18 research outputs found
Covering and gluing of algebras and differential algebras
Extending work of Budzynski and Kondracki, we investigate coverings and
gluings of algebras and differential algebras. We describe in detail the gluing
of two quantum discs along their classical subspace, giving a C*-algebra
isomorphic to a certain Podles sphere, as well as the gluing of
U_{\sqrt{q}}(sl_2)-covariant differential calculi on the discs.Comment: latex2e, 27 page
Connections on locally trivial quantum principal fibre bundles
Following the approach of Budzy\'nski and Kondracki, we define covariant
differential algebras and connections on locally trivial quantum principal
fibre bundles. We also consider covariant derivatives, connection forms and
curvatures and explore the relations between these notions. As an example, a
U(1) quantum principal bundle over a glued quantum sphere and a connection in
this bundle is constructed. This connection may be interpreted as a q-deformed
Dirac monopole.Comment: 42 page
The Peri-Saccadic Perception of Objects and Space
Eye movements affect object localization and object recognition. Around saccade onset, briefly flashed stimuli appear compressed towards the saccade target, receptive fields dynamically change position, and the recognition of objects near the saccade target is improved. These effects have been attributed to different mechanisms. We provide a unifying account of peri-saccadic perception explaining all three phenomena by a quantitative computational approach simulating cortical cell responses on the population level. Contrary to the common view of spatial attention as a spotlight, our model suggests that oculomotor feedback alters the receptive field structure in multiple visual areas at an intermediate level of the cortical hierarchy to dynamically recruit cells for processing a relevant part of the visual field. The compression of visual space occurs at the expense of this locally enhanced processing capacity
Optic Flow Statistics and Intrinsic Dimensionality
Different kinds of visual sub-structures can be distinguished by the intrinsic dimensionality of the local signals. The concept of intrinsic dimensionality has been mostly exercised using discrete formulations. A recent work (Kruger and Felsberg, 2003; Felsberg and Kruger, 2003) introduced a continuous definition and showed that the inherent structure of the intrinsic dimensionality has essentially the form of a triangle. The current study work analyzes the distribution of signals according to the continuous interpretation of intrinsic dimensionality and the relation to orientation and optic flow features of image patches. Among other things, we give a quantitative interpretation of the distribution of signals according to their intrinsic dimensionality that reveals specific patterns associated to established sub-structures in computer vision. Furthermore, we link quantitative and qualitative properties of the distribution of optic-flow error estimates to these patterns