21 research outputs found
Coverage, Continuity and Visual Cortical Architecture
The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure
Predicted contextual modulation varies with distance from pinwheel centers in the orientation preference map
In the primary visual cortex (V1) of some mammals, columns of neurons with the full range of orientation preferences converge at the center of a pinwheel-like arrangement, the ‘pinwheel center' (PWC). Because a neuron receives abundant inputs from nearby neurons, the neuron's position on the cortical map likely has a significant impact on its responses to the layout of orientations inside and outside its classical receptive field (CRF). To understand the positional specificity of responses, we constructed a computational model based on orientation preference maps in monkey V1 and hypothetical neuronal connections. The model simulations showed that neurons near PWCs displayed weaker but detectable orientation selectivity within their CRFs, and strongly reduced contextual modulation from extra-CRF stimuli, than neurons distant from PWCs. We suggest that neurons near PWCs robustly extract local orientation within their CRF embedded in visual scenes, and that contextual information is processed in regions distant from PWCs
On the number of modes of a Gaussian mixture
We consider a problem intimately related to the creation of maxima under Gaussian blurring: the number of modes of a Gaussian mixture in D dimensions. To our knowledge, a general answer to this question is not known. We conjecture that if the components of the mixture have the same covariance matrix (or the same covariance matrix up to a scaling factor), then the number of modes cannot exceed the number of components. We demonstrat