated movements significantly impacts the ability to change coordination patterns-a fundamental feature of the HKB model. Our results demonstrate that synchronized bimanual coordination, mirroring a state of healthy variability, instigates earlier transitions of coordinated movements compared to other variability conditions. This suggests a heightened adaptability when movements possess a healthy variability. We anticipate our study to show the necessity of adapting the HKB model to encompass variability, particularly in predictive applications such as neuroimaging, cognition, skill development, biomechanics, and beyond.

The effect of inherent and incidental constraints on bimanual force control in simulated Martian gravity

The ability to coordinate actions between the limbs is important for many operationally relevant tasks associated with space exploration. A future milestone in space exploration is sending humans to Mars. Therefore, an experiment was designed to examine the influence of inherent and incidental constraints on the stability characteristics associated with the bimanual control of force in simulated Martian gravity. A head-up tilt (HUT)/head-down tilt (HDT) paradigm was used to simulate gravity on Mars (22.3° HUT). Right limb dominant participants (N = 11) were required to rhythmically coordinate patterns of isometric forces in 1:1 in-phase and 1:2 multifrequency patterns by exerting force with their right and left limbs. Lissajous displays were provided to guide task performance. Participants performed 14 twenty-second practice trials at 90° HUT (Earth). Following a 30-min rest period, participants performed 2 test trials for each coordination pattern in both Earth and Mars conditions. Performance during the test trials were compared. Results indicated very effective temporal performance of the goal coordination tasks in both gravity conditions. However, results indicated differences associated with the production of force between Earth and Mars. In general, participants produced less force in simulated Martian gravity than in the Earth condition. In addition, force production was more harmonic in Martian gravity than Earth gravity for both limbs, indicating that less force distortions (adjustments, hesitations, and/or perturbations) occurred in the Mars condition than in the Earth condition. The force coherence analysis indicated significantly higher coherence in the 1:1 task than in the 1:2 task for all force frequency bands, with the highest level of coherence in the 1-4 Hz frequency band for both gravity conditions. High coherence in the 1-4 Hz frequency band is associated with a common neural drive that activates the two arms simultaneously and is consistent with the requirements of the two tasks. The results also support the notion that neural crosstalk stabilizes the performance of the 1:1 in-phase task. In addition, significantly higher coherence in the 8-12 Hz frequency bands were observed for the Earth condition than the Mars condition. Force coherence in the 8-12 Hz bands is associated with the processing of sensorimotor information, suggesting that participants were better at integrating visual, proprioceptive, and/or tactile feedback in Earth than for the Mars condition. Overall, the results indicate less neural interference in Martian gravity; however, participants appear to be more effective at using the Lissajous displays to guide performance under Earth's gravity.

A synergetic turn in cognitive neuroscience of brain diseases

Despite significant improvements in our understanding of brain diseases, many barriers remain. Cognitive neuroscience faces four major challenges: complex structure-function associations; disease phenotype heterogeneity; the lack of transdiagnostic models; and oversimplified cognitive approaches restricted to the laboratory. Here, we propose a synergetics framework that can help to perform the necessary dimensionality reduction of complex interactions between the brain, body, and environment. The key solutions include low-dimensional spatiotemporal hierarchies for brain-structure associations, whole-brain modeling to handle phenotype diversity, model integration of shared transdiagnostic pathophysiological pathways, and naturalistic frameworks balancing experimental control and ecological validity. Creating whole-brain models with reduced manifolds combined with ecological measures can improve our understanding of brain disease and help identify novel interventions. Synergetics provides an integrated framework for future progress in clinical and cognitive neuroscience, pushing the boundaries of brain health and disease toward more mature, naturalistic approaches.

Energetic and Cognitive Demands of Treading Water: Effects of Technique and Expertise

Being able to tread water effectively can improve the likelihood of survival following accidental immersion. People tread water in various ways, ranging from rudimentary 'doggy-paddle' to more elaborate techniques like the eggbeater, but little is known about the energetic and cognitive requirements of treading water. We therefore aimed to measure the demands of treading water techniques for people of different experience levels. Three cohorts, comprising 21 adult water treading experts (water polo players), 15 intermediate swimmers and 16 inexperienced swimmers, treaded water for 3 min each using four different techniques while cognitive and energetic economy measures were taken. For inexperienced swimmers, the flutter kick and breaststroke patterns produced the lowest self-reported physical and task load (rating of perceived exertion, NASA task load index), while cognitive (probe reaction time), cardiac (heart rate) and metabolic (oxygen consumption) load did not differ between techniques. In contrast, for expert water treaders, both breaststroke and eggbeater patterns produced lower cognitive, cardiac and metabolic loads. For intermediate swimmers, breaststroke resulted in the lowest cardiac and metabolic loads, as well as self-reported task load. Probe reaction time was highest while performing the eggbeater technique, indicating that this technique was challenging to coordinate and cognitively demanding. While the energetic demands of antiphase kicking patterns (such as eggbeater in experts or flutter kick in beginners) may be similarly low, the symmetric coordination of upright breaststroke may explain why this pattern's cognitive economy was favourable for all groups. As the eggbeater can be challenging to perform for many people, an upright breaststroke technique is an adequate alternative to adopt in survival situations.

Social and nonlinear dynamics unite: musical group synchrony

Synchronization, the human tendency to align behaviors in time with others, is necessary for many survival skills. The ability to synchronize actions with rhythmic (predictable) sound patterns is especially well developed in music making. Recent models of synchrony in musical ensembles rely on pairwise comparisons between group members. This pairwise approach to synchrony has hampered theory development, given current findings from social dynamics indicating shifts in members' influence within larger groups. We draw on social theory and nonlinear dynamics to argue that emergent properties and novel roles arise in musical group synchrony that differ from individual or pairwise behaviors. This transformational shift in defining synchrony sheds light on successful outcomes as well as on disruptions that cause negative behavioral outcomes.

Abduction and Deduction in Dynamical Cognitive Science

This paper reviews the recent history of a subset of research in dynamical cognitive science, in particular that subset that allies itself with the sciences of complexity and casts cognitive systems as interaction dominant, noncomputational, and nonmodular. I look at this history in the light of C.S. Peirce's understanding of scientific reasoning as progressing from abduction to deduction to induction. In particular, I examine the development of a controversy concerning the use of the interaction dominance of human cognitive systems as an explanation of the ubiquitous 1/f noise, multifractality, and complexity matching in human behavior.

Auditory-motor synchronization varies among individuals and is critically shaped by acoustic features

The ability to synchronize body movements with quasi-regular auditory stimuli represents a fundamental trait in humans at the core of speech and music. Despite the long trajectory of the study of such ability, little attention has been paid to how acoustic features of the stimuli and individual differences can modulate auditory-motor synchrony. Here, by exploring auditory-motor synchronization abilities across different effectors and types of stimuli, we revealed that this capability is more restricted than previously assumed. While the general population can synchronize to sequences composed of the repetitions of the same acoustic unit, the synchrony in a subgroup of participants is impaired when the unit's identity varies across the sequence. In addition, synchronization in this group can be temporarily restored by being primed by a facilitator stimulus. Auditory-motor integration is stable across effectors, supporting the hypothesis of a central clock mechanism subserving the different articulators but critically shaped by the acoustic features of the stimulus and individual abilities.

Coordination tending towards an anti-phase relationship determines greater sway reduction during entrainment with a simulated partner

The increased risk of falls in the older aged population demands the development of assistive robotic devices capable of effective balance support. For the development and increased user acceptance of such devices, which provide balance support in a human-like way, it is important to understand the simultaneous occurrence of entrainment and sway reduction in human-human interaction. However, sway reduction has not been observed yet during a human touching an external, continuously moving reference, which rather increased human body sway. Therefore, we investigated in 15 healthy young adults (27.20±3.55 years, 6 females) how different simulated sway-responsive interaction partners with different coupling modes affect sway entrainment, sway reduction and relative interpersonal coordination, as well as how these human behaviours differ depending on the individual body schema accuracy. For this, participants were lightly touching a haptic device that either played back an average pre-recorded sway trajectory ("Playback") or moved based on the sway trajectory simulated by a single-inverted pendulum model with either a positive (Attractor) or negative (Repulsor) coupling to participant's body sway. We found that body sway reduced not only during the Repulsor-interaction, but also during the Playback-interaction. These interactions also showed a relative interpersonal coordination tending more towards an anti-phase relationship, especially the Repulsor. Moreover, the Repulsor led to the strongest sway entrainment. Finally, a better body schema contributed to a reduced body sway in both the "reliable" Repulsor and the "less reliable" Attractor mode. Consequently, a relative interpersonal coordination tending more towards an anti-phase relationship and an accurate body schema are important to facilitate sway reduction.

Dynamical systems model of development of the action differentiation in early infancy: a requisite of physical agency

Young infants are sensitive to whether their body movements cause subsequent events or not during the interaction with the environment. This ability has been revealed by empirical studies on the reinforcement of limb movements when a string is attached between an infant limb and a mobile toy suspended overhead. A previous study reproduced the experimental observation by modeling both the infant's limb and a mobile toy as a system of coupled oscillators. The authors then argued that emergence of agency could be explained by a phase transition in the dynamical system: from a weakly coupled state to a state where the both movements of the limb and the toy are highly coordinated. However, what remains unexplained is the following experimental observation: When the limb is connected to the mobile toy by a string, the infant increases the average velocity of the arm's movement. On the other hand, when the toy is controlled externally, the average arm's velocity is greatly reduced. Since young infants produce exuberant spontaneous movements even with no external stimuli, the inhibition of motor action to suppress the formation of spurious action-perception coupling should be also a crucial sign for the emergence of agency. Thus, we present a dynamical system model for the development of action differentiation, to move or not to move, in the mobile task. In addition to the pair of limb and mobile oscillators for providing positive feedback for reinforcement in the previous model, bifurcation dynamics are incorporated to enhance or inhibit self-movements in response to detecting contingencies between the limb and mobile movements. The results from computer simulations reproduce experimental observations on the developmental emergence of action differentiation between 2 and 3 months of age in the form of a bifurcation diagram. We infer that the emergence of physical agency entails young infants' ability not only to enhance a specific action-perception coupling, but also to decouple it and create a new mode of action-perception coupling based on the internal state dynamics with contingency detection between self-generated actions and environmental events.

Network Physiology of Exercise: Beyond Molecular and Omics Perspectives

Molecular Exercise Physiology and Omics approaches represent an important step toward synthesis and integration, the original essence of Physiology. Despite the significant progress they have introduced in Exercise Physiology (EP), some of their theoretical and methodological assumptions are still limiting the understanding of the complexity of sport-related phenomena. Based on general principles of biological evolution and supported by complex network science, this paper aims to contrast theoretical and methodological aspects of molecular and network-based approaches to EP. After explaining the main EP challenges and why sport-related phenomena cannot be understood if reduced to the molecular level, the paper proposes some methodological research advances related to the type of studied variables and measures, the data acquisition techniques, the type of data analysis and the assumed relations among physiological levels. Inspired by Network Physiology, Network Physiology of Exercise provides a new paradigm and formalism to quantify cross-communication among diverse systems across levels and time scales to improve our understanding of exercise-related phenomena and opens new horizons for exercise testing in health and disease.

A brief review of motor imagery and bimanual coordination

Motor imagery is increasingly being used in clinical settings, such as in neurorehabilitation and brain computer interface (BCI). In stroke, patients lose upper limb function and must re-learn bimanual coordination skills necessary for the activities of daily living. Physiotherapists integrate motor imagery with physical rehabilitation to accelerate recovery. In BCIs, users are often asked to imagine a movement, often with sparse instructions. The EEG pattern that coincides with this cognitive task is captured, then used to execute an external command, such as operating a neuroprosthetic device. As such, BCIs are dependent on the efficient and reliable interpretation of motor imagery. While motor imagery improves patient outcome and informs BCI research, the cognitive and neurophysiological mechanisms which underlie it are not clear. Certain types of motor imagery techniques are more effective than others. For instance, focusing on kinesthetic cues and adopting a first-person perspective are more effective than focusing on visual cues and adopting a third-person perspective. As motor imagery becomes more dominant in neurorehabilitation and BCIs, it is important to elucidate what makes these techniques effective. The purpose of this review is to examine the research to date that focuses on both motor imagery and bimanual coordination. An assessment of current research on these two themes may serve as a useful platform for scientists and clinicians seeking to use motor imagery to help improve bimanual coordination, either through augmenting physical therapy or developing more effective BCIs.

Mathematization of nature: how it is done

Natural phenomena can be quantitatively described by means of mathematics, which is actually the only way of doing so. Physics is a convincing example of the mathematization of nature. This paper gives an answer to the question of how mathematization of nature is done and illustrates the answer. Here nature is to be taken in a wide sense, being a substantial object of study in, among others, large domains of biology, such as epidemiology and neurobiology, chemistry, and physics, the most outspoken example. It is argued that mathematization of natural phenomena needs appropriate core concepts that are intimately connected with the phenomena one wants to describe and explain mathematically. Second, there is a scale on and not beyond which a specific description holds. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis, which has meanwhile been confirmed on many occasions. Furthermore, a mathematical description can, as in physics, but need not be universally valid, as in biology. Finally, the history of science shows that only an intensive gauging of theory, i.e., mathematical description, by experiment leads to progress. That is, appropriate core concepts and appropriate scales are a necessary condition for mathematizing nature, and so is its verification by experiment.

Global entrainment in the brain-body-environment: retrospective and prospective views

We celebrate the 60th anniversary of Biological Cybernetics. It has also been 30 years since "Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment" was published in Biological Cybernetics (Taga et al. in Biol Cybern 65(3):147-159, 1991). I would like to look back on the creation of this paper and discuss its subsequent development and future perspectives.