相关论文: Stability of discrete empirical interpolation and …

Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…

In the present paper we consider Laplace deconvolution for discrete noisy data observed on the interval whose length may increase with a sample size. Although this problem arises in a variety of applications, to the best of our knowledge,…

Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…

Sampling and Variational Inference (VI) are two large families of methods for approximate inference that have complementary strengths. Sampling methods excel at approximating arbitrary probability distributions, but can be inefficient. VI…

Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…

A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…

We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…

We present a new analysis of the stability of extended Floater-Hormann interpolants, in which both noisy data and rounding errors are considered. Contrary to what is claimed in the current literature, we show that the Lebesgue constant of…

This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive…

We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…

We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…

Diffraction-based methods have become an invaluable tool for the detailed assessment of residual strain and stress within experimental mechanics. These methods typically measure a component of the average strain within a gauge volume. It is…

The over-damped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is…

We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…

Tomographic imaging is in general an ill-posed inverse problem. Typically, a single regularized image estimate of the sought-after object is obtained from tomographic measurements. However, there may be multiple objects that are all…

We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…

This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is…

In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…

This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of…

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…