Homotheties and topology of tangent sphere bundles

We prove a Theorem on homotheties between two given tangent sphere bundles SrM of a Riemannian manifold (M,g) of dim ≥ 3, assuming different variable radius functions r and weighted Sasaki metrics induced by the conformal class of g. New examples are shown of manifolds with constant positive or with constant negative scalar curvature which are not Einstein. Recalling results on the associated almost complex structure I^G and symplectic structure ω^G on the manifold TM , generalizing the well-known structure of Sasaki by admitting weights and connections with torsion, we compute the Chern and the Stiefel-Whitney characteristic classes of the manifolds TM and SrM.

On a Limit of Perturbed Conservation Laws with Diffusion and Non-Positive Dispersion

We consider a conservation law perturbed by a linear diffusion and a general form of non-positive dispersion. We prove the convergence of the corresponding solution to the entropy weak solution of the hyperbolic conservation law.

Detection of Glass pattern configurations by the primary visual cortex

The neurons in the primary visual cortex that respond to the orientation of visual stimuli were discovered in the late 1950s (Hubel, D.H. & Wiesel, T.N. 1959. J. Physiol. 148:574-591) but how they achieve this response is poorly understood. Recently, experiments have demonstrated that the visual cortex may use the image processing techniques of cross or auto-correlation to detect the streaks in random dot patterns (Barlow, H. & Berry, D.L. 2010. Proc. R. Soc. B. 278: 2069-2075). These experiments made use of sinusoidally modulated random dot patterns and of the so-called Glass patterns - where randomly positioned dot pairs are oriented in a parallel configuration (Glass, L. 1969. Nature. 223: 578-580). The image processing used by the visual cortex could be inferred from how the threshold of detection of these patterns in the presence of random noise varied as a function of the dot density in the patterns. In the present study, the detection thresholds have been measured for other types of patterns including circular, hyperbolic, spiral and radial Glass patterns and an indication of the type of image processing (cross or auto-correlation) by the visual cortex is presented. As a result, it is hoped that this study will contribute to an understanding of what David Marr called the ‘computational goal’ of the primary visual cortex (Marr, D. 1982. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. New York: Freeman.)