In this paper, the symmetric character of the thermal conductivity tensor for anisotropic materials is established based on arguments from tensor analysis and the physical constraints on the domain of definition of the conductivity tensor. The non-si...
In this paper, a tensor splitting AOR iterative method for solving the
The statement of the eigenvalue problem for a tensor–block matrix (TBM) of any order and of any even rank is formulated, and also some of its special cases are considered. In particular, using the canonical presentation of the TBM of the tensor...
In this paper, we aim to develop an efficient algorithm for the solving Tensor Robust Principal Component Analysis (TRPCA) problem, which focuses on obtaining a low-rank approximation of a tensor by separating sparse and impulse noise. A common appro...
We develop a systematic way to solve linear equations involving tensors of arbitrary rank. We start off with the case of a rank 3 tensor, which appears in many applications, and after finding the condition for a unique solution we derive this solutio...
Low-rank tensor recovery has attracted much attention among various tensor recovery approaches. A tensor rank has several definitions, unlike the matrix rank—e.g., the CP rank and the Tucker rank. Many low-rank tensor recovery methods are focused on...
Tensor rank decomposition is a useful tool for geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able to estimate how man...
This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that un...
In this paper an efficient method for signal change detection in multidimensional data streams is proposed. A novel tensor model is suggested for input signal representation and analysis. The model is built from a part of the multidimensional stream...
In the present paper, we study two different approaches of tensor decomposition. The first part aims to study some properties of tensors that result from the fact that some components are vanishing in certain coordinates. It is proven that these cond...
Due to increasingly strong and varied performance requirements, cooperative wireless communication systems today occupy a prominent place in both academic research and industrial development. The technological and economic challenges for future sixth...
In this paper, we proposed an image inpainting algorithm, including an interpolation step and a non-local tensor completion step based on a weighted tensor nuclear norm. Specifically, the proposed algorithm adopts the triangular based linear interpol...
In this paper, we extend the definition of tensor products from using an invertible matrix to utilising right-invertible matrices, exploring the algebraic properties of these new tensor products. Based on this novel definition, we define the concepts...
We write the Kerr–Schild tetrads in terms of the flat space–time tetrads and of a (1, 1) tensor
Herein, we investigate scalar–tensor and bi-scalar–tensor modified theories of gravity that can alleviate the
An intensity tensor of quadrupole doublets and an electric field gradient tensor for Fe3+ at M1 sites in aegirine–augite ((Ca0.16Na0.86)∑1.02(Mg0.13Fe2+0.04Fe3+0.72 Al0.07)∑0.96Si2.01O6) are determined using single-crystal Mössbaue...
In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensor...
Matrix completion, the problem of completing missing entries in a data matrix with low-dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog that attempts to impute missing tensor...
The paper deals with the study of Z-symmetric manifolds
The rendering of tensor glyphs is a progressive process of visualizing the vector space both in fluid dynamics and the latest medical scanning. Nowadays, the rendering accuracy is ensured by numerical methods based on interpolation of tensor function...
Most metal plates are orthorhombic aggregates of cubic crystallites. First, we discuss the representations of the stress tensor, the strain tensor, the elasticity tensor, and the rotation tensor under the Kelvin notation. Then, we give the decomposit...
This paper presents a tensor approximation algorithm, based on the Levenberg–Marquardt method for the nonlinear least square problem, to decompose large-scale tensors into the sum of the products of vector groups of a given scale, or to obtain...
Quaternion tensor decompositions have recently been the center of focus due to their wide potential applications in color data processing. In this paper, we establish a simultaneous decomposition for a quaternion tensor quaternity under Einstein prod...
Tensor-based multi-view spectral clustering methods are promising in practical clustering applications. However, most of the existing methods adopt the
We discuss the non-uniqueness of the rank 1 tensor decomposition for rank 4 tensors of format
As a promising data analysis technique, sparse modeling has gained widespread traction in the field of image processing, particularly for image recovery. The matrix rank, served as a measure of data sparsity, quantifies the sparsity within the Kronec...
Most modern communication systems, such as those intended for deployment in IoT applications or 5G and beyond networks, utilize multiple domains for transmission and reception at the physical layer. Depending on the application, these domains can inc...
Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for...
The fundamental challenge of salient object detection is to find the decision boundary that separates the salient object from the background. Low-rank recovery models address this challenge by decomposing an image or image feature-based matrix into a...
Let
Many tasks in computer vision suffer from missing values in tensor data, i.e., multi-way data array. The recently proposed tensor tubal nuclear norm (TNN) has shown superiority in imputing missing values in 3D visual data, like color images and video...
A tensor representation structure based on the multilayer tensor spectrum pyramid (MLTSP) is introduced in this work. The structure is “truncated”, i.e., part of the high-frequency spectrum coefficients is cut-off, and on the retained low-frequency c...
Nonlinear (NL) and multilinear (ML) systems play a fundamental role in engineering and science. Over the last two decades, active research has been carried out on exploiting the intrinsically multilinear structure of input–output signals and/or...
A linear transformation from vector space to another vector space can be represented as a matrix. This close relationship between the matrix and the linear transformation is helpful for the study of matrices. In this paper, the tensor is regarded as...
The rapid development of sensor technology gives rise to the emergence of huge amounts of tensor (i.e., multi-dimensional array) data. For various reasons such as sensor failures and communication loss, the tensor data may be corrupted by not only sm...
Interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used for supervised l...
Tensor restoration finds applications in various fields, including data science, image processing, and machine learning, where the global low-rank property is a crucial prior. As the convex relaxation to the tensor rank function, the traditional tens...
In this article, a-Browder’s classical theorem is considered through the property
A 2D metric space has a limited number of properties through which it can be described. This metric space may comprise objects such as a scalar, a vector, and a rank-2 tensor. The paper provides a comprehensive description of relations between object...
Radio-frequency (RF) tomographic imaging is a promising technique for inferring multi-dimensional physical space by processing RF signals traversed across a region of interest. Tensor-based approaches for tomographic imaging are superior at detecting...
In this paper, we study the existence, construction and number of
Video Object Tracking (VOT) is a critical task in computer vision. While Siamese-based and Transformer-based trackers are widely used in VOT, they struggle to perform well on the OTB100 benchmark due to the lack of dedicated training sets. This chall...
The paper is concerned with some generalized versions
In an m-person symmetric game, all players are identical and indistinguishable. In this paper, we find that the payoff tensor of the player k in an m-person symmetric game is k-mode symmetric, and the payoff tensors of two different individuals are t...
In this paper, we discuss the cone of copositive tensors and its approximation. We describe some basic properties of copositive tensors and positive semidefinite tensors. Specifically, we show that a non-positive tensor (or Z-tensor) is copositive if...
We construct the smooth vector bundle of tensor densities of arbitrary weight in a coordinate-independent way. We prove the general existence of a globally smooth tensor density field, as well as the existence of a globally smooth metric density for...
Multi-channel audio signals provide a better auditory sensation to the audience. However, missing data may occur in the collection, transmission, compression, or other processes of audio signals, resulting in audio quality degradation and affecting t...
Retinal vessel segmentation is one of the preliminary tasks for developing diagnosis software systems related to various retinal diseases. In this study, a fully automated vessel segmentation system is proposed. Firstly, the vessels are enhanced usin...
The objective of our study is to generalize the results on product states of the tensor product of two JC-algebras to infinite tensor product JC-algebras. Also, we characterize the tracial product state of the tensor product of two JC-algebras, and t...
Resolution of fuzzy relational inequalities (FRIs) plays a significant role in decision-making, image compression and fuzzy control. This paper studies the resolution of a kind of FRIs with Boolean semi-tensor product composition. First, by resorting...
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