Ranked data sets, where m judges/voters specify a preference ranking of n objects/candidates, are increasingly prevalent in contexts such as political elections, computer vision, recommender systems, and bioinformatics. The vote counts for each can be viewed an n! vector lying on the permutahedron, which is Cayley graph symmetric group with vertices labeled by permutations edge when two differ ...

PARSEVAL, the default paradigm for evaluating constituency parsers, calculates parsing success (Precision/Recall) as a function of the number of matching labeled brackets across the test set. Nodes in constituency trees, however, are connected together to reflect important linguistic relations such as predicate-argument and direct-dominance relations between categories. In this paper, we presen...

We develop a unifying perspective on several decompositions exhibiting directional parabolic scaling. In each decomposition, the individual atoms are highly anisotropic at fine scales, with effective support obeying the parabolic scaling principle length ≈ width. Our comparisons allow to extend Theorems known for one decomposition to others. We start from a Continuous Curvelet Transform f → Γf ...

We consider classes of reconstruction systems (RS’s) for finite dimensional real or complex Hilbert spaces H, called group reconstruction systems (GRS’s), that are associated with representations of finite groups G. These GRS’s generalize frames with high degree of symmetry, such as harmonic or geometrically uniform ones. Their canonical dual and canonical Parseval are shown to be GRS’s. We est...