相关论文: Generic consistency and nondegeneracy of verticall…

This paper is concerned with global existence as well as infinite-time blowups of classical solutions to the following fully parabolic kinetic system \begin{equation} \begin{cases} u_t=\Delta (\gamma (v)u) v_t-\Delta v+v=u \end{cases}…

Monotone variational inequalities (VIs) provide a unifying framework for convex minimization, equilibrium computation, and convex-concave saddle-point problems. Extragradient-type methods are among the most effective first-order algorithms…

We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…

We propose a novel zeroth-order optimization algorithm based on an efficient sampling strategy. Under mild global regularity conditions on the objective function, we establish non-asymptotic convergence rates for the proposed method.…

This paper treats the global stabilization problem of continuous-time switched affine systems that have rank-deficient convex combinations of their dynamic matrices. For these systems, the already known set of attainable equilibrium points…

A good generalization of the Euclidean dimension to disordered systems and non crystalline structures is commonly required to be related to large scale geometry and it is expected to be independent of local geometrical modifications. The…

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

It is known that up to certain pathologies, a compact metric graph with standard vertex conditions has a Baire-generic set of choices of edge lengths such that all Laplacian eigenvalues are simple and have eigenfunctions that do not vanish…

In this paper, a method of improving vertical positioning accuracy with the Global Positioning System (GPS) information and barometric pressure values is proposed. Firstly, we clear null values for the raw data collected in various…

For the 2D and 3D Virtual Element Methods (VEM), a new approach to improve the conditioning of local and global matrices in the presence of badly-shaped polytopes is proposed. It defines the local projectors and the local degrees of freedom…

Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in…

Parameterless stopping criteria for recursive polynomial expansions to construct the density matrix in electronic structure calculations are proposed. Based on convergence order estimation the new stopping criteria automatically and…

The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…

We provide a partially affirmative answer to the following question on robustness of polynomial stability with respect to sampling: ``Suppose that a continuous-time state-feedback controller achieves the polynomial stability of the…

We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix.…

We consider a complete, unbounded, hyperbolic metric space $X$ and a concave, nonzero and nondecreasing function $\omega:[0,+\infty)\to[0,+\infty)$ with $\omega(0)=0$ and study the space $\mathcal{C}_\omega(X)$ of uniformly continous…

The purpose of this note is to establish, in terms of the primary coefficients in the framework of the tridiagonal theory developed by Delsarte and Genin in the environment of nonnegative definite Toeplitz matrices, necessary and sufficient…

The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of…

In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…

We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps,…