We consider the problem of commutative rank computation of a given matrix space, B ⊆ Fn×n. The problem is fundamental, as it generalizes several computational problems from algebra and combinatorics. For instance, checking if the commutative rank of the space is n, subsumes problems such as testing perfect matching in graphs and identity testing of algebraic branching programs. An efficient det...

We propose a simple variant of kd-trees, called rankbased kd-trees, for sets of points in R. We show that a rank-based kd-tree, like an ordinary kd-tree, supports range search queries in O(n1−1/d + k) time, where k is the output size. The main advantage of rank-based kd-trees is that they can be efficiently kinetized: the KDS processes O(n) events in the worst case, assuming that the points fol...

The matrix separation problem aims to separate a low-rank matrix and a sparse matrix from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications. Nuclear-norm minimization models have been proposed for matrix separation and proved to yield exact separations under suitable conditions. These models, however, typically require...

This paper is concerned with the fast computation of Fourier integral operators of the general form ∫ Rd e f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a standard homogeneity condition, and f is a given input. This is of interest for such fundamental computations are connected with the problem of finding numerical solutions to wave equations, and also frequently ...

Mathematical concepts of order and ordering relations play multiple roles in semantic technologies. Discrete totally ordered data characterize both input streams and top-k rank-ordered recommendations and query output, while temporal attributes establish numerical total orders, either over time points or in the more complex case of startend temporal intervals. But also of note are the fully par...

PURPOSE To develop parallel imaging techniques that simultaneously exploit coil sensitivity encoding, image phase prior information, similarities across multiple images, and complementary k-space sampling for highly accelerated data acquisition. METHODS We introduce joint virtual coil (JVC)-generalized autocalibrating partially parallel acquisitions (GRAPPA) to jointly reconstruct data acquir...