相关论文: Optimal Ramp Schemes and Related Combinatorial Obj…

1. A standard Gaussian random matrix has full rank with probability 1 and is well-conditioned with a probability quite close to 1 and converging to 1 fast as the matrix deviates from square shape and becomes more rectangular. 2. If we…

Close connections between various notions of entropy and the apparatus of category theory have been observed already in the 1980s and more vigorously developed in the past ten years. The starting point of the paper is the recent categorical…

This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…

This paper concerns the geometric structure of optimizers for frame potentials. We consider finite, real or complex frames and rotation or unitarily invariant potentials, and mostly specialize to Parseval frames, meaning the frame potential…

Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the…

Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…

In this paper, incremental adaptive mechanisms are presented and characterized, to provide design hints for the development of continuous-time adaptive systems. The comparison with the conventional integral adaptive systems indicates that…

A locally-optimal structure is a combinatorial structure such as a maximal independent set that cannot be improved by certain (greedy) local moves, even though it may not be globally optimal. It is trivial to construct an independent set in…

Spherical configurations that are very massive must be surrounded by apparent horizons. These in turn, when placed outside a collapsing body, must propagate outward with a velocity equal to the velocity of radially outgoing photons. That…

We propose the Hit-and-Run algorithm for planning and sampling problems in non-convex spaces. For sampling, we show the first analysis of the Hit-and-Run algorithm in non-convex spaces and show that it mixes fast as long as certain…

In this article we determine five previously unknown covering array numbers (CANs). We do so using properties of so called balanced covering arrays together with a computational result for these. The balance properties allow us to…

A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…

We introduce spiky rank, a new matrix parameter that enhances blocky rank by combining the combinatorial structure of the latter with linear-algebraic flexibility. A spiky matrix is block-structured with diagonal blocks that are arbitrary…

We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular $T$-optimality criterion are derived, which in many…

When is a topological branched self-cover of the sphere equivalent to a rational map on CP^1? William Thurston gave one answer in 1982, giving a negative criterion (an obstruction to a map being rational). We give a complementary, positive…

This paper combines two ingredients in order to get a rather surprising result on one of the most studied, elegant and powerful tools for solving convex feasibility problems, the method of alternating projections (MAP). Going back to names…

We introduce a new family of jump operators on Borel equivalence relations; specifically, for each countable group $\Gamma$ we introduce the $\Gamma$-jump. We study the elementary properties of the $\Gamma$-jumps and compare them with other…

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…

Planning collision free trajectories in complex environments remains a core challenge in robotics. Existing corridor based planners which rely on decomposition of the free space into collision free subsets scale poorly with environmental…

Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…