相关论文: On some properties of contracting matrices

While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…

This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…

The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…

This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy,…

This paper studies non-trivial consensus--a relatively novel and unexplored convergence behavior--on directed signed matrix-weighted networks subject to both additive and multiplicative measurement noises under time-varying topologies.…

We adopt an operator-theoretic perspective to study convergence of linear fixed-point iterations and discrete- time linear systems. We mainly focus on the so-called Krasnoselskij-Mann iteration x(k+1) = ( 1 - \alpha(k) ) x(k) + \alpha(k) A…

We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a…

An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique…

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…

We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…

We study the problem of minimizing the sum of potentially non-differentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the…

Starting from the definition of a stiffness matrix, the authors present a new formulation of the Cartesian stiffness matrix of parallel mechanisms. The proposed formulation is more general than any other stiffness matrix found in the…

Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint…

We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…

We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces $\ell_1$ and $\ell_{\infty}$. We first establish properties of mappings which are monotone with respect to the non-Euclidean norms…

In this work some results on the structure-preserving diagonalization of selfadjoint and skewadjoint matrices in indefinite inner product spaces are presented. In particular, necessary and sufficient conditions on the symplectic…

We consider bipartite tight-binding graphs composed by $N$ nodes split into two sets of equal size: one set containing nodes with on-site loss, the other set having nodes with on-site gain. The nodes are connected randomly with probability…

Time-parallel algorithms, such as Parareal, are well-understood for linear problems, but their convergence analysis for nonlinear, chaotic systems remains limited. This paper introduces a new theoretical framework for analysing…