相关论文: Note on the Construction of Structure Tensor

Pairwise Fisher graphs capture local covariance information, but they cannot distinguish an irreducible multi-observable radiation pattern from a collection of ordinary pairwise correlations. We show that this missing structure is naturally…

Inspired by the ConvNets with structured hidden representations, we propose a Tensor-based Neural Network, TCNN. Different from ConvNets, TCNNs are composed of structured neurons rather than scalar neurons, and the basic operation is neuron…

We introduce a new consistency-based approach for defining and solving nonnegative/positive matrix and tensor completion problems. The novelty of the framework is that instead of artificially making the problem well-posed in the form of an…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

A notion of distorted torsion tensor was introduced by Okubo, in the establishment of the Nijenhuis-Bianchi identity and of BRST-like operators. These quantities are constructed with the help of the Nijenhuis tensor, which in turn is…

We re-consider the graviton self-energy induced by a loop of massless, minimally coupled scalars on de Sitter background. On flat space background it can be represented as a sum of two tensor differential operators acting on scalar…

We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…

We define three types of upper (and lower) triangular blocked tensors, which are all generalizations of the triangular blocked matrices. We study some basic properties and characterizations of these three types of triangular blocked…

This paper introduces Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR), a novel tensor regression framework that enhances interpretability and performance through mode-specific hybrid regularization and nonnegativity…

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…

We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the…

We explain spin structure for a spin-one hadron, in which there are new structure functions, in addition to the ones ($F_1$, $F_2$, $g_1$, $g_2$) which exist for the spin-1/2 nucleon, associated with its tensor structure. The new structure…

In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to intermediate variables (``states'') of dimension lower than the…

Kastor and Traschen constructed totally anti-symmetric conserved currents that are linear in the Riemann curvature in spacetimes admitting Killing-Yano tensors. The construction does not refer to any field equations and is built on the…

Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…

Mathematical foundation of the novel concept of quantum tensor product by Zanardi et al is rigorously established. The concept of relative quantum entanglement is naturally introduced and its meaning is made clear both mathematically and…