相关论文: A new S-type eigenvalue localization set for tenso…

In this paper, we mainly focus on how to generalize some conclusions from nonnegative irreducible tensors to nonnegative weakly irreducible tensors. To do so, a basic and important lemma is proven using new tools. First, we give the…

In the past few years, the slice-rank lemma of Tao has been applied successfully to many problems in extremal combinatorics. In this paper, first, we define a new notion of triangular tensors which generalizes that of triangular matrices…

In this text, we consider an N by N random matrix X such that all but o(N) rows of X have W non identically zero entries, the other rows having lass than $W$ entries (such as, for example, standard or cyclic band matrices). We always…

In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking…

Circulant tensors naturally arise from stochastic process and spectral hypergraph theory. The joint moments of stochastic processes are symmetric circulant tensors. The adjacency, Laplacian and signless Laplacian tensors of circulant…

In this paper, we introduce a new semi-norm of operators on a semi-Hilbertian space, which generalizes the A-numerical radius and A-operator semi-norm. We study the basic properties of this semi-norm, including upper and lower bounds for…

In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors. We formulate the invariance properties of the loss function and show that critical points detected by…

Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator $O$ we define a set $\Lambda_n\subset \mathbb{R}$, and we show that it converges to…

Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…

We apply a method developed by one of the authors, see \cite{Arl1}, to localize the numerical range of \textit{quasi-sectorial} contractions semigroups. Our main theorem establishes a relation between the numerical range of quasi-sectorial…

This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…

We classify tensors with maximal and next to maximal dimensional symmetry groups under a natural genericity assumption (1-genericity), in dimensions greater than 7. In other words, we classify minimal dimensional orbits in the space of…

We construct a lower bound of the tensor rank for a new class of tensors, which we call persistent tensors. We present three specific families of persistent tensors, of which the lower bound is tight. We show that there is a chain of…

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases. We formulate irreducibility and symmetry properties of a…

In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work, Niyogi, Smale, and Weinberger studied samples of $C^2$…

We measure electron localization in different materials by means of a ``localization tensor'', based on Berry phases and related quantities. We analyze its properties, and we actually compute such tensor from first principles for several…

We compute the signed distribution of the eigenvalues/vectors of the complex order-three random tensor by computing a partition function of a four-fermi theory, where signs are from a Hessian determinant associated to each eigenvector. The…

We show how methods of algebraic geometry can produce criteria for the identifiability of specific tensors that reach beyond the range of applicability of the celebrated Kruskal criterion. More specifically, we deal with the symmetric…

The higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recently, polynomial time algorithms…