On the Closure of the Tame Automorphism Group of Affine Three-Space

We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of C3 is not closed, when the latter is seen as an infinite-dimensional algebraic group.

Using space to represent categories: Insights from gaze position

We investigated the boundaries among imagery, memory, and perception by measuring gaze during retrieved versus imagined visual information. Eye fixations during recall were bound to the location at which a specific stimulus was encoded. However, eye position information generalized to novel objects of the same category that had not been seen before. For example, encoding an image of a dog in a specific location enhanced the likelihood of looking at the same location during subsequent mental imagery of other mammals. The results suggest that eye movements can also be launched by abstract representa- tions of categories and not exclusively by a single episode or a specific visual exemplar.