Related papers: A variational approach based on perturbed eigenval…

We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable and we quantitatively investigate the rate of convergence of…

Applying perturbation theory methods, the absence of the point spectrum for some nonselfadjoint integro-differential operators is investigated. The considered differential operators are of arbitrary order and act in either…

In order to reach the sensitivity required to detect gravitational waves, pulsar timing array experiments need to mitigate as much noise as possible in timing data. A dominant amount of noise is likely due to variations in the dispersion…

Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are…

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…

We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of…

This paper proposes robust estimators of the variogram, a statistical tool that is commonly used in geostatistics to capture the spatial dependence structure of data. The new estimators are based on the highly robust minimum covariance…

In this paper we introduce a family of stochastic gradient estimation techniques based of the perturbative expansion around the mean of the sampling distribution. We characterize the bias and variance of the resulting Taylor-corrected…

In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…

Variational phase-field models of fracture are widely used to simulate nucleation and propagation of cracks in brittle materials. They are based on the approximation of the solutions of free-discontinuity fracture energy by two smooth…

This paper introduces a new algorithm to improve the accuracy of numerical phase-averaging in oscillatory, multiscale, differential equations. Phase-averaging is a timestepping method which averages a mapped variable to remove highly…

We propose a new nonparametric procedure for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second- order) piecewise stationary process, which also identifies the components of…

Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…

Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…

In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…

Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key…

This paper proposes a robust test for assessing isotropy based on the variogram of spatial data on a two-dimensional regular grid. The test is based on the non-robust subsampling test for isotropy of Guan et al. (2004), which uses the idea…

We develop and analyze quadrature blending schemes that minimize the dispersion error of isogeometric analysis up to polynomial order seven with maximum continuity in the span ($C^{p-1}$). The schemes yield two extra orders of convergence…

This study presents a nonlinear signal processing method for accurate radar-based heartbeat interval estimation by exploiting the periodicity of higher-order harmonics inherent in heartbeat signals. Unlike conventional approaches that…