A stochastic optimized-submovement model is proposed for Pitts' law, the classic logarithmic tradeoff between the duration and spatial precision of rapid aimed movements. According to the model, an aimed movement toward a specified target region involves a primary submovement and an optional secondary corrective submovement. The submovements are assumed to be programmed such that they minimize average total movement time while maintaining a high frequency of target hits. The programming process achieves this minimization by optimally adjusting the average magnitudes and durations of noisy neuromotor force pulses used to generate the submovements. Numerous results from the literature on human motor performance may be explained in these terms. Two new experiments on rapid wrist rotations yield additional support for the stochastic optimizedsubmovement model. Experiment 1 revealed that the mean durations of primary submovements and of secondary submovements, not just average total movement times, conform to a square-root approximation of Pitts' law derived from the model. Also, the spatial endpoints of primary submovements have standard deviations that increase linearly with average primary-submovement velocity, and the average primary-submovement velocity influences the relative frequencies of secondary submovements, as predicted by the model. During Experiment 2, these results were replicated and extended under conditions in which subjects made movements without concurrent visual feedback. This replication suggests that submovement optimization may be a pervasive property of movement production. The present conceptual framework provides insights into principles of motor performance, and it links the study of physical action to research on sensation, perception, and cognition, where psychologists have been concerned for some time about the degree to which mental processes incorporate rational and normative rules. An enduring issue in the study of the human mind concerns of mathematical probability theory and statistical decision thethe rationality and optimality of the mental processes that guide ory (e.g.,

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The principal protein excreted in male rat urine, urinary alpha 2-globulin and the homologous mouse protein, major urinary protein, have been well characterized, although their functions remain unclear. Male rat urine affects the behaviour and sexual response of female rats, leading to the proposal that rodent urinary proteins are responsible for binding pheromones and their subsequent release from drying urine. Urinary alpha 2-globulin is also involved in hyaline droplet nephropathy, an important toxicological syndrome in male rats resulting from exposure to a number of industrial chemicals and characterized by the accumulation of liganded urinary alpha 2-globulin in lysosomes in the kidney, followed by the induction of renal cancer. We now report the three-dimensional structures of mouse major urinary protein (at 2.4 A resolution) and rat urinary alpha 2-globulin (at 2.8 A resolution). The results corroborate the role of these proteins in pheromone transport and elaborate the structural basis of ligand binding.

Some alternative relations between the speed and accuracy of aimed limb movements are considered. According to one relation, Pitts' law, movement time is a logarithmic function of the movement distance divided by the width of the target toward which the movement proceeds [ T = C, + C 2 log 2 (2.D/ W)], According to a second relation, discovered by Schmidt, Zelaznik, Hawkins, Frank, and Quinn (1979), movement error (deviation from the target center) is a linear function of the movement distance divided by the movement time [ W e = K(D/ T)]. Previous explanations of this second relation, based on an asymmetric impulse-variability model, are mathematically faulty and violate well-known physical principles. However, a new symmetric impulse-variability model can explain the linear relation more adequately. The latter model assumes that a limb is driven by the product of a force parameter and a time function with certain welldefined qualitative properties, including symmetry, curvilinearity, and force-time rescalabUity. In combination, these properties correctly predict the observed linear speed-accuracy trade-off for aimed movements and agree with other known aspects of movement dynamics. They may be realized in terms of underlying biomechanical (e.g., mass-spring) and neurophysiological (e.g., electromyographic) mechanisms. The symmetric impulse-variability model also provides a possible way to account for Pitts' law, unifying the logarithmic speedaccuracy trade-off with the linear trade-off.In moving a limb such as an arm from one less accurate on the average, and movements position to another, it is often necessary for having greater spatial accuracy can usually a person to make some compromise between occur only at the expense of being slower on the duration and spatial precision of the the average. Thus a speed-accuracy trade-off movement. Faster movements can usually influences movement control just as it does occur only at the expense of being spatially mental processes like perception, memory, and thought (Pachella, 1974). .Of course, there are certain limits to this The authors express their gratitude to Sylvan Korn-trade-off. It does not seem to have much, if blum for many helpful criticisms and suggestions about any, effect on movements with very low vean earlier version of this paper We also thank Richard lodty and me tempora i precision of move-SSS^^ ™nts ^n actually increase as their velocity University of Michigan's Human Performance Center increases (Newell, 1980). Nevertheless, the and at Bell Laboratories for enthusiastic discussions and trade-off between speed and spatial accuracy encouragement regarding the material presented here. j s an important phenomenon whose nature Requests for reprints should be sent to David E. h rnainr rompmienres for manv tvnes of Meyer, Human Performance Center, Department of has maj °r con S ec l u ences tor many types OI Psychology, University of Michigan, 330 Packard Road, amwxl movement. Whenever someone moves Ann Arbor, Michigan 48104.an arm to point toward some lo...

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