Neurons in primary visual cortex are widely considered to be oriented filters or energy detectors that perform one-dimensional feature analysis. The main deviations from this picture are generally thought to include gain controls and modulatory influences. Here we investigate receptive field (RF) properties of single neurons with localized two-dimensional stimuli, the two-dimensional Hermite functions (TDHs). TDHs can be grouped into distinct complete orthonormal bases that are matched in contrast energy, spatial extent, and spatial frequency content but differ in two-dimensional form, and thus can be used to probe spatially specific nonlinearities. Here we use two such bases: Cartesian TDHs, which resemble vignetted gratings and checkerboards, and polar TDHs, which resemble vignetted annuli and dartboards. Of 63 isolated units, 51 responded to TDH stimuli. In 37/51 units, we found significant differences in overall response size (21/51) or apparent RF shape (28/51) that depended on which basis set was used. Because of the properties of the TDH stimuli, these findings are inconsistent with simple feedforward nonlinearities and with many variants of energy models. Rather, they imply the presence of nonlinearities that are not local in either space or spatial frequency. Units showing these differences were present to a similar degree in cat and monkey, in simple and complex cells, and in supragranular, infragranular, and granular layers. We thus find a widely distributed neurophysiological substrate for two-dimensional spatial analysis at the earliest stages of cortical processing. Moreover, the population pattern of tuning to TDH functions suggests that V1 neurons sample not only orientations, but a larger space of two-dimensional form, in an even-handed manner.
We describe a novel method for the analysis of multivariate time series that exploits the dynamic relationships among the multiple signals. The approach resolves the multivariate time series into hierarchically dependent underlying sources, each driven by noise input and influencing subordinate sources in the hierarchy. Implementation of this hierarchical decomposition (HD) combines principal components analysis (PCA), autoregressive modeling, and a novel search strategy among orthogonal rotations. For model systems conforming to this hierarchical structure, HD accurately extracts the underlying sources, whereas PCA or independent components analysis does not. The interdependencies of cortical, subcortical, and brainstem networks suggest application of HD to multivariate measures of brain activity. We show first that HD indeed resolves temporal lobe ictal electrocorticographic data into nearly hierarchical form. A previous analysis of these data identified characteristic nonlinearities in the PCA-derived temporal components that resembled those seen in absence (petit mal) seizure electroencephalographic traces. However, the components containing these characteristic nonlinearities accounted for only a small fraction of the power. Analysis of these data with HD reveals furthermore that components containing characteristic nonlinearities, though small, can be at the origin of the hierarchy. This finding supports the link between temporal lobe and absence epilepsy.
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