Zobrazeno 1 - 10
of 226
pro vyhledávání: '"Bernardi, Alessandra"'
The decomposition locus of a tensor is the set of rank-one tensors appearing in a minimal tensor-rank decomposition of the tensor. For tensors lying on the tangential variety of any Segre variety, but not on the variety itself, we show that the decom
Externí odkaz:
http://arxiv.org/abs/2407.18138
Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or application under
Externí odkaz:
http://arxiv.org/abs/2405.19134
Starting from an integral projective variety $Y$ equipped with a very ample, non-special and not-secant defective line bundle $\mathcal{L}$, the paper establishes, under certain conditions, the regularity of $(Y \times \mathbb P^2,\mathcal{L}[t])$ fo
Externí odkaz:
http://arxiv.org/abs/2312.01933
Publikováno v:
Journal de Math\'ematiques Pures et Appliqu\'ees 188, 2024, pp. 446-469
We define and explicitly construct schemes evinced by generalized additive decompositions (GADs) of a given $d$-homogeneous polynomial $F$. We employ GADs to investigate the regularity of $0$-dimensional schemes apolar to $F$, focusing on those satis
Externí odkaz:
http://arxiv.org/abs/2309.12961
Publikováno v:
In Journal de mathématiques pures et appliquées August 2024 188:446-469
The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper bound is
Externí odkaz:
http://arxiv.org/abs/2101.03148
We introduce the notion of r-th Terracini locus of a variety and we compute it for at most three points on a Segre variety.
Comment: 27 pages, 3 figures
Comment: 27 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/2012.00574
We give an upper-bound for the $X$-rank of points with respect to a non-degenerate irreducible variety $X$ in the case that sub-generic $X$-rank points generate a hypersurface. We give examples where this bound is sharp and it improves the existing o
Externí odkaz:
http://arxiv.org/abs/2007.14760
Rank-2 and rank-3 tensors are almost all identifiable with only few exceptions. We classify them all together with the dimensions and the structures of all the sets evincing the rank.
Comment: Accepted for publication by Mediterranean J. of Math
Comment: Accepted for publication by Mediterranean J. of Math
Externí odkaz:
http://arxiv.org/abs/2001.10497
We propose a new method to estimate plant biodiversity with R{\'e}nyi and Rao indexes through the so called High Order Singular Value Decomposition (HOSVD) of tensors. Starting from NASA multispectral images we evaluate biodiversity and we compare or
Externí odkaz:
http://arxiv.org/abs/1911.13076