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A computational neural network model is presented that combines information on current position and target of a movement by multiplying the two values together. An adaptive network then learns to take the combined population information and create a new population that represents the appropriate motor command. This is a concrete example of combining multiple input populations to produce an output population with desired behavior.
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Baraduc P., Guigon E., Burnod Y. Recoding arm position to learn visuomotor transformations. Cereb. Cortex. 11:2001;906-917 A computational neural network model is presented that combines information on current position and target of a movement by multiplying the two values together. An adaptive network then learns to take the combined population information and create a new population that represents the appropriate motor command. This is a concrete example of combining multiple input populations to produce an output population with desired behavior.
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The authors show that neurons in the frontal eye field respond to both lateral motion and motion in depth, thereby coding 3D movement. This is an example of coding of multiple co-ordinates by the same population, and the authors propose that it may be helpful for controlling eye movements that are related to three-dimensional movements of the hand in space.
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Fukushima K., Yamanobe T., Shinmei Y., Fukushima J., Kurkin S., Peterson B.W. Coding of smooth eye movements in three-dimensional space by frontal cortex. Nature. 419:2002;157-162 The authors show that neurons in the frontal eye field respond to both lateral motion and motion in depth, thereby coding 3D movement. This is an example of coding of multiple co-ordinates by the same population, and the authors propose that it may be helpful for controlling eye movements that are related to three-dimensional movements of the hand in space.
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This investigation of the representational capacity of populations concludes that cosine tuning is appropriate if preferred directions are nonuniformly distributed, but that other forms of tuning may be appropriate if preferred directions are uniformly distributed.
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Baraduc P., Guigon E. Population computation of vectorial transformations. Neural. Comput. 14:2002;845-871 This investigation of the representational capacity of populations concludes that cosine tuning is appropriate if preferred directions are nonuniformly distributed, but that other forms of tuning may be appropriate if preferred directions are uniformly distributed.
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Pouget A., Deneve S., Ducom J.-C. Narrow versus wide tuning curves: what's best for a population code? Neural. Comput. 11:1999;85-90.
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It has been proposed that a population can be considered optimal for coding a particular representation if any small change in the population would worsen the quality of the coding. The authors argue that such methods do not provide adequate evidence for optimality of a population.
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Carreira-Perpinan M.A., Goodhill G.J. Are visual cortex maps optimized for coverage? Neural. Comput. 14:2002;1545-1560 It has been proposed that a population can be considered optimal for coding a particular representation if any small change in the population would worsen the quality of the coding. The authors argue that such methods do not provide adequate evidence for optimality of a population.
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Reina G.A., Moran D.W., Schwartz A.B. On the relationship between joint angular velocity and motor cortical discharge during reaching. J. Neurophysiol. 85:2001;2576-2589 This paper follows in the long tradition of using linear correlation based methods in an attempt to determine which of several co-ordinate systems is most closely related to a neural representation. The authors compare whether joint angles or hand positions in 3D space are better linear predictors of cell firing in motor cortex, and whether population vectors based on joint angles or hand positions are better predictors of the actual motion trajectories. They found that both coordinate systems were well correlated, but the joint angles that were more closely linked to hand position were better predictors of cell firing than those that were less linked to hand position. Although this might seem to imply that the motor cortical representation has been optimized for representing hand position, it is difficult to draw such conclusions from a purely linear analysis unless we assume that the brain itself is limited to linear analytic techniques. A Bayesian or information-theoretic analysis might well lead to very different conclusions.
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Crammond D.J., Kalaska J.F. Prior information in motor and premotor cortex: activity during the delay period and effect on pre-movement activity. J. Neurophysiol. 84:2000;986-1005.
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Gomez J.E., Fu Q., Flament D., Ebner T.J. Representation of accuracy in the dorsal premotor cortex. Eur. J. Neurosci. 12:2000;3748-3760.
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This study investigates the effect on Fisher information of introducing local correlations into the spike generators of a population of cells. The information increases both for very low and very high correlations. The authors point out some pitfalls of using maximum-likelihood estimators in this type of population.
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Wu S., Amari S., Nakahara H. Population coding and decoding in a neural field: a computational study. Neural. Comput. 14:2002;999-1026 This study investigates the effect on Fisher information of introducing local correlations into the spike generators of a population of cells. The information increases both for very low and very high correlations. The authors point out some pitfalls of using maximum-likelihood estimators in this type of population.
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Abbott L.F., Dayan P. The effect of correlated variability on the accuracy of a population code. Neural. Comput. 11:1999;91-101.
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The authors investigate the effect of the dimensionality of the input data x on the Fisher information for populations that have Poisson-type noise, additive noise, or local correlations in spike generators. Additive noise has lower reconstruction error for high input dimensionality, but it leads to worse reconstruction for large populations when there are local correlations. They derive the important result that populations with highly varied tuning curves may have better representational properties than populations in which all tuning curves share a similar shape.
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Wilke S.D., Eurich C.W. Representational accuracy of stochastic neural populations. Neural. Comput. 14:2002;155-189 The authors investigate the effect of the dimensionality of the input data x on the Fisher information for populations that have Poisson-type noise, additive noise, or local correlations in spike generators. Additive noise has lower reconstruction error for high input dimensionality, but it leads to worse reconstruction for large populations when there are local correlations. They derive the important result that populations with highly varied tuning curves may have better representational properties than populations in which all tuning curves share a similar shape.
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Poliakov A.V., Schieber M.H. Limited functional grouping of neurons in the motor cortex hand area during individuated finger movements: a cluster analysis. J. Neurophysiol. 82:1999;3488-3505.
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This is one of a series of papers in which the authors examine the role of signal-dependent noise and predict that the properties of tuning curves may be determined by an attempt to minimize the effects of noise.
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Todorov E. Cosine tuning minimizes motor errors. Neural. Comput. 14:2002;1233-1260 This is one of a series of papers in which the authors examine the role of signal-dependent noise and predict that the properties of tuning curves may be determined by an attempt to minimize the effects of noise.
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