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A Theoretical Model of Phase Transitions in Human Hand Movements
Abstract
Earlier experimental studies by one of us (Kelso, 1981a, 1984) have shown that abrupt phase transitions occur in human hand movements under the influence of scalar changes in cycling frequency. Beyond a critical frequency the originally prepared out-of-phase, antisymmetric mode is replaced by a symmetrical, in-phase mode involving simultaneous activation of homologous muscle groups. Qualitatively, these phase transitions are analogous to gait shifts in animal locomotion as well as phenomena common to other physical and biological systems in which new "modes" or spatiotemporal patterns arise when the system is parametrically scaled beyond its equilibrium state (Haken, 1983). In this paper a theoretical model, using concepts central to the interdisciplinary field of synergetics and nonlinear oscillator theory, is developed, which reproduces (among other features) the dramatic change in coordinative pattern observed between the hands.
... These circuits, for instance found in the brainstem or spinal cord, exhibit stable periodicities once activated and can be theorized as internal oscillators 25,26 . Additionally, differences in spontaneous rates can be a result of specific biomechanical or anatomical constraints pertaining to the effector system in use, resulting in different states of minimal energy expenditure [27][28][29] . For example, the weight and length of a limb place rigid constraints on the speed at which it moves naturally 30 . ...
Spontaneous rhythmic movements are part of everyday life, e.g., in walking, clapping or music making. Humans perform such spontaneous motor actions at different rates that reflect specific biomechanical constraints of the effector system in use. However, there is some evidence for intra-individual consistency of specific spontaneous rates arguably resulting from common underlying processes. Additionally, individual and contextual factors such as musicianship and circadian rhythms have been suggested to influence spontaneous rates. This study investigated the relative contributions of these factors and provides a comprehensive picture of rates among different spontaneous motor behaviors, i.e., melody production, walking, clapping, tapping with and without sound production, the latter measured online before and in the lab. Participants (n = 60) exhibited high intra-individual stability across tasks. Task-related influences included faster tempi for spontaneous production rates of music and wider ranges of spontaneous motor tempi (SMT) and clapping rates compared to walking and music making rates. Moreover, musicians exhibited slower spontaneous rates across tasks, yet we found no influence of time of day on SMT as measured online in pre-lab sessions. Tapping behavior was similar in pre-lab and in-lab sessions, validating the use of online SMT assessments. Together, the prominent role of individual factors and high stability across domains support the idea that different spontaneous motor behaviors are influenced by common underlying processes.
... How people attend to others plays a pivotal role in the emergence of interpersonal coordination. Contemporary models of motor control (e.g., Haken-Kelso-Bunz Equation 10 ) show that, along with similar movement frequencies, the degree to which components of a system are coupled governs both spontaneous and intentional instances of coordination 11 . Coupling dictates the extent to which information exchange occurs between system components. ...
Interpersonal coordination is a key determinant of successful social interaction but can be disrupted when people experience symptoms related to social anxiety or autism. Effective coordination rests on individuals directing their attention towards interaction partners. Yet little is known about the impact of the attentional behaviours of the partner themselves. As the gaze of others has heightened salience for those experiencing social anxiety or autism, addressing this gap can provide insight into how symptoms of these disorders impact coordination. Using a novel virtual reality task, we investigated whether partner gaze (i.e., direct vs. averted) influenced the emergence of interpersonal coordination. Results revealed: (i) spontaneous coordination was diminished in the averted (cf. direct) gaze condition; (ii) spontaneous coordination was positively related to symptoms of social anxiety, but only when partner gaze was averted. This latter finding contrasts the extant literature and points to the importance of social context in shaping the relationship between symptoms of psychopathology and interpersonal coordination.
... The notion that social attention shapes coordination dynamics is consistent with contemporary research. Guiding this work is an influential model of motor control, the Haken-Kelso-Bunz (HKB) equation (Haken et al., 1985). Having seen wide application as a framework for studying coordination in biological systems (Kelso, 1995;Schmidt & Richardson, 2008), the HKB equation specifies two key parameters, frequency matching and coupling strength, that govern the emergence of coordination. ...
As a foundation for social interaction, interpersonal coordination is facilitated by positive social qualities (e.g., cooperation), but undermined in negative contexts (e.g., conflict). Exactly how social factors shape coordination is less clear. Previous literature notes that the way people attend to others impacts how interactions unfold. It is possible therefore, that patterns of social attention also govern coordination. We examined this proposition by using virtual reality to investigate how attentional focus (self vs. other) and partner gaze (direct vs. averted) influence the spontaneous emergence of coordination. The results indicated that: (i) coordination was enhanced in the other (cf. self) focus condition; (ii) coordination was diminished in the averted (cf. direct) gaze condition. These findings suggest that changes in social attention impact interpersonal coordination. More broadly, this work provides further evidence that the emergence of interpersonal coordination fluctuates as a function of social context.
... It is currently attributed to an age-related increase in neural noise (e.g., Li et al., 2001; Hultsch and MacDonald, 2004). However, in bimanual coordination tasks, the consequences of increased neural noise on behavioral variability might be magnified by an age-related decrease in bimanual coupling strength (see Haken et al., 1985 for a theoretical account and Temprado et al., 2010 for consistent results). In brain activation literature, Globe et al. find out that compared to young adults, older adults showed increased activity during the AP as compared to the IP coordination mode in several brain areas typically ascribed to more cognitive aspects of performance. ...
La méditation de pleine conscience (MPC) est une pratique mentale, impliquant des mécanismes cognitifs et émotionnels, qui consiste à porter son attention sur le moment présent (pensées, sensations, émotions), sans attente, sans filtre et sans jugement. Des résultats encourageants sont en faveur de bénéfices comportementaux de la MPC dans les domaines psychologique, cognitif et moteur. Cependant, des zones d’ombre persistent concernant leurs modérateurs, leurs mécanismes d’action, et l’efficacité de la modalité de pratique en ligne. L’objectif de cette thèse est d’apporter une meilleure compréhension des effets comportementaux de la MPC en cherchant à lever ces verrous scientifiques à travers une investigation chez différentes populations saines (adultes, étudiants, pratiquants ou novices en MPC). Premièrement, nous avons étudié l’efficacité de la MPC en ligne sur la santé mentale et les capacités attentionnelles d’étudiants pendant la crise sanitaire de la COVID-19. Deuxièmement, nous avons investigué les effets aigus de la MPC sur les capacités cognitives de pratiquants et novices en MPC. Pour finir, également chez des pratiquants et novices, nous avons étudié les effets aigus de la MPC sur le contrôle moteur, en cherchant à déterminer s’ils pouvaient être médiés par ses bénéfices cognitifs. Ce travail apporte des preuves de l’efficacité à court et moyen termes de la MPC dans les domaines psychologique, cognitif et moteur, tout en suggérant certains modérateurs de ses effets. De plus, à travers l’étude du lien cognition-motricité, il apporte les premières données concernant les potentiels mécanismes d’action de la MPC dans le domaine moteur.
... Many examples pertain to the "mirror game" (Noy et al., 2011), a paradigmatic motor task in which participants are instructed to execute motion ⋆ This work was in part supported by the Research Project that is both "synchronized and interesting". For instance, Zhai et al. (Zhai et al., 2014) combined the Haken-Kelso-Bunz (HKB) model (Haken et al., 1985) and a nonlinear feedback controller to make an avatar play the mirror game, either leading or following the motion of a person. Subsequently, in Zhai et al. (2016), a model describing the motion of two players was identified and used to design a CA capable of improvising joint motion with a person. ...
As interactions with autonomous agents-ranging from robots in physical settings to avatars in virtual and augmented realities-become more prevalent, developing advanced cognitive architectures is critical for enhancing the dynamics of human-avatar groups. This paper presents a reinforcement-learning-based cognitive architecture, trained via a sim-to-real approach, designed to improve synchronization in periodic motor tasks, crucial for applications in group rehabilitation and sports training. Extensive numerical validation consistently demonstrates improvements in synchronization. Theoretical derivations and numerical investigations are complemented by preliminary experiments with real participants, showing that our avatars can integrate seamlessly into human groups, often being indistinguishable from humans.
... For almost forty years, the HKB model has been studied in the context of phase transitions in human physiology. Initially, said model was derived as a phenomenological explanation 2 of the transition from anti-phase to in-phase coordination in hand movements, and also of bistable regimes (Haken et al., 1985), but it is shown to apply in many other contexts (Kelso, 2021a). The simplest model considers a degree of freedom φðtÞ that changes according to a phenomenological potential V ðφÞ defined as follows: ...
Many theoretical studies defend the existence of ongoing phase transitions in the brain dynamics that could explain its enormous plasticity to cope with the environment. However, tackling the ever-changing landscapes of brain dynamics seems a hopeless task with complex models. This paper uses a simple Haken-Kelso-Bunz (HKB) model to illustrate how phase transitions that change the number of attractors in the landscape for the relative phase between two neural assemblies can occur, helping to explain a qualitative agreement with empirical decision-making measures. Additionally, the paper discusses the possibility of interpreting this agreement with the aid of Irruption Theory (IT). Being the effect of symmetry breakings and the emergence of non-linearities in the fundamental equations, the order parameter governing phase transitions may not have a complete microscopic determination. Hence, many requirements of IT, particularly the Participation Criterion, could be fulfilled by the HKB model and its extensions. Briefly stated, triggering phase transitions in the brain activity could thus be conceived of as a consequence of actual motivations or free will participating in decision-making processes.
Resilience has traditionally been conceptualized as resisting, bouncing back from, and growing from a stressor. However, recent literature has pointed out that these are different processes with bouncing back coming closest to the literal meaning of the term resilience. To detect whether an individual demonstrates one of these three stressor-responses, different analysis strategies have been suggested. However, deeper theoretical explanations for how patterns of resistance, resilience, and growth come about, have been lacking. To address this gap, this paper proposes a coherent framework based on a dynamical systems approach. We first discuss how adapting to stressors emerges from complex interactions between multiple levels of organization within the system. These interactions unfold on different time scales: What appears as resistance on slower or macro scales may actually consist of bouncing back at micro scales that change much faster. Next, we discuss how the different trajectories that distinguish resistance, resilience, and growth can be understood through attractor dynamics. We address the fixed-point attractors, which are commonly used in the resilience literature to detect early warning signals of bifurcations following resilience losses. Moreover, we describe the implications of limit cycles and strange attractors which capture multiple pathways to adapt to stressors that can lead to growth patterns. We conclude that resisting, bouncing back from, or growing from a stressor represent distinct phenomena that can be distinguished both empirically and theoretically from a dynamical systems perspective. These distinctions may drive future development of theoretical models, empirical measurements, and theory-driven interventions.
Previous work suggests that synergistic activity among motor elements implicated in force production tasks underlies enhanced performance stability associated with visual feedback. A hallmark of synergistic activity is reciprocal compensation, that is, covariation in the states of motor elements that stabilizes critical performance variables. The present study examined if characteristics of reciprocal compensation are indicators of individuals’ capacity to respond adaptively to variations in the resolution of visual feedback about criterion performance. Twenty healthy adults (19.25 ± 1.25 years; 15 females and five males) pressed two sensors with their index fingers to produce a total target force equivalent to 20% of their maximal voluntary contraction under nine conditions that differed in the spatial resolution of real-time feedback about their performance. By combining within-trial uncontrolled manifold and sample entropy analyses, we quantified the amount and degree of irregularity (i.e., non-repetitiveness) of reciprocal compensations over time. We found a U-shaped relationship between performance stability and gain. Importantly, this relationship was moderated by the degree of irregularity of reciprocal compensation. Lower irregularity in reciprocal compensation patterns was related to individuals’ capacity to maintain (or minimize losses in) performance under changes in feedback resolution. Results invite future investigation into how interindividual variations in reciprocal compensation patterns relate to differences in control strategies supporting adaptive responses in complex, visually guided motor tasks.
In this paper, we explore the application of principles from cogni-tive science and nonlinear dynamics to the study of natural phenomena , aiming to extract new patterns and develop novel mathematical structures. Drawing on the concept of phase transitions, we outline a framework for identifying critical points in natural systems and measuring their dynamic behavior. Using tools like Recurrence Quantifica-tion Analysis (RQA) and power spectral analysis, we analyze changes in entropy and power-law behavior to predict the emergence of new structures. By integrating interdisciplinary approaches from physics, biology, and cognitive science, we propose a comprehensive methodology for understanding and modeling complex systems in nature. This paper provides a detailed roadmap for researchers to uncover deeper insights into dynamic behaviors and construct predictive models that can transform our understanding of natural phenomena.
This indispensable sourcebook covers conceptual and practical issues in research design in the field of social and personality psychology. Key experts address specific methods and areas of research, contributing to a comprehensive overview of contemporary practice. This updated and expanded second edition offers current commentary on social and personality psychology, reflecting the rapid development of this dynamic area of research over the past decade. With the help of this up-to-date text, both seasoned and beginning social psychologists will be able to explore the various tools and methods available to them in their research as they craft experiments and imagine new methodological possibilities.
The present article represents an initial attempt to offer a principled solution to a fundamental problem of movement identified by Bernstein (1967) namely, how the degrees of freedom of the motor system are regulated. Conventional views of movement control focus on motor programs or closed-loop devices and have little or nothing to say on this matter. As an appropriate conceptual framework we offer lberall and his colleagues' physical theory
of homeokinetics first elaborated for movement by Kugler, Kelso, and Turvey (1980). Homeokinetic theory characterizes biological systems as ensembles of non-linear, limit cycle oscillatory processes coupled and mutually entrained at al levels of organization. Patterns of interlimb coordination may be predicted from the properties of non-linear, limit cycle oscillators. In a set of experiments and formal demonstrations we show that cyclical, two-handed movements maintain fixed amplitude and frequency (a stable limit cycle organization) under the following conditions: (a) when brief and constantly applied load perturbations are imposed on one hand or the other, (b) regardless of the presence or absence of fixed mechanical constraints, and (c) in the face of a range of external driving frequencies from a visual source. In addition, we observe a tight phasic relationship between the hands before and after
perturbations (quantified by cross correlation techniques), a tendency of one limb to entrain the other (mutual entrainment) and that limbs cycling at different frequencies reveal non-arbitrary sub-harmonic relationships (small integer, subharmonic entrainment). In short all the above patterns of interlimb coordination fall out of a non-linear oscillator design. Discussion focuses on the compatibility of these results with past and present neurobiological work, and the theoretical insights into problems of movement offered by homeokinetic physics. Among these are, we think, the beginnings of a principled solution to the degrees of freedom problem, and the tentative claim that coordination and control are emergent consequences of dynamical interactions among non-linear, limit cycle oscillatory processes.
In many disciplines of science we deal with systems composed of many subsystems. A few examples, mainly taken from topics in this book, are listed in Fig. 1. Very often the properties of the large system can not be explained by a mear random superposition of actions of the subsystems. Quite on the contrary the subsystems behave in a well organized manner, so that the total system is in an ordered state or shows actions which one might even call purposeful. Furthermore one often observes more or less abrupt changes between disorder and order or transitions between different states of order. Thus the question arises, who are the mysterious demons who tell the subsystems in which way to behave so to create order, or, in a more scientific language, which are the principles by which order is created.
Speech is a sequence of individual sounds, each of which is produced by highly automated learned motor programs. We explore whether some of the principles utilized in limb movement control and in particular locomotion can apply to speech motor control. The different ways peripheral information can be utilized are reviewed and also the overall central organization. The possibility that some learned motor programs result from a recombination of different parts of innate motor programs is discussed at some length.