Related papers: Critical length: an alternative approach

We survey the state of the art on the algorithmic analysis of discrete linear dynamical systems, focussing in particular on reachability, model-checking, and invariant-generation questions, both unconditionally as well as relative to…

We present randomized algorithms based on block Krylov space method for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. Using the properties of Chebyshev polynomial and Gaussian random matrix, we…

This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…

Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in…

The definition of the standard differential operator is extended from integer steps to arbitrary stepsize. The classical, nonrelativistic Hamiltonian is quantized, using these new continuous operators. The resulting Schroedinger type…

We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be…

Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of…

We investigate the problem of numerical differentiation of bivariate functions from weighted Wiener classes using Chebyshev polynomial expansions. We develop and analyze a new version of the truncation method based on Chebyshev polynomials…

We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…

Some existence results for a parametric Dirichlet problem defined on the Sierpi\'nski fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well…

The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differential equation has a zero in a given interval of real numbers. This is a fundamental reachability problem for continuous linear dynamical systems,…

Real linear operators emerge in a range of mathematical physics applications. In this paper spectral questions of compact real linear operators are addressed. A Lomonosov-type invariant subspace theorem for antilinear compact operators is…

Regular expressions and automata models with capture variables are core tools in rule-based information extraction. These formalisms, also called regular document spanners, use regular languages in order to locate the data that a user wants…

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…

Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted…

In this work, firstly the maximal sectorial linear relations are described. Later on, the discreteness of the spectrum of the linear maximal sectorial operators and asymptotical behaviour of the eigenvalues of such operators in terms of the…

We study the Steklov problem on hypersurfaces of revolution with two boundary components in Euclidean space. In a recent article, the phenomenon of critical length, at which a Steklov eigenvalue is maximized, was exhibited and multiple…

We treat a version of the multiple-choice secretary problem called the multiple-choice duration problem, in which the objective is to maximize the time of possession of relatively best objects. It is shown that, for the $m$--choice duration…

The purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in order to write a fractional differential…

In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to…