Controlling variability

In human motor control, there is uncertainty in both estimation of initial sensory state and prediction of the outcome of motor commands. With practice, increasing precision can often be achieved, but such precision incurs costs in time, effort, and neural resources. Therefore, motor planning must account for variability, uncertainty, and noise, not just at the endpoint of movement but throughout the movement. The author presents a mathematical basis for understanding the time course of uncertainty during movement. He shows that it is possible to achieve accurate control of the endpoint of a movement even with highly inaccurate and variable controllers. The results provide a first step toward a theory of optimal control for variable, uncertain, and noisy systems that must nevertheless accomplish real-world tasks reliably.     

Cognitive variability

Children's thinking is highly variable at every level of analysis, from neural and associative levels to the level of strategies, theories, and other aspects of high-level cognition. This variability exists within people as well as between them; individual children often rely on different strategies or representations on closely related problems presented close in time. Recognizing such variability can help us both describe development more accurately and better explain how cognitive change occurs.     

Effects of practice on variability, effects of variability on transfer

Five experiments examined how practice early in skill acquisition affected variability and accuracy during skill retention (Experiments 1-5) and skill transfer (Experiments 3, 4, 5). Lag constraints required that each path from apex to base of a computer-generated pyramid display differ from some number (the lag) of immediately prior paths. Location constraints specified end points at which paths must exit the pyramid. In all experiments, an early optimal period for acquiring a variability level was identified. Both low and high levels of variability were sustained during retention; high levels facilitated transfer. The results suggest that (a) early practice that requires high variability sensitizes learners to changes in condition and (b) such perception-performance links facilitate transfer by activating appropriate alternative strategies/schema or initiating their construction.     

Entropy and variability discrimination

Two experiments examined college students' discrimination of complex visual displays that involved different degrees of variability or "entropy." Displays depicted 16 black and white line drawings of various types (e.g., a brain, a clock, a hand); the participants were required to classify a display in terms of its variability (e.g., a low-variability display contains many identical items, whereas a high-variability display contains few identical items). The participants' accuracy and reaction time scores on a 2-alternative forced-choice discrimination disclosed that people can and do use entropy to classify different levels of visual display variability. Individuals differed in their use of absolute rather than relative entropy.     

Language localization and variability

Language localization data from 11 neurosurgical patients undergoing cortical resection for medically intractable focal epilepsy were obtained by mapping with bipolar electrical stimulation at current levels below sensory and after-discharge thresholds, during an object-naming task. The topographical extent of language cortex in an individual subject can be wider than that proposed in the classic maps. Within this zone, language is discretely localized, with different sites variably committed to language as measured by the naming function. The naming data from the left cortex of eight patients, all left-brain-dominant, were pooled to determine the variability within the primary language zone. Only a narrow band of posterior, inferior frontal lobe, immediately anterior to motor strip, showed involvement in all of the patients in whom it was sampled. This is a motor speech area; it constitutes only a small portion of the frontal language area. Other infero-frontal, parietal, and postero-temporal sites showed considerable variability, with naming involvement in only 50–80% of the patients sampled. There is a suggestion that some of these patterns of language localization may correlate with poorer verbal abilities. Data were also obtained on language localization in the left insula in a patient who was left-hemisphere-dominant for language. Mapping of the right hemisphere in a left-brain-dominant patient demonstrated no naming function. Mapping of the right hemisphere in one and the left hemisphere in another patient, both of whom were right-hemisphere-dominant for language, suggests more diffuse language representation with right hemisphere dominance.     

Bilingual corpus callosum variability

Magnetic resonance imaging was used to produce midsagittal images of the corpus callosum of 19 right-handed adult male and female subjects. The preliminary findings of this study indicate that significant adaptation in the anterior midbody of the corpus callosum has occurred to accommodate multiple language capacity in bilingual individuals compared to monolingual individuals. The main interpretation of this finding is that the precentral gyrus is involved in bilingual faculty adaptation assuming a role consistent with the somatotopical input to areas dedicated to the mouth, and input to association tracts connecting the premotor and supplementary motor cortices. This paper discusses possible implications to neuroscientists, second language educators, and their students.     

Reinforcing saccadic amplitude variability

Saccadic endpoint variability is often viewed as the outcome of neural noise occurring during sensorimotor processing. However, part of this variability might result from operant learning. We tested this hypothesis by reinforcing dispersions of saccadic amplitude distributions, while maintaining constant their medians. In a first experiment we reinforced the least frequent saccadic amplitudes to increase variability, and then reinforced the central part of the amplitude distributions to reduce variability. The target was placed at a constant distance from the fovea after the saccade to maintain the postsaccadic visual signal constant and an auditory reinforcement was delivered depending on saccadic amplitude. The second experiment tested the effects of the contingency. We reinforced high levels of variability in 4 participants, whereas 4 other participants were assigned to a yoked control group. On average, saccadic amplitude standard deviations were doubled while the medians remained mostly unchanged in the experimental participants in both experiments, and variability returned to baseline level when low variability was reinforced. In the control group no consistent changes in amplitude distributions were observed. These results, showing that variability can be reinforced, challenge the idea of a stochastic neural noise. We instead propose that selection processes constrain saccadic amplitude distributions.     

Focus on variability: New tools to study intra-individual variability in developmental data

In accordance with dynamic systems theory, we assume that variability is an important developmental phenomenon. However, the standard methodological toolkit of the developmental psychologist offers few instruments for the study of variability. In this article we will present several new methods that are especially useful for visualizing and describing intra-individual variability in individual time-serial data of repeated observations. In order to illustrate these methods, we apply them to data of early language development. After reviewing the common techniques and measures, we present new methods that show variability in developmental time-series data: the moving min–max graph, and the progmax–regmin graph. In addition, we demonstrate a technique that is able to detect sudden increases of variability: the critical frequency method. Also, we propose a technique that is based on a central assumption of the measurement-error-hypothesis: namely the symmetric distribution of error. Finally, as traditional statistical techniques have little to offer in testing variability hypotheses, we examine the possibilities that are provided by random sampling techniques. Our aim with the present discussion of variability and the demonstration of some simple yet illustrative techniques is to help researchers focus on rich additional sources of information that will lead to more interesting hypotheses and more powerful testing procedures, adapted to the unique nature of developmental data.     

The effect of external perturbations on variability in joint coupling and single joint variability

This paper explores the effect of goal-oriented external perturbations created by elastic tubes attached to the hip and ankles on lower limb joint variability and hip–knee and knee–ankle coordination variability during running. Kinematics of ten healthy male runners were analysed prior to and following a 7-week tube running intervention while running with and one without this constraint. The training intervention was based on variable training aspects to increase within-movement variability and adaptability of the running pattern. To analyse the effects of the tubes on the running pattern, the phase plot vector length deviation (i.e., the standard deviation of the phase plot vector length) for the within-joint variability and the continuous relative phase variability for the joint coupling variability were calculated. Results revealed acute increases of variability in both parameters. However, after the intervention, variability of the tube running situation returned to normal for all couplings and joints except the knee. No transfer effects to normal running were observed. This suggests very rapid adaptations to such perturbations. In the long-term, it may ask for more or different variations.     

Stability and variability in extinction

Some studies have found that extinction leaves response structures unaltered; others have found that response variability is increased. Responding by Long-Evans rats was extinguished after 3 schedules. In one, reinforcement depended on repetitions of a particular response sequence across 3 operanda. In another, sequences were reinforced only if they varied. In the third, reinforcement was yoked: not contingent upon repetitions or variations. In all cases, rare sequences increased during extinction--variability increased--but the ordering of sequence probabilities was generally unchanged, the most common sequences during reinforcement continuing to be most frequent in extinction. The rats' combination of generally doing what worked before but occasionally doing something very different may maximize the possibility of reinforcement from a previously bountiful source while providing necessary variations for new learning.