Time scales of adaptive behavior and motor learning in the presence of stochastic perturbations.

In this paper, the major assumptions of influential approaches to the structure of variability in practice conditions are discussed from the perspective of a generalized evolving attractor landscape model of motor learning. The efficacy of the practice condition effects is considered in relation to the theoretical influence of stochastic perturbations in models of gradient descent learning of multiple dimension landscapes. A model for motor learning is presented combining simulated annealing and stochastic resonance phenomena against the background of different time scales for adaptation and learning processes. The practical consequences of the model's assumptions for the structure of practice conditions are discussed, together with their implications for teaching and coaching.

Learning the pedalo locomotion task.

The authors examined the learning function of a multiple biomechanical degrees of freedom coordination task. Four adult participants practiced the pedalo locomotion task for 350 trials over 7 days. On the basis of the Cauchy theorem, the authors applied a movement pattern difference score that provides a measure of convergence to a fixed point as the criterion for quantifying learning. The findings showed a significant reduction of the movement pattern difference score over practice. Neither an exponential (0.11) nor a power law (0.10) function accommodated a large percentage of the variance of the pattern difference measure on individual learning functions, but the respective fits were higher, although not different, for movement time (.57, .55). Principal components analysis showed a decrease of components over practice; the analysis also showed that 3-5 components were required to accommodate 90% of the variance of the whole-body motion at the end of the final practice session. Those findings on the learning functions for movement and outcome scores are discussed in relation to the redundancy of the biomechanical system in moving to a dynamical stable fixed point in this task.

Time scales in motor learning and development.

A theoretical framework based on the concepts and tools of nonlinear dynamical systems is advanced to account for both the persistent and transitory changes traditionally shown for the learning and development of motor skills. The multiple time scales of change in task outcome over time are interpreted as originating from the system's trajectory on an evolving attractor landscape. Different bifurcations between attractor organizations and transient phenomena can lead to exponential, power law, or S-shaped learning curves. This unified dynamical account of the functions and time scales in motor learning and development offers several new hypotheses for future research on the nature of change in learning theory.

Non-linear mechanisms in the brain.

Non-linear dynamical models of brain activity can describe the spontaneous emergence of large-scale coherent structures both in a temporal and spatial domain. We discuss a number of discrete time dynamical neuron models that illustrate some of the mechanisms involved. Of special interest is the phenomenon of spatio-temporal stochastic resonance in which coherent structures emerge as a result of the interaction of the neuronal system with external noise at a given level punitive data. We then discuss the general role of stochastic noise in brain dynamics and how similar concepts can be studied in the context of networks of connected brains on the Internet.

The Sequential Structure of Movement Outcome in Learning a Discrete Timing Task.

The sequential structure of discrete movement outcomes in an elbow-flexion movement task was examined with a crossed design of 2 movement-time (125 and 500 ms) and 2 range-of-motion (5° and 20°) conditions over sets of 200 trials of practice. Traditional analyses of error score techniques, time-series analyses of the quantitative raw and differenced data, and a symbolic dynamic analysis of qualitative events arising from the data were conducted. The differenced data revealed a consistent order over 3-trial strings that was more apparent with larger steps in the data scores, but quantitative time-series and symbolic dynamic analyses of the raw movement-time data showed weaker relations. There were a few patterns of structure evident in the raw data time-series that were a function of the movement condition and the skill level of the subject. The analyses of the movement-time scores revealed that, in learning the discrete timing task, there is more order apparent in the intrinsic frame of reference of the difference scores than in the extrinsic frame of reference.

Localized measures for nonstationary time-series of physiological data.

We will discuss localized measures related to the concepts of dimension, Lyapunove exponents (entropy), and recurrence diagrams. We stress the relevance of localized events and coincidences in physiological time series that often are lost when statistical averaging methods are applied. We suggest event-based statistics as an alternative to spectral or averaged-based statistics. The use of wavelets bases for characterizing localized structures is discussed as a potential alternative to Fourier-based analysis. Finally we mention how local domains in state space could be applied as triggers for external stimuli and thereby improve the statistics of ERP recordings.

Bifurcations and intrinsic chaotic and 1/f dynamics in an isolated perfused rat heart.

The application of the theory of chaotic dynamical systems has gradually evolved from computer simulations to assessment of erratic behavior of physical, chemical, and biological systems. Whereas physical and chemical systems lend themselves to fairly good experimental control, biologic systems, because of their inherent complexity, are limited in this respect. This has not, however, prevented a number of investigators from attempting to understand many biologic periodicities. This has been especially true regarding cardiac dynamics: the spontaneous beating of coupled and non-coupled cardiac pacemakers provides a convenient comparison to the dynamics of oscillating systems of the physical sciences. One potentially important hypothesis regarding cardiac dynamics put forth by Goldberger and colleagues, is that normal heart beat fluctuations are chaotic, and are characterized by a 1/f-like power spectrum. To evaluate these conjectures, we studied the heart beat intervals (R wave to R wave of the electrocardiogram) of isolated, perfused rat hearts and their response to a variety of external perturbations. The results indicate bifurcations between complex patterns, states with positive dynamical entropies, and low values of fractal dimensions frequently seen in physical, chemical and cellular systems, as well as power law scaling of the spectrum. Additionally, these dynamics can be modeled by a simple, discrete map, which has been used to describe the dynamics of the Belousov-Zhabotinsky reaction.