Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Santarsiero, Pierpaola"'
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. In this paper we propose a systematic study of basic properties of signature tensors, starting from their rank, symmetries and conciseness. We prove a sha
Externí odkaz:
http://arxiv.org/abs/2407.20405
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
Autor:
Breiding, Paul, Santarsiero, Pierpaola
Subspace varieties are algebraic varieties whose elements are tensors with bounded multilinear rank. In this paper, we compute their degrees by computing their volumes.
Comment: 14 pages, comments are welcome!
Comment: 14 pages, comments are welcome!
Externí odkaz:
http://arxiv.org/abs/2402.12217
After a few results on curves, we characterize the smallest nonempty Terracini loci of Veronese and Segre-Veronese varieties. For del Pezzo surfaces, we give a full description of the Terracini loci. Moreover, we present an algorithm to explicitly co
Externí odkaz:
http://arxiv.org/abs/2311.09067
Autor:
Améndola, Carlos, Galuppi, Francesco, Ortiz, Ángel David Ríos, Santarsiero, Pierpaola, Seynnaeve, Tim
The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature variety. W
Externí odkaz:
http://arxiv.org/abs/2308.11571
Inspired by recent work of Kopparty-Moshkovitz-Zuiddam and motivated by problems in combinatorics and hypergraphs, we introduce the notion of the symmetric geometric rank of a symmetric tensor. This quantity is equal to the codimension of the singula
Externí odkaz:
http://arxiv.org/abs/2303.17537
Autor:
Santarsiero, Pierpaola
In this thesis we work on problems related to tensor decomposition from a geometrical perspective. In the first part of the thesis we focus on the identifiability problem, which amounts to understand in how many ways a tensor can be decomposed as a m
Externí odkaz:
https://hdl.handle.net/11572/335243
Publikováno v:
La Matematica, 3 753-776 (2024)
The essential variety is an algebraic subvariety of dimension $5$ in real projective space $\mathbb R\mathrm P^{8}$ which encodes the relative pose of two calibrated pinhole cameras. The $5$-point algorithm in computer vision computes the real points
Externí odkaz:
http://arxiv.org/abs/2212.01596
Autor:
Santarsiero, Pierpaola
We present an algorithm aimed to recognize if a given tensor is a non-identifiable rank-3 tensor.
Comment: 23 pages, with an appendix together with E. Ballico and A. Bernardi. Comments are welcome!
Comment: 23 pages, with an appendix together with E. Ballico and A. Bernardi. Comments are welcome!
Externí odkaz:
http://arxiv.org/abs/2211.06384
Autor:
Améndola, Carlos, Galuppi, Francesco, Ríos Ortiz, Ángel David, Santarsiero, Pierpaola, Seynnaeve, Tim
Publikováno v:
In Journal of Pure and Applied Algebra January 2025 229(1)
