We a¢ rm a conjecture of Sacks [1972] by showing that every countable distributive lattice is isomorphic to an initial segment of the hyperdegrees, Dh. In fact, we prove that every sublattice of any hyperarithmetic lattice (and so, in particular, every countable locally …nite lattice) is isomorphic to an initial segment of Dh. Corollaries include the decidability of the two quanti…er theory of ...

Locally parallel dense patterns—sometimes called texture flows—define a perceptually coherent structure of particular significance to perceptual organization. We argue that with applications ranging from image segmentation and edge classification to shading analysis and shape interpretation, texture flows deserve attention equal to edge segment grouping and curve completion. This paper develops...

We verify a conjecture of Vershik by showing that Hall's universal countable locally finite group can be embedded as dense subgroup in the isometry Urysohn space and automorphism random graph. In fact, we show same for all groups known infinite ultraextensive spaces. These include, addition, rational space, ultrametric spaces, Kn-free graph n≥3. Furthermore, actions on metric spaces or some rel...

1. Let X be a locally compact Hausdorff space, E a (real) locally convex, complete, linear topological space, and (C*(X, E), ß) the locally convex linear space of all bounded continuous functions on X to E topologized with the strict topology ß. When E is the real numbers we denote C*(X, E) by C*(X) as usual. When E is not the real numbers, C*(X, E) is not in general an algebra, but it is a mod...

AbstractAnomaly detection can be conceived either through generative modelling of regular training data or by discriminating with respect to negative data. These two approaches exhibit different failure modes. Consequently, hybrid algorithms present an attractive research goal. Unfortunately, dense anomaly requires translational equivariance and very large input resolutions. requirements disqua...