Typical l 1-recovery limit of sparse vectors represented by concatenations of random orthogonal matrices Abstract. We consider the problem of recovering an N-dimensional sparse vector x from its linear transformation y = Dx of M (< N) dimension. Minimizing the l 1-norm of x under the constraint y = Dx is a standard approach for the recovery problem, and earlier studies report that the critical ...

An infinite product IIT= lMi of matrices converges (on the right) if limi __ M, . . . Mi exists. A set Z = (Ai: i > l} of n X n matrices is called an RCP set (rightconvergent product set) if all infinite products with each element drawn from Z converge. Such sets of matrices arise in constructing self-similar objects like von Koch’s snowflake curve, in various interpolation schemes, in construc...

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of space and run-time. Prompted by this observation, we study a convex optimization scheme for block-sparse recovery from linear measurements. To obtain linear ...

The aim of our research was to obtain porous matrices from collagen and collagen-hyaluronic acid and to investigate their effect on two types of human cells: fibroblasts and osteoblasts. In order to fabricate the collagenous matrices, type I collagen solution and a mixture of type I collagen and hyaluronic acid solutions, in a weight ratio of 5:1 were conditioned as sponges by freeze-drying. ES...

The reconstruction of phylogenetic relationships in the primate fossil record is dependent upon a thorough understanding of the phylogenetic utility of craniodental characters. Here, we test three previously proposed hypotheses for the propensity of primate craniomandibular data to exhibit homoplasy, using a study design based on the relative congruence between cranial distance matrices and a c...

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...

Identifying promoters is the key to understanding gene expression in bacteria. Promoters lie in tightly constrained positions relative to the transcription start site (TSS). In this paper, we address the problem of predicting transcription start sites in Escherichia coli. Knowing the TSS position, one can then predict the promoter position to within a few base pairs, and vice versa. The accepte...

 In this paper we characterize all $2times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2times 2$ matrix  over a UFD is nil-clean.

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.