The paper is devoted to the generalization of Lusztig’s q-analog of weight multiplicities to the Lie superalgebras gl(n,m) and spo(2n,M). We define such qanalogs Kλ,μ(q) for the typical modules and for the irreducible covariant tensor gl(n,m)-modules of highest weight λ. For gl(n,m), the defined polynomials have nonnegative integer coefficients if the weight μ is dominant. For spo(2n,M), we sho...

It is well-known that tensor decompositions show separations, is, constraints on local terms (such as positivity) may entail an arbitrarily high cost in their representation. Here we many of these separations disappear the approximate case. Specifically, for every approximation error $\varepsilon$ and norm, define rank minimum element $\varepsilon$-ball with respect to norm. For positive semide...

Generalizing the idea of viewing a digraph as a model of a linear map, we suggest a multi-variable analogue of a digraph, called a hydra, as a model of a multi-linear map. Walks in digraphs correspond to usual matrix multiplication while walks in hydras correspond to the tensor multiplication introduced by Robert Grone in 1987. By viewing matrix multiplication as a special case of this tensor m...

This paper presents a new class of tensor factorization called positive semidefinite tensor factorization (PSDTF) that decomposes a set of positive semidefinite (PSD) matrices into the convex combinations of fewer PSD basis matrices. PSDTF can be viewed as a natural extension of nonnegative matrix factorization. One of the main problems of PSDTF is that an appropriate number of bases should be ...

in this paper for a given prescribed ritz values that satisfy in the some special conditions, we nd a symmetric nonnegative matrix, such that the given set be its ritz values.

Tensor-based methods have been widely studied to attack inverse problems in hyperspectral imaging since a image (HSI) cube can be naturally represented as third-order tensor, which perfectly retain the spatial information image. In this article, we extend linear tensor method nonlinear and propose low-rank unmixing algorithm solve generalized bilinear model (GBM). Specifically, parts of GBM bot...

Motivated by results on the rationality of equivariant Hilbert series some hierarchical models in algebraic statistics we introduce Segre product formal languages and apply it to establish new cases. To this end show that two regular is again regular. We also prove every filtration algebras given as a tensor families with rational has series. The term used broadly include action monoid nonnegat...

We solve tensor balancing, rescaling an N th order nonnegative tensor by multiplying N tensors of order N −1 so that every fiber sums to one. This generalizes a fundamental process of matrix balancing used to compare matrices in a wide range of applications from biology to economics. We present an efficient balancing algorithm with quadratic convergence using Newton’s method and show in numeric...

this paper presents a modified digital image watermarking method based on nonnegative matrix factorization. firstly, host image is factorized to the product of three nonnegative matrices. then, the centric matrix is transferred to discrete cosine transform domain. watermark is embedded in low frequency band of this matrix and next, the reverse of the transform is computed. finally, watermarked ...