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Pinwheel Stability in a Non-Euclidean Model of Pattern Formation in the Visual Cortex
J. Michael Herrmann,Minoru Asada,Norbert Michael Mayer,Theo Geisel 한국물리학회 2007 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.50 No.1I
The structure of neural maps in the primary visual cortex arises from the problem of representing a high-dimensional stimulus manifold on an essentially two-dimensional piece of cortical tissue. In order to treat the problem theoretically, stimuli are usually represented by a set of features, such as centroid position, orientation, spatial frequency, phase etc. Inputs to the cortex are, however, activity distributions over aerent nerve .bers; i.e., they require, in principle, a description as high- dimensional vectors. We study the relation between high-dimensional maps, which can be assumed to rely on a Euclidean geometry, and low-dimensional feature maps, which need to be formulated in Riemannian space in order to represent high-dimensional maps to a good accuracy. We show numerically that the Riemannian framework allows for a suggestive explanation of the abundance of typical structural units (\pinwheels") in feature maps emerging in the course of the adaptation process from an initially unstructured state.0
Photocatalytic efficiencies of self-cleaning glasses. Influence of physical factors
Peruchon, L.,Puzenat, E.,Herrmann, J.M.,Guillard, C. Korean Society of Photoscience 2009 Photochemical & photobiological sciences Vol.8 No.7
Two commercial types of self-cleaning glass (SCG) have been tested to confirm the real photocatalytic nature of their properties. This was done by using four photocatalytic tests: (i) in the gas phase with the total oxidation of acetylene; (ii) in water with the total degradation of malic acid, (iii) in water with the total degradation of methylene blue, and (iv) in the solid phase with the total oxidative degradation of a layer of stearic acid deposited on the self-cleaning glass surface, in contact with the superficial titania coating. The influence of various factors (temperature, humidity, wavelength, radiant flux, presence of inorganic particles stuck at the glass surface) was explained in line with the fundamentals of photocatalysis. The results helped to understand the behaviour of self-cleaning glass.