Practicing Elements Versus Practicing Coordination: Changes in the Structure of Variance

ABSTRACT

The authors explored effects of practice of a 2-finger accurate force production task on components of finger force variance quantified within the uncontrolled manifold (UCM) hypothesis, V_UCM, that had no effect on total force and V_ORT that affected total force. A variable task with graded instability was designed to encourage use of variable solutions. Two groups of subjects (n = 9 each) were tested prior to a 1.5-hr practice session, after the session, and 2 weeks later (retention test). Group 1 practiced 1 finger at a time, while Group 2 practiced the task with 2 fingers (index and middle) pressing together. Both groups showed comparable improvements in the performance indices. Both groups showed a decrease in V_ORT, while only Group 2 showed an increase in V_UCM. These effects persisted during the retention test. The results show that practicing elements and practicing redundant groups of elements may lead to similar changes in performance (i.e., in the variability of the total force produced by the set of fingers), accompanied by dramatically different changes in the structure of variance: A drop in V_UCM after the single-finger practice and an increase following the 2-finger practice. The strong retention effects promise applications of the method to rehabilitation.     

Riemannian Newton and trust-region algorithms for analytic rotation in exploratory factor analysis

In exploratory factor analysis, latent factors and factor loadings are seldom interpretable until analytic rotation is performed. Typically, the rotation problem is solved by numerically searching for an element in the manifold of orthogonal or oblique rotation matrices such that the rotated factor loadings minimize a pre-specified complexity function. The widely used gradient projection (GP) algorithm, although simple to program and able to deal with both orthogonal and oblique rotation, is found to suffer from slow convergence when the number of manifest variables and/or the number of latent factors is large. The present work examines the effectiveness of two Riemannian second-order algorithms, which respectively generalize the well-established truncated Newton and trust-region strategies for unconstrained optimization in Euclidean spaces, in solving the rotation problem. When approaching a local minimum, the second-order algorithms usually converge superlinearly or even quadratically, better than first-order algorithms that only converge linearly. It is further observed in Monte Carlo studies that, compared to the GP algorithm, the Riemannian truncated Newton and trust-region algorithms require not only much fewer iterations but also much less processing time to meet the same convergence criterion, especially in the case of oblique rotation.     

Changes in motor synergies for tracking movement and responses to perturbations depend on task-irrelevant dimension constraints

We investigated the changes in the motor synergies of target-tracking movements of hands and the responses to perturbation when the dimensionalities of target positions were changed. We used uncontrolled manifold (UCM) analyses to quantify the motor synergies. The target was changed from one to two dimensions, and the direction orthogonal to the movement direction was switched from task-irrelevant directions to task-relevant directions. The movement direction was task-relevant in both task conditions. Hence, we evaluated the effects of constraints on the redundant dimensions on movement tracking. Moreover, we could compare the two types of responses to the same directional perturbations in one- and two-dimensional target tasks. In the one-dimensional target task, the perturbation along the movement direction and the orthogonal direction were task-relevant and -irrelevant perturbations, respectively. In the two-dimensional target task, the both perturbations were task-relevant perturbations. The results of the experiments showed that the variabilities of the hand positions in the two-dimensional target-tracking task decreased, but the variances of the joint angles did not significantly change. For the task-irrelevant perturbations, the variances of the joint angles within the UCM that did not affect hand position (UCM component) increased. For the task-relevant perturbations, the UCM component tended to increase when the available UCM was large. These results suggest that humans discriminate whether the perturbations were task-relevant or -irrelevant and then adjust the responses of the joints by utilizing the available UCM.     

Application of local linear embedding to nonlinear exploratory latent structure analysis

In this paper we discuss the use of a recent dimension reduction technique called Locally Linear Embedding, introduced by Roweis and Saul, for performing an exploratory latent structure analysis. The coordinate variables from the locally linear embedding describing the manifold on which the data reside serve as the latent variable scores. We propose the use of semiparametric penalized spline methods for reconstruction of the manifold equations that approximate the data space. We also discuss a crossvalidation strategy that can guide in selecting an appropriate number of latent variables. Synthetic as well as real data sets are used to illustrate the proposed approach. A nonlinear latent structure representation of a data set also serves as a data visualization tool.     

Diminished joint coordination with aging leads to more variable hand paths

Differences in joint coordination between arms and due to aging were studied in healthy young and older adults reaching to either a fixed, central target or to the same target when it could unexpectedly change location after reach initiation. Joint coordination was investigated by artificially removing the covariation of each joint’s motions with other joints’ motions. Uncontrolled manifold analysis was used to partition joint configuration variance into variance reflecting motor abundance (V_UCM) and variance causing hand path variability (V_ORT). The extent to which V_ORT, related to the consistency of the hand path, increased after removing a joint’s covariation indicated the strength of its coordination with other joints. Young adults exhibited stronger indices of joint coordination, evidenced by a larger increase in V_ORT after removing joint covariation than for older adults. This effect was more striking for the dominant right compared to the left arm for young adults, but not for older adults, especially with target uncertainty. The results indicate that interjoint coordination in young adults leads to less hand path variability compared to older adults.     

Embodied simulation: From neurons to phenomenal experience

The same neural structures involved in the unconscious modeling of our acting body in space also contribute to our awareness of the lived body and of the objects that the world contains. Neuroscientific research also shows that there are neural mechanisms mediating between the multi-level personal experience we entertain of our lived body, and the implicit certainties we simultaneously hold about others. Such personal and body-related experiential knowledge enables us to understand the actions performed by others, and to directly decode the emotions and sensations they experience. A common functional mechanism is at the basis of both body awareness and basic forms of social understanding: embodied simulation. It will be shown that the present proposal is consistent with some of the perspectives offered by phenomenology.     

Goal equivalent manifold analysis of task performance in non-specific LBP and healthy subjects during repetitive trunk movement: Effect of load,velocity, symmetry

Motor abundance allows reliability of motor performance despite its variability. The nature of this variability provides important information on the flexibility of control strategies. This feature of control may be affected by low back pain (LPB) and trunk flexion/extension conditions.Goal equivalent manifold (GEM) analysis was used to quantify the ability to exploit motor abundance during repeated trunk flexion/extension in healthy individuals and people with chronic non-specific LBP (CNSLBP).Kinematic data were collected from 22 healthy volunteers and 22 CNSLBP patients during metronomically timed, repeated trunk flexion/extension in three conditions of symmetry, velocity, and loading; each at two levels. A goal function for the task was defined as maintaining a constant movement time at each cycle. Given the GEM, flexibility index and performance index were calculated respectively as amounts of goal-equivalent variability and the ratio of goal-equivalent to non-goal-equivalent variability.CNSLBP group was as similar as healthy individuals in both flexibility index (p = 0.41) and performance index (p = 0.24). Performance index was higher in asymmetric (p < 0.001), high velocity (p < 0.001), and loaded (p = 0.006) conditions.Performance and flexibility in using motor abundance were influenced by repeated trunk flexion/extension conditions. However, these measures were not significantly affected by CNSLBP.     

Synergies and Motor Equivalence in Voluntary Sway Tasks: The Effects of Visual and Mechanical Constraints

The authors used two analyses developed within the framework of the uncontrolled manifold hypothesis to quantify multimuscle synergies during voluntary body sway: analysis of intertrial variance and analysis of motor equivalence with respect to the center of pressure (COP) trajectory. Participants performed voluntary sway tasks in the anteroposterior direction at 0.33 and 0.66 Hz. Muscle groups were identified in the space of muscle activations and used as elemental variables in the synergy analyses. Changing mechanical and vision feedback–based constraints led to significant changes in indices of sway performance such as COP deviations in the uninstructed, mediolateral direction and indices of spontaneous postural sway. In contrast, there were no significant effects on synergy indices. These findings show that the neural control of performance and of its stability may involve different control variables and neurophysiological structures. There were strong correlations between the indices of motor equivalence and those computed using the intercycle variance analysis. This result is potentially important for studies of patients with movement disorders who may be unable to perform multiple trials (cycles) at any given task, making analysis of motor equivalence of single trials a viable alternative to explore changes in stability of actions.     

Uncontrolled manifold analysis of joint angle variability during table tennis forehand

This study was conducted with the objective of evaluating the variance structure of the trunk and racket arm joint angles in table tennis topspin forehand using the uncontrolled manifold (UCM) approach, regarding racket orientation as the task variable. Nine advanced and eight intermediate male collegiate table tennis players performed the topspin strokes against backspin balls. The trunk, upper limb, and racket were modeled as six rigid-link segments with a total of 16 rotation degrees of freedom. The UCM analysis was conducted using 30 trial datasets per participant to quantify the degree of redundancy exploitation needed to stabilize the vertical and horizontal angles of the racket. Irrespective of the performance level, the variance of the joint angle vector increased towards ball impact. The degree of redundancy exploitation increased towards ball impact. As a result, the variability of the racket angles was minimal at impact. Both groups of players used the relative movement between the racket and the hand to stabilize the racket angles at ball impact. The variance of the joint angle vector that affected the vertical racket face angle at ball impact was significantly smaller for advanced players than for intermediate players, and the degree of redundancy exploitation to stabilize that angle at impact tended to be larger for the advanced players. The ability to use the redundancy of the joint configuration to stabilize the vertical racket face angle at impact may be a critical factor that affects performance level.