Related papers: Resolvent estimates with mild trapping

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…

A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides…

We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…

We consider infinite-dimensional parabolic rough evolution equations. Using regularizing properties of analytic semigroups we prove global-in-time existence of solutions and investigate random dynamical systems for such equations.

We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…

Experimental mean flows are commonly used to study wall-bounded turbulence. However, these measurements are often unable to resolve the near-wall region and thus introduce ambiguity in the velocity closest to the wall. This poses a source…

Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being…

We study nonlinear stability of pulled fronts in scalar parabolic equations on the real line of arbitrary order, under conceptual assumptions on existence and spectral stability of fronts. In this general setting, we establish sharp…

In this paper we show how to obtain decay estimates for the damped wave equation on a compact manifold without geometric control via knowledge of the dynamics near the un-damped set. We show that if replacing the damping term with a…

We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…

We consider a family of spherically symmetric, asymptotically Euclidean manifolds with two trapped sets, one which is unstable and one which is semi-stable. The phase space structure is that of an inflection transmission set. We prove a…

Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…

Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…

Representation learning (RL) methods learn objects' latent embeddings where information is preserved by distances. Since distances are invariant to certain linear transformations, one may obtain different embeddings while preserving the…

Recent empirical and theoretical work has shown that the dynamics of the large eigenvalues of the training loss Hessian have some remarkably robust features across models and datasets in the full batch regime. There is often an early period…

In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators under strong absorption conditions. We establish improved geometric regularity along the free boundary, for a sharp value…

Model averaging techniques based on resampling methods (such as bootstrapping or subsampling) have been utilized across many areas of statistics, often with the explicit goal of promoting stability in the resulting output. We provide a…

In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…

In this note, we obtain the rigidity of the sharp Cheng-Yau gradient estimate for positive harmonic functions on surfaces with nonegative Gaussian curvature, the rigidity of the sharp Li-Yau gradient estimate for positive solutions to heat…