Faculty Bibliography

Coordinate systems for movement planning are comprised of an anchor point (e.g., retinocentric coordinates) and a representation (encoding) of the desired movement. One of two representations is often assumed: a final-position code describing desired limb endpoint position and a vector code describing movement direction and extent. The existence of movement-planning systems using both representations is controversial. In our experiments, participants completed reaches grouped by target location (providing practice for a final-position code) and the same reaches grouped by movement vector (providing vector-code practice). Target-grouped reaches resulted in the isotropic (circular) distribution of errors predicted for position-coded reaches. The identical reaches grouped by vector resulted in error ellipses aligned with the reach direction, as predicted for vector-coded reaches. Manipulating only recent movement history to provide better learning for one or the other movement code, we provide definitive evidence that both movement representations are used in the identical task.

We examine the possibility that sensory and motor adaptation may be induced via a sinusoidally incremented perturbation. This sinewave adaptation method provides superior data for fitting a parametric model than when using the standard step-function method of perturbation, due to the relative difficulty of fitting a decaying exponential vs. a sinusoid. Using both experimental data and simulations, we demonstrate the difficulty of detecting the presence of motor adaptation using a step-function perturbation, compared to detecting motor adaptation using our sinewave perturbation method.

In the study of visual-motor control, perhaps the most familiar findings involve adaptation to externally imposed movement errors. Theories of visual-motor adaptation based on optimal information processing suppose that the nervous system identifies the sources of errors to effect the most efficient adaptive response. We report two experiments using a novel perturbation based on stimulating a visually induced reflex in the reaching arm. Unlike adaptation to an external force, our method induces a perturbing reflex within the motor system itself, i.e., perturbing forces are self-generated. This novel method allows a test of the theory that error source information is used to generate an optimal adaptive response. If the self-generated source of the visually induced reflex perturbation is identified, the optimal response will be via reflex gain control. If the source is not identified, a compensatory force should be generated to counteract the reflex. Gain control is the optimal response to reflex perturbation, both because energy cost and movement errors are minimized. Energy is conserved because neither reflex-induced nor compensatory forces are generated. Precision is maximized because endpoint variance is proportional to force production. We find evidence against source-identified adaptation in both experiments, suggesting that sensory-motor information processing is not always optimal.

We analyze the problem of obstacle avoidance from a Bayesian decision-theoretic perspective using an experimental task in which reaches around a virtual obstacle were made toward targets on an upright monitor. Subjects received monetary rewards for touching the target and incurred losses for accidentally touching the intervening obstacle. The locations of target-obstacle pairs within the workspace were varied from trial to trial. We compared human performance to that of a Bayesian ideal movement planner (who chooses motor strategies maximizing expected gain) using the Dominance Test employed in Hudson et al. (2007). The ideal movement planner suffers from the same sources of noise as the human, but selects movement plans that maximize expected gain in the presence of that noise. We find good agreement between the predictions of the model and actual performance in most but not all experimental conditions.

When movement outcome differs consistently from the intended movement, errors are used to correct subsequent movements (e.g., adaptation to displacing prisms or force fields) by updating an internal model of motor and/or sensory systems. Here, we examine changes to an internal model of the motor system under changes in the variance structure of movement errors lacking an overall bias. We introduced a horizontal visuomotor perturbation to change the statistical distribution of movement errors anisotropically, while monetary gains/losses were awarded based on movement outcomes. We derive predictions for simulated movement planners, each differing in its internal model of the motor system. We find that humans optimally respond to the overall change in error magnitude, but ignore the anisotropy of the error distribution. Through comparison with simulated movement planners, we found that aimpoints corresponded quantitatively to an ideal movement planner that updates a strictly isotropic (circular) internal model of the error distribution. Aimpoints were planned in a manner that ignored the direction-dependence of error magnitudes, despite the continuous availability of unambiguous information regarding the anisotropic distribution of actual motor errors.

Although horizontal binocular retinal disparity between images in the two eyes resulting from their different views of the world has long been the centerpiece for understanding the unique characteristics of stereovision, it does not suffice to explain many binocular phenomena. Binocular depth contrast (BDC), the induction of an appearance of visual pitch in a centrally located line by pitched-from-vertical flanking lines, has particularly been the subject of a good deal of attention in this regard. In the present article, we show that BDC does not cross the median plane but is restricted to the side of the visual field containing a unilateral inducer. These results cannot be explained by the use of retinal disparity alone or in combination with any additional factors or processes previously suggested to account for stereovision. We present a two-channel three-stage neuromathematical model that accounts quantitatively for present and previous BDC results and also accounts for a large number of the most prominent features of binocular pitch perception: Stage 1 of the differencing channel obtains the difference between the retinal orientations of the images in the two eyes separately for the inducer and the test line; stage 1 of the summing channel obtains the corresponding sums. Signals from inducer and test stimuli are combined linearly in each channel in stage 2, and in stage 3 the outputs from the two channels are combined along with a bias signal from the body-referenced mechanism to yield ', the model's prediction for the perception of pitch.

Motor control requires the generation of a precise temporal sequence of control signals sent to the skeletal musculature. We describe an experiment that, for good performance, requires human subjects to plan movements taking into account uncertainty in their movement duration and the increase in that uncertainty with increasing movement duration. We do this by rewarding movements performed within a specified time window, and penalizing slower movements in some conditions and faster movements in others. Our results indicate that subjects compensated for their natural duration-dependent temporal uncertainty as well as an overall increase in temporal uncertainty that was imposed experimentally. Their compensation for temporal uncertainty, both the natural duration-dependent and imposed overall components, was nearly optimal in the sense of maximizing expected gain in the task. The motor system is able to model its temporal uncertainty and compensate for that uncertainty so as to optimize the consequences of movement.

We examined how subjects plan speeded reaching movements when the precise target of the movement is not known at movement onset. Before each reach, subjects were given only a probability distribution on possible target positions. Only after completing part of the movement did the actual target appear. In separate experiments we varied the location of the mode and the scale of the prior distribution for possible targets. In both cases we found that subjects made use of prior probability information when planning reaches. We also devised two tests (Composite Benefit and Row Dominance tests) to determine whether subjects' performance met necessary conditions for optimality (defined as maximizing expected gain). We could not reject the hypothesis of optimality in the experiment where we varied the mode of the prior, but departures from optimality were found in response to changes in the scale of prior distributions.

Statistical decision theory suggests that choosing an ideal action requires taking several factors into account: (1) prior knowledge of the probability of various world states, (2) sensory information concerning the world state, (3) the probability of outcomes given a choice of action, and (4) the loss or gain associated with those outcomes. In previous work, we found that, in many circumstances, humans act like ideal decision makers in planning a reaching movement. They select a movement aim point that maximizes expected gain, thus taking into account outcome uncertainty (motor noise) and the consequences of their actions. Here, we ask whether humans can optimally combine prior knowledge and uncertain sensory information in planning a reach. Subjects rapidly pointed at unseen targets, indicated with dots drawn from a distribution centered on the invisible target location. Target location had a prior distribution, the form of which was known to the subject. We varied the number of dots and hence target spatial uncertainty. An analysis of the sources of uncertainty impacting performance in this task indicated that the optimal strategy was to aim between the mean of the prior (the screen center) and the mean stimulus location (centroid of the dot cloud). With increased target location uncertainty, the aim point should have moved closer to the prior. Subjects used near-optimal strategies, combining stimulus uncertainty and prior information appropriately. Observer behavior was well modeled as having three additional sources of inefficiency originating in the motor system, calculation of centroid location, and calculation of aim points.

Earlier work described the presence of a significant connection between an individual's ability to disregard distracting aspects of a visual field in the classical rod-and-frame test (RFT), in which a subject is required to set a rod so that it will appear vertical in the presence of a square frame that is roll tilted from vertical, and in paper-and-pencil tests, in which the subject is required to find a hidden figure embedded in a more complex figure (the Embedded Figures Test [EFT]; see, e.g., Witkin, Dyk, Faterson, Goodenough, & Karp, 1962; Witkin et al., 1954; Witkin, Oltman, Raskin, & Karp, 1971). This has led to a belief in the existence of a bipolar dimension of cognitive style that is utilized in such disembedding tasks--namely, the extent to which an individual is dependent on or independent from the influence of a distracting visual field. The influence of an inducing visual field on the perception of elevation measured by the setting of a visual target to appear at eye level (the visually perceived eye level [VPEL] discrimination) has also been found to be correlated with the RFT. We have thus explored the possible involvement of the dependence/independence cognitive style on the VPEL discrimination. Measurements were made on each of 18 subjects (9 of them female, 9 male) setting a small target to the VPEL in the presence of a pitched visual field across a range of six pitches from -30 degrees (topbackward) to +20 degrees (topforward) and on each of three tests generally recognized as tests of cognitive spatial abilities: the EFT, the Gestalt Completion Test, and the Snowy Pictures Test (SPT). Although there were significant pairwise correlations relating performance on the three cognitive tests (+.73, +.48, and +.71), the correlation of each of these three with the slope of the VPEL-versus-pitch function was not significant, as it was with the slope of the perception of visual pitch of the field (PVP)-versus-pitch function. VPEL, PVP, and a cognitive factor separated into three essentially independent factors in a multiple-factor analysis, with the three cognitive tests clustering at the cognitive factor, and with no significant loading on either of the other two factors. From the above considerations and a multiple-factor analytic treatment including additional results from this and other laboratories, we conclude that the cognitive-processing style held to be involved in the performance on the EFT and the perception of vertical as measured by the RFT is not general for egocentric space perception; it does not involve the perception of elevation.