Sensorimotor integration is described as geometrical mapping among the coordinates of nonorthogonal frames that are intrinsic to the system; in such a case, sensors represent (covariant) afferents and motor effectors represent (contravariant) motor efferents. The neuronal networks that perform such a function are viewed as general tensor transformations among different expressions and metric tensors determining the geometry of neural functional spaces. Although the nonorthogonality of a coordinate system does not impose a specific geometry on the space, this tensor network theory of brain function allows for the possibility that the geometry is non-Euclidean. The non-Euclidean nature of the geometry is the key to understand brain function and to interpret neuronal network function. This chapter discusses some contemporary applications of such a theoretical modeling approach. The first is the analysis and interpretation of multi-electrode recordings. The internal geometries of neural networks controlling external behavior of the skeletomuscle system is experimentally determinable using such multi-unit recordings. The second application of this geometrical approach to brain theory is modeling the control of posture and movement. © 1993, Academic Press Inc.
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