Related papers: Stability results for solutions of obstacle proble…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…
Resilience broadly describes a quality of withstanding perturbations. Measures of system resilience have gathered increasing attention across applied disciplines, yet existing metrics often lack computational accessibility and…
In this paper, we develop a general approach to prove stability for the non linear second step of hybrid inverse problems. We work with general functionals of the form $\sigma|\nabla u|^p$, $0 < p \leq 1$, where $u$ is the solution of the…
We introduce the boundary measure at scale r of a compact subset of the n-dimensional Euclidean space. We show how it can be computed for point clouds and suggest these measures can be used for feature detection. The main contribution of…
We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP--hard…
We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…
Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general…
Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is…
The conformal method in general relativity aims to successfully parametrise the set of all initial data associated with globally hyperbolic spacetimes. One such mapping was suggested by David Maxwell. I verify that the solutions of the…
The aim of this note is to review some recent developments on the regularity theory for the stationary and parabolic obstacle problems. After a general overview, we present some recent results on the structure of singular free boundary…
In this paper, we study stochastic stability of a dynamical system with shadowing property, which evolves under small random perturbation. We prove that time averages along the pseudo-trajectory converge with respect to stationary measure…
We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…
This paper focuses on using the first curvature $\kappa(t)$ of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems [Y. Wang, H. Sun, Y. Song et al.,…
In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions…
We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the…