Bruce A. Kay

Distinguishing the noise and attractor strength of coordinated limb movements using recurrence analysis

The variability of coupled rhythmic limb movements is assumed to be a consequence of the strength of a movement’s attractor dynamic and a constant stochastic noise process that continuously perturbs the movement system away from this dynamic. Recently, it has been suggested that the nonlinear technique of recurrence analysis can be used to index the effects of noise and attractor strength on movement variability. To test this, three experiments were conducted in which the attractor strength of bimanual wrist-pendulum movements (using coordination mode, movement frequency and detuning), as well as the magnitude of stochastic perturbations affecting the variability of these movements (using a temporally fluctuating visual metronome) was manipulated. The results of these experiments demonstrate that recurrence analysis can index parametric changes in the attractor strength of coupled rhythmic limb movements and the magnitude of metronome induced stochastic perturbations independently. The results of Experiments 1 and 2 also support the claim that differences between the variability of inphase and antiphase coordination, and between slow and fast movement frequencies are due to differences in attractor strength. In contrast to the standard assumption that the noise that characterizes interlimb coordination remains constant for different magnitudes of detuning (Δ ω) the results of Experiment 3 suggest that the magnitude of noise increases with increases in |Δ ω|.

Comparing the attractor strength of intra- and interpersonal interlimb coordination using cross-recurrence analysis

Previous research has demonstrated that intra- and interpersonal rhythmic interlimb coordination are both constrained by the self-organizing entrainment process of coupled oscillators. Despite intra- and interpersonal coordination exhibiting the same stable macroscopic movement patterns the variability of the coordination is typically found to be much greater for inter- compared to intrapersonal coordination. Researchers have assumed that this is due to the interpersonal visual-motor coupling producing a weaker attractor dynamic than the intrapersonal neuromuscular coupling. To determine whether this assumption is true, two experiments were conducted in which pairs of participants coordinated hand-held pendulums swung about the wrist, either intra- and interpersonally. Using the cross-recurrence statistics of percent recurrence and maxline to independently index the level of noise and the attractor strength of the coordination, respectively, the results confirmed that the attractor strength was significantly weaker for inter- compared to intrapersonal coordination and that a similar magnitude of noise underlies both.

Environmental coupling modulates the attractors of rhythmic coordination

A simple instance of coupling behavior to the environment is oscillating the hands in pace with metronome beats. This environmental coupling can be weaker (1 beat per cycle) or stronger (2 beats per cycle). The authors examined whether strength of environmental coupling enhanced the stability of in-phase bimanual coordination. Detuning by manipulanda that produced different left and right eigenfrequencies shifted the relative phase angle from 0 degrees, with the size of the shift larger for higher movement frequencies. Stronger environmental coupling was found to decrease this relative-phase shift, with accompanying increase and reduction, respectively, in recurrence quantification measures related to coordination stability and coordination noise. Stronger environmental coupling also increased oscillation amplitude. Results are considered from the perspective of parametric stabilization.

Effects of intention and learning on attention to information in dynamic touch.

The current research distinguishes two types of attention shifts: those entailed by perceptual learning and those entailed by changing intention. In perceptual learning, participants given feedback have been shown to gradually shift attention toward the optimal (i.e., specifying) information variable for the task. A shift in variable use is also expected when intention changes, because an intention to perceive some property entails attunement to information about that property. We compared the effects of feedback and intention in a dynamic (kinesthetic) touch task by representing both as changes of locus in an information space of inertial variables. Participants wielded variously sized, unseen, rectangular parallelepipeds and made length or width judgments about them. When given feedback, participants made gradual attentional shifts toward the optimal variable, which demonstrates the education of attention. When asked to report a new property, participants made large attentional jumps to the ballpark of the optimal variable for the new property. Exploratory movements were measured on 6 participants and were found to differ as a function of intention and to change with learning.

Spontaneous Interentity Coordination in a Dissipative Structure

ABSTRACT Humans and other creatures display remarkable interorganism coordination. For ecological theorists, interorganism coordination poses a challenge because it appears to be an especially “representation-hungry” phenomenon (Clark, 1999). Ecological researchers have proposed that interorganism coordination arises from fundamental laws of pattern formation and synchronization. A key example in support of the ecological approach to coordination is the phase locking of 2 or more weakly coupled metronomes. Here we provide a complementary example of interentity coordination in a system that is more closely analogous to living systems. We show that two self-organizing dissipative structures, coupled in a single electrical field, spontaneously exhibit fairly complex motion coordination. Further, the degree of coordination predicts the rate of entropy production for the system as a whole. We suggest that the complex behavior of motion coordination fulfills a rudimentary end-directedness of the system: evolve to states that create higher rates of entropy production.

Effects of visual and auditory guidance on bimanual coordination complexity

Perceptual guidance of movement with simple visual or temporal information can facilitate performance of difficult coordination patterns. Guidance may override coordination constraints that usually limit stability of bimanual coordination to only in-phase and anti-phase. Movement dynamics, however, might not have the same characteristics with and without perceptual guidance. Do visual and auditory guidance produce qualitatively different dynamical organization of movement? An anti-phase wrist flexion and extension coordination task was performed under no specific perceptual guidance, under temporal guidance with a metronome, and under visual guidance with a Lissajous plot. For the time series of amplitudes, periods and relative phases, temporal correlations were measured with Detrended Fluctuation Analysis and complexity levels were measured with multiscale entropy. Temporal correlations of amplitudes and relative phases deviated from the typical 1/f variation towards more random variation under visual guidance. The same was observed for the series of periods under temporal guidance. Complexity levels for all time series were lower in visual guidance, but higher for periods under temporal guidance. Perceptual simplification of the tasks goal may produce enhancement of performance, but it is accompanied by changes in the details of movement organization that may be relevant to explain dependence and poor retention after practice under guidance.

Dissipative structures, machines, and organisms: A perspective

Self-organization in nonequilibrium systems resulting in the formation of dissipative structures has been studied in a variety of systems, most prominently in chemical systems. We present a study of a voltage-driven dissipative structure consisting of conducting beads immersed in a viscous medium of oil. In this simple system, we observed remarkably complex organism-like behavior. The dissipative structure consists of a tree structure that spontaneously forms and moves like a worm and exhibits many features characteristic of living organisms. The complex motion of the beads driven by the applied field, the dipole-dipole interaction between the beads, and the hydrodynamic flow of the viscous medium result in a time evolution of the tree structure towards states of lower resistance or higher dissipation and thus higher rates of entropy production. The resulting end-directed evolution manifests as the tree moving to locations seeking higher current, the current that sustains its structure and dynamics. The study of end-directed evolution in the dissipative structure gives us a means to distinguish the fundamental difference between machines and organisms and opens a path for the formulation of physics of organisms.

Age-Related Differences in Postural and Goal-Directed Movements During Medial–Lateral Rhythmic Stepping

Lateral stability and weight transfer are important for successful stepping and are associated with falls in older adults (OAs). This study assessed the influence of step pacing frequency during medial-lateral stepping in place on body center of mass and lower limb movement in young adults, middle-aged adults, and OAs. Medial-lateral center of mass and stepping limb motion and lower limb loading data were collected. Center of mass motion decreased with increasing pacing frequency and increased to a lesser extent with decreasing pacing frequency. Step length was relatively resistant to changes in pacing frequency. OAs exhibited reductions in whole body and stepping motion compared with younger adults. OAs exhibited greater support limb loading. OAs adapt both postural and stepping strategies to successfully step under time-critical conditions.

End-Directedness and Context in Nonliving Dissipative Systems

The extensive study of thermodynamically open, non-equilibrium systems in the context of self-organization has revealed that biological phenomena such as clocking, pattern formation, and chemotaxis may also be found more generally in non-living (e.g., chemical) systems. We show that another fundamental biological phenomenon, end-directedness, also appears in non-living systems. We present a non-living dissipative system that exhibits end-directed processes in seeking and drawing the energy needed to form and maintain its structure. The system can become sensitive to its context, defined as gradients other than its primary energy source, and use context to coordinate with its environment. Implications for biological systems will be discussed.