The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second and third authors have recently proposed a dimension-incremental approach, which only scales almost linear in the number of required sampling values and alm...

Recently, a number of authors have presented several geometries for rankstructured matrix and tensor spaces, namely the set of matrices or tensors with fixed matrix, Tucker or TT rank. In this talk we present a unifying approach for establishing a smooth, differential structure on the set of tensors with fixed hierarchical Tucker rank. Our approach describes this set as a smooth submanifold, gl...

In many applications, users specify target values for certain attributes, without requiring exact matches to these values in return. Instead, the result to such queries is typically a rank of the “top k” tuples that best match the given attribute values. In this paper, we study the advantages and limitations of processing a top-k query by translating it into a single range query that traditiona...

Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix M , the goal is to compute a matrix M ′ of given rank r in a linear or affine subspace E of matrices (usually encoding a specific structure) such that the Frobenius distance ‖M −M ′‖ is small. We propose a Newton-like iteration for solving ...

  It has been shown that acute inflammation reduces the effectiveness of sympathetic nerves in the regulation of knee joint blood flow. To investigate the role of vascular β- adrenoceptors in this event, 12 NZW rabbits were maintained anaesthetized by 1 % halothane in N2O/O2, and acute knee joint inflammation was induced by intra-articular injection of 1 ml of 2% carageenan solution 24 hours be...

Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices that are not themselves rank-deficient, but have off-diagonal blocks that are; specifically, the class of so called Hierarchically Semi-Separable (HSS) matric...

The well-known symmetric rank-one trust-region method—where the Hessian approximation is generated by the symmetric rank-one update—is generalized to the problem of minimizing a real-valued function over a d-dimensional Riemannian manifold. The generalization relies on basic differential-geometric concepts, such as tangent spaces, Riemannian metrics, and the Riemannian gradient, as well as on t...