Related papers: On stable patterns and properties on permutations …

Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…

We study the recently introduced notion of output-input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. The subject of this paper is developing the theory of output-input…

In this paper we show that the dynamics of a class of kinetic compartmental models with bounded capacities, monotone reaction rates and a strongly connected interconnection structure is persistent. The result is based on the chemical…

This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…

In this work, we show that Latent Flow-Matching (LFM) models are robust to different types of perturbations, including data reduction and model capacity shrinkage. We characterize this stability by their tendency to generate similar outputs…

We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not…

We present some results on the proportion of permutations of length $n$ containing certain mesh patterns as $n$ grows large, and give exact enumeration results in some cases. In particular, we focus on mesh patterns where entire rows and…

We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…

We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…

We investigate how the following properties are related to each other: i)-A manifold is "transversally" exponentially stable; ii)-The "transverse" linearization along any solution in the manifold is exponentially stable; iii)-There exists a…

We study generically stable types/measures in both classical and continuous logics, and their connection with randomization and modes of convergence of types/measures.

The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…

Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability…

We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…

Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…

We show that evolutionarily stable states in general (nonlinear) population games (which can be viewed as continuous vector fields constrained on a polytope) are asymptotically stable under a multiplicative weights dynamic (under…

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of…

The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…

Using the approach suggested in [arXiv:1002.2761] we present below a sufficient condition guaranteeing that two collections of patterns of permutations have the same exponential generating functions for the number of permutations avoiding…

Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…