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Schweighofer N., Doya K., Kawato M. Electrophysiological properties of inferior olive neurons: a compartmental model. J Neurophysiol. 82:1999;804-817. A detailed biophysical model of an inferior olive neuron was developed. The model comprises the soma and the dentritic compartments, and is based on known spatial distributions of gap junctions and diverse ionic conductances. The model reproduced many peculiar characteristics found in electrophysiological experiments in vitro. Most surprisingly, it showed that electrical junctions have desynchronization effects on coupled inferior olive neurons for a wide range of parameters.
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Previous adaptation studies introduced force fields that are dependent only on velocity and position (e.g. viscous force fields, Coriolis forces, spring force fields), but inertial force fields were difficult to implement even with a high-performance robotic manipulandum. The authors utilized an air sled system and an off-axis load to introduce an interesting novel inertial force field. Generalization of learning was limited to a small range of direction angles, which is in accordance with previous studies using viscous force fields [51,52] or kinematic rotation [49].
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Sainburg R.L., Ghez C., Kalakainis D. Intersegmental dynamics are controlled by sequential anticipatory, error correction, and postural mechanisms. J Neurophysiol. 81:1999;1045-1055. Previous adaptation studies introduced force fields that are dependent only on velocity and position (e.g. viscous force fields, Coriolis forces, spring force fields), but inertial force fields were difficult to implement even with a high-performance robotic manipulandum. The authors utilized an air sled system and an off-axis load to introduce an interesting novel inertial force field. Generalization of learning was limited to a small range of direction angles, which is in accordance with previous studies using viscous force fields [51,52] or kinematic rotation [49].
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A viscous, rotating-type force field was applied by a robotic interface to the arm. Subjects were trained with a reaching movement having a specific amplitude and duration. Then, generalization was examined for different durations and amplitudes. Most surprisingly, and in contrast to almost all previous studies (particularly [54]), generalization was best modeled by a linear map - that is, generalization was global rather than local. It is possible that parallel fiber inputs to the cerebellum encode velocity information by their firing rates while other information, such as position and direction, is encoded by population coding. Thus, we expect good generalization only for velocities because only velocity-dependent terms are represented linearly in Purkinje cell outputs on this assumption.
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Goodbody S.J., Wolpert D.M. Temporal and amplitude generalization in motor learning. J Neurophysiol. 79:1998;1825-1838. A viscous, rotating-type force field was applied by a robotic interface to the arm. Subjects were trained with a reaching movement having a specific amplitude and duration. Then, generalization was examined for different durations and amplitudes. Most surprisingly, and in contrast to almost all previous studies (particularly [54]), generalization was best modeled by a linear map - that is, generalization was global rather than local. It is possible that parallel fiber inputs to the cerebellum encode velocity information by their firing rates while other information, such as position and direction, is encoded by population coding. Thus, we expect good generalization only for velocities because only velocity-dependent terms are represented linearly in Purkinje cell outputs on this assumption.
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Multiplicity of internal models for dynamic and kinematic transformations was investigated in order to determine whether multiple internal model can be composed or decomposed when occasion calls. When subjects learned a visuomotor rotation and viscous curl field first, reaching errors were smaller for a combination of these transformation than without prior experiences.
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Flanagan R., Nakano E., Imamizu H., Osu R., Yoshioka T., Kawato M. Composition and decomposition of internal models in motor learning under altered kinematic and dynamic environments. J Neurosci. 19(Rapid Communication 34):1999;1-5. Multiplicity of internal models for dynamic and kinematic transformations was investigated in order to determine whether multiple internal model can be composed or decomposed when occasion calls. When subjects learned a visuomotor rotation and viscous curl field first, reaching errors were smaller for a combination of these transformation than without prior experiences.
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It was postulated that the best way to control learning and the contributions of different motor primitives (controllers, or inverse models) is to use the prediction goodness of corresponding predictors (forward models). This basic idea, strengthened by a responsibility predictor, provides an attractive Bayesian framework to explain rich behaviors in complicated environments.
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Wolpert D.M., Kawato M. Multiple paired forward and inverse models for motor control. Neural Networks. 11:1998;1317-1329. It was postulated that the best way to control learning and the contributions of different motor primitives (controllers, or inverse models) is to use the prediction goodness of corresponding predictors (forward models). This basic idea, strengthened by a responsibility predictor, provides an attractive Bayesian framework to explain rich behaviors in complicated environments.
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••]. Multiple pairs of forward and inverse models were automatically acquired for different behavioral situations. A finite number of multiple models were shown to be able to deal with a much larger number of situations. The 'size-weight illusion' was also simulated.
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••]. Multiple pairs of forward and inverse models were automatically acquired for different behavioral situations. A finite number of multiple models were shown to be able to deal with a much larger number of situations. The 'size-weight illusion' was also simulated.
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The authors proposed a constrained optimization model to explain known regularities between velocity profiles and hand path curvature. For an observed path of the hand in space, the velocity profile along that path will be the one that minimizes jerk. This model explains the data better than the 2/3 power-law.
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Todorov E.V., Jordan M.I. Smoothness maximization along a predefined path accurately predicts the speed profiles of complex arm movements. J Neurophysiol. 80:1998;696-714. The authors proposed a constrained optimization model to explain known regularities between velocity profiles and hand path curvature. For an observed path of the hand in space, the velocity profile along that path will be the one that minimizes jerk. This model explains the data better than the 2/3 power-law.
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The kinematics of reaching movements was examined when a visual obstacle was set in three-dimensional space. The distribution of the near points, where the paths came closest to the obstacle, showed a strong anisotropy, clustering at the poles of a preferred axis through the center of the obstacle. The mobility minor axis, which represents the most inertially stable direction to a force perturbation, was not significantly different from the preferred near point axis. These results suggest that the dynamic characteristics of the arm are taken into account in the trajectory planning process.
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Sabes P.N., Jordan M.I., Wolpert D.M. The role of inertial sensitivity in motor planning. J Neurosci. 18:1998;5948-5957. The kinematics of reaching movements was examined when a visual obstacle was set in three-dimensional space. The distribution of the near points, where the paths came closest to the obstacle, showed a strong anisotropy, clustering at the poles of a preferred axis through the center of the obstacle. The mobility minor axis, which represents the most inertially stable direction to a force perturbation, was not significantly different from the preferred near point axis. These results suggest that the dynamic characteristics of the arm are taken into account in the trajectory planning process.
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As a computable version of the minimum motor-command change model, a minimum commanded torque change model was proposed and compared with other optimization models based on a large database of horizontal and vertical two-joint arm movements. The best performance of the model supports dynamic trajectory planning while taking into account not only environmental and link dynamics but also muscle dynamics.
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Nakano E., Imamizu H., Osu R., Uno Y., Gomi H., Yoshioka T., Kawato M. Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. J Neurophysiol. 81:1999;2140-2155. As a computable version of the minimum motor-command change model, a minimum commanded torque change model was proposed and compared with other optimization models based on a large database of horizontal and vertical two-joint arm movements. The best performance of the model supports dynamic trajectory planning while taking into account not only environmental and link dynamics but also muscle dynamics.
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L.R. Harris, & M. Jenkin. Cambridge: Cambridge University Press. The final posture of the arm in a reaching movement can be predicted according to a criterion that is related to energy expenditure, and the hand paths during planar arm movements can be at least partly predicted by another criterion (minimum muscle force change) that is also related to energy expenditure. The authors conclude that movement planning must involve dynamics.
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Soechting J.F., Flanders M. Movement planning: kinematics, dynamics, both or neither? Harris L.R., Jenkin M. Vision and Action. 1998;332-349 Cambridge University Press, Cambridge. The final posture of the arm in a reaching movement can be predicted according to a criterion that is related to energy expenditure, and the hand paths during planar arm movements can be at least partly predicted by another criterion (minimum muscle force change) that is also related to energy expenditure. The authors conclude that movement planning must involve dynamics.
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A unifying theory on trajectory formation of saccades and arm movements is proposed. It is assumed that the neural control signals are corrupted by noise, which increases with the size of the control signal. A simple principle to minimize the variance of the final eye or hand position could thus reproduce known invariant trajectory characteristics, Fitts' law, and the 2/3 power law. The final position error is the time integral of the noise in the motor command, which is filtered by time-variant linearized dynamics of the motor plant. In this interpretation, the minimum variance model could be viewed as a temporally weighted version of the minimum motor-command change model, because the noise variance is related to the square of the motor command.
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Harris C.M., Wolpert D.M. Signal-dependent noise determines motor planning. Nature. 394:1998;780-784. A unifying theory on trajectory formation of saccades and arm movements is proposed. It is assumed that the neural control signals are corrupted by noise, which increases with the size of the control signal. A simple principle to minimize the variance of the final eye or hand position could thus reproduce known invariant trajectory characteristics, Fitts' law, and the 2/3 power law. The final position error is the time integral of the noise in the motor command, which is filtered by time-variant linearized dynamics of the motor plant. In this interpretation, the minimum variance model could be viewed as a temporally weighted version of the minimum motor-command change model, because the noise variance is related to the square of the motor command.
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••]. Pars opecularis and pars triangularis were shown to be functionally connected with this part of the cerebellum. This is interesting because some theories advocate that language evolution is an extension of human tool usage capability.
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••]. Pars opecularis and pars triangularis were shown to be functionally connected with this part of the cerebellum. This is interesting because some theories advocate that language evolution is an extension of human tool usage capability.
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