We propose a new approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on constrained sensing vectors and a two-stage reconstruction method that consists of two standard convex optimization programs that are solved sequentially. Various methods for compre...

Assume we are given a sum of linear measurements of s different rank-r matrices of the form y = ∑s k=1Ak(Xk). When and under which conditions is it possible to extract (demix) the individual matrices Xk from the single measurement vector y? And can we do the demixing numerically efficiently? We present two computationally efficient algorithms based on hard thresholding to solve this low rank de...

We study random convex cones defined as positive hulls of d-dimensional walks and bridges. compute expectations various geometric functionals these such the number k-dimensional faces sums conic quermassintegrals their faces. These are expressed in terms Stirling numbers both kinds B-analogues.

‎Let $n$ and $k$ be two positive integers‎, ‎$kleq n$ and $A$ be an $n$-square quaternion matrix‎. ‎In this paper‎, ‎some results on the $k-$numerical range of $A$ are investigated‎. ‎Moreover‎, ‎the notions of $k$-numerical radius‎, ‎right $k$-spectral radius and $k$-norm of $A$ are introduced‎, ‎and some of their algebraic properties are studied‎.

We study the problem of reconstructing low-rank matrices from their noisy observations. We formulate the problem in the Bayesian framework, which allows us to exploit structural properties of matrices in addition to low-rankedness, such as sparsity. We propose an efficient approximate message passing algorithm, derived from the belief propagation algorithm, to perform the Bayesian inference for...

We provide stronger and more general primal-dual convergence results for FrankWolfe-type algorithms (a.k.a. conditional gradient) for constrained convex optimization, enabled by a simple framework of duality gap certificates. Our analysis also holds if the linear subproblems are only solved approximately (as well as if the gradients are inexact), and is proven to be worst-case optimal in the sp...

For any finitely generated module M with non-zero rank over a commutative one-dimensional Noetherian local domain, we study numerical invariant h(M) based on partial trace ideal of M. We its properties and explore relations between this the colength conductor. Finally apply to universally finite differentials ΩR/k, where R is complete k-algebra k perfect field, long-standing conjecture due R. W...

In the study of convexity spaces, the most common convex invariants are based on notions of independence with respect to taking convex hulls. In [D.B. Parker, R.F. Westhoff and M.J. Wolf, Discuss. Math. Graph Theory 29 (2009), 51–69], H-independence, R-independence and convex independence were studied to prove results about the Helly number, Radon number and rank of a clone-free multipartite to...

The tanaid genus Hexapleomera has long been considered to be monotypic, comprising a cosmopolitan species predominantly commensal on turtles, or, more rarely, manatees. Recent discovery of material of a distinct species of Hexapleomera living on the hulls of yachts in south-west England encouraged re-assessment of the literature on this taxon, and re-examination of free-living benthic material ...

a method for determination of juglone in leaves and hulls of pterocarya fraxinifolia was developed, based on rp-hplc. this compound was extracted from leaves and hulls by chloroform refluxing about 2 hours. the chloroform was evaporated under low pressure at   50 ºc to produce a dry residue. the remained materials were dissolved in acetonitrile to be used for determination of this compound. app...