Related papers: The rank invariant stability via interleavings

We study the stability of general weakly coupled systems subject to a reduced number of local or boundary controls. We show that, under Kalman's rank condition, the exponential stability of the underlying scalar equation implies polynomial…

This study presents a theoretical analysis on the efficiency of interleaving, an efficient online evaluation method for rankings. Although interleaving has already been applied to production systems, the source of its high efficiency has…

Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…

In a previous paper [JCAP06, 033 (2018)] we have proved that it is possible to have a stable false vacuum in a potential that is unbounded from below. In this paper we discuss the Physics related to our theoretical and numerical results. We…

We study the invasion of an unstable state by a propagating front in a peculiar but generic situation where the invasion process exhibits a remnant instability. Here, remnant instability refers to the fact that the spatially constant…

We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…

Answering questions of Y. Rabinovich, we prove "stability" versions of upper bounds on maximal independent set counts in graphs under various restrictions. Roughly these say that being close to the maximum implies existence of a large…

We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of…

The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…

We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…

Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before…

Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…

Based on the eigenvalue idea and the time-varying weighted vector norm in state space we construct here the lower and upper bounds on the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the…

Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…

In this work the stability of perturbed linear time-varying systems is studied. The main features of the problem are threefold. Firstly, the time-varying dynamics is not required to be continuous but allowed to have jumps. Also the system…

Necessary and sufficient conditions for the internal stability of formations whose dynamics are obtained is determined by linear differential equations.

We prove that the upper bounds for the consistency strength of certain instances of mutual stationarity considered by Liu-Shelah~\cite{MR1469093} are close to optimal. We also consider some related and, as it turns out, stronger properties.

Toward explaining the persistence of biased inferences, we propose a framework to evaluate competing (mis)specifications in strategic settings. Agents with heterogeneous (mis)specifications coexist and draw Bayesian inferences about their…

We introduce a novel framework of ranking with abstention, where the learner can abstain from making prediction at some limited cost $c$. We present a extensive theoretical analysis of this framework including a series of $H$-consistency…

The interleaving distance, although originally developed for persistent homology, has been generalized to measure the distance between functors modeled on many posets or even small categories. Existing theories require that such a poset…