A dimension reduction framework for understanding cortical maps

@article{Durbin1990ADR,
  title={A dimension reduction framework for understanding cortical maps},
  author={Richard Durbin and Graeme J. Mitchison},
  journal={Nature},
  year={1990},
  volume={343},
  pages={644-647}
}
WE argue that cortical maps, such as those for ocular dominance, orientation and retinotopic position in primary visual cortex1, can be understood in terms of dimension-reducing mappings from many-dimensional parameter spaces to the surface of the cortex. The goal of these mappings is to preserve as far as possible neighbourhood relations in parameter space so that local computations in parameter space can be performed locally in the cortex. We have found that, in a simple case2, certain self… 
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This paper uses a dimension reduction model to generate maps of simple, many- dimensional feature spaces onto a model two-dimensional cortex, and suggests that geometrical factors do not sharply limit the ability of the cortex to represent combinations of parameters in spatially superimposed maps of similar periodicity.
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In primary visual cortex of ferret, the relationships between the maps of visual space and response features are predicted by a "dimension-reduction" model, and a clear influence of the visual map on each feature map is demonstrated.
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The most salient features of these maps can be understood from a few basic design principles: local correlation, modularity, isotropy, and homogeneity, which are common properties of the models and of biological maps.
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Anisotropic Correlation Properties in the Spatial Structure of Cortical Orientation Maps
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Information-theoretic insights are provided about spatial arrangements of simple cell receptive fields in several biologically plausible orientation maps, by studying both autocorrelation and directional mutual information of cortical activity.
Alteration of Visual Input Results in a Coordinated Reorganization of Multiple Visual Cortex Maps
TLDR
The number of feature maps in a cortical area influences the relationships between them, and inputs to the cortex have a significant role in generating these relationships.
Pattern selection in the visual cortex
The orientation map in the primary visual cortex is an important model system for studying cortical development. By quantifying large sets of functional brain imaging data we find that the statistics
Topological analysis of point singularities in stimulus preference maps of the prim ary visual cortex
  • Shigeru Tanaka
  • Mathematics
    Proceedings of the Royal Society of London. Series B: Biological Sciences
  • 1995
A large population of neurons in the primary visual cortex optimally respond to the orientation and phase of a grating stimulus in luminance. I demonstrate here that the topology of the stimulus
Topographical maps of orientation specificity
  • L. Costa
  • Mathematics, Computer Science
    Biological Cybernetics
  • 2004
TLDR
A spatially congruent framework for orientation encoding in the primate striate visual cortex is proposed and discussed, which provides a reasonable explanation for the centric organization of the orientation specificity and accounts for a series of experimentally verified intriguing phenomena.
The influence of restricted orientation rearing on map structure in primary visual cortex
TLDR
A computational model of map formation based on dimension-reduction principles is used to predict the effect on map relationships of presenting only a single orientation to one eye and the orthogonal orientation to the other eye and provides a way to further test the adequacy of dimension reduction principles for explaining map structure under perturbed as well as normal rearing conditions.
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