相关论文: Global Uniqueness and Solvability for Tensor Compl…

Matrix representations of quantum operators are computationally complete but often obscure the structural topology of information flow within a quantum circuit \cite{nielsen2000}. In this paper, we introduce a generalized graph-theoretic…

Partitioned global address space (PGAS) is a parallel programming model for the development of applications on clusters. It provides a global address space partitioned among the cluster nodes, and is supported in programming languages like…

In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the…

A tensor ${\mathcal A}$ of order $m$ and dimension $n$ is called a ${\rm Q}$-tensor if the tensor complementarity problem has a solution for all ${\bf q} \in {\mathbb R}^{n}$. This means that for every vector ${\bf q}$, there exists a…

Processing multidomain data defined on multiple graphs holds significant potential in various practical applications in computer science. However, current methods are mostly limited to discrete graph filtering operations. Tensorial partial…

A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…

We extend the notion of localic completion of generalised metric spaces by Steven Vickers to the setting of generalised uniform spaces. A generalised uniform space (gus) is a set X equipped with a family of generalised metrics on X, where a…

Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural…

We prove the congruence subgroup property for the centralizer of a finite subgroup $G$ in the mapping class group of a hyperbolic oriented and connected surface of finite topological type $S$ such that the genus of the quotient surface…

Copositivity of tensors plays an important role in vacuum stability of a general scalar potential, polynomial optimization, tensor complementarity problem and tensor generalized eigenvalue complementarity problem. In this paper, we propose…

CP decomposition is a powerful tool for data science, especially gene analysis, deep learning, and quantum computation. However, the application of tensor decomposition is largely hindered by the exponential increment of the computational…

In this article, we examine the possibility that there exist special scalar-tensor theories of gravity with completely nonsingular FRW solutions. Our investigation in fact shows that while most probes living in such a Universe never see the…

This article is devoted to the study of existence of a mass conserving global solution for the collision-induced nonlinear fragmentation model which arises in particulate processes, with the singular type of collision kernel. The above…

We introduce and study the Doubly Balanced Connected graph Partitioning (DBCP) problem: Let $G=(V,E)$ be a connected graph with a weight (supply/demand) function $p:V\rightarrow \{-1,+1\}$ satisfying $p(V)=\sum_{j\in V} p(j)=0$. The…

Existing tensor completion formulation mostly relies on partial observations from a single tensor. However, tensors extracted from real-world data are often more complex due to: (i) Partial observation: Only a small subset (e.g., 5%) of…

Orthogonal decomposition of tensors is a generalization of the singular value decomposition of matrices. In this paper, we study the spectral theory of orthogonally decomposable tensors. For such a tensor, we give a description of its…

Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode…

Sormani and Wei proved in 2004 that a compact geodesic space has a categorical universal cover if and only if its covering/critical spectrum is finite. We add to this several equivalent conditions pertaining to the geometry and topology of…

In this paper, we study rigidity aspects of Penrose's singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces…

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications…