1 Chris Laing, Southampton Institute, Technology Faculty, Southampton, SO14 0YN, UK, [email protected] 2 Alan Robinson, Southampton Institute, Technology Faculty, Southampton, SO14 0YN, UK, [email protected] Abstract  Previously it has been proposed that explanations of non-traditional withdrawal might be defined by the underlying characteristics of the teaching and learn...

This paper describes new vector indexing algorithms for Lattice Vector Quantization (LVQ). The techniques described apply to a large class of lattices such as Z n , A n , D n , D ++ n (including as special cases the Gosset Lattice E 8 , and the lattice of Barnes-wall 1 6), widely used in signal compression. Relying on a partitioning of the events sources, based on a notion of leaders, they allo...

The Shortest Vector Problem (SVP) is the most famous and widely studied computational problem on lattices. Given a lattice L (typically represented by a basis), SVP asks to find the shortest nonzero vector in L. The problem can be defined with respect to any norm, but the Euclidean norm is the most common (see the entry lattice for a definition). A variant of SVP (commonly studied in computatio...

We show how to compute the probability of any given local configuration in a random tiling of the plane with dominos. That is, we explicitly compute the measures of cylinder sets for the measure of maximal entropy μ on the space of tilings of the plane with dominos. We construct a measure ν on the set of lozenge tilings of the plane, show that its entropy is the topological entropy, and compute...

We study the modulation instability in a two-dimensional nonlinear single feedback system with a photonic lattice and reveal a sharp transition in the instability regimes as the lattice strength is increased. For a shallow lattice, the instability modes are enhanced parallel to the lattice wave vector, while in stronger lattices, these modes are suppressed.

If F is a vector space over an ordered division ring, C a convex subset of V and L the lattice of convex subsets of C, then we call L a convexity lattice. We give necessary and sufficient conditions for an abstract lattice to be a convexity lattice in the finite dimensional case.

We study excitations of the local field (locsitons) in nanoscale two-dimensional (2D) lattices of strongly interacting resonant atoms and various unusual effects associated with them. Locsitons in low-dimensional systems and the resulting spatial strata and more complex patterns on a scale of just a few atoms were predicted by us earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett. 101, 133...

Improving on the Voronoi cell based techniques of [28, 24], we give a Las Vegas Õ(2n) expected time and space algorithm for CVPP (the preprocessing version of the Closest Vector Problem, CVP). This improves on the Õ(4n) deterministic runtime of the Micciancio Voulgaris algorithm [24] (henceforth MV) for CVPP 1 at the cost of a polynomial amount of randomness (which only affects runtime, not cor...