Related papers: Stable Invariants for Multiparameter Persistence
We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our…
Persistent homology is a popular technique in topological data analysis that tracks the lifespans of homological features in a nested sequence of spaces. This data is typically presented in a multi-set called a persistence diagram or a…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
The proposed feature selection method builds a histogram of the most stable features from random subsets of a training set and ranks the features based on a classifier based cross-validation. This approach reduces the instability of…
To get a good understanding of a dynamical system, it is convenient to have an interpretable and versatile model of it. Timed discrete event systems are a kind of model that respond to these requirements. However, such models can be…
The matter of the stability for multi-asset American option pricing problems is a present remaining challenge. In this paper a general transformation of variables allows to remove cross derivative terms reducing the stencil of the proposed…
Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…
We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
This article grew out of the theoretical part of my Master's thesis at the Faculty of Mathematics and Information Science at Ruprecht-Karls-Universit\"at Heidelberg under the supervision of PD Dr. Andreas Ott. Following the work of G.…
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds, networks, and functions. However, their use in statistical…
This work studies robustness to system disturbance and measurement noise of some popular general practical stabilization techniques, namely, Dini aiming, optimization-based stabilization and inf-convolution stabilization. Common to all…
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…
In this paper, we demonstrate that in many NP-complete variants of the stable matching problem, such as the Stable Hypergraph Matching problem, the Stable Multicommodity Flow problem, and the College Admission problem with common quotas, a…
Multiparameter persistence modules can be uniquely decomposed into indecomposable summands. Among these indecomposables, intervals stand out for their simplicity, making them preferable for their ease of interpretation in practical…
While powerful methods have been developed for high-dimensional hypothesis testing assuming orthogonal parameters, current approaches struggle to generalize to the more common non-orthogonal case. We propose Stable Distillation (SD), a…
Elastic constants are central material properties, frequently reported in experimental and theoretical studies. While their computation is straightforward in the absence of thermal fluctuations, finite--temperature methods often suffer from…
Updating machine learning models with new information usually improves their predictive performance, yet, in many applications, it is also desirable to avoid changing the model predictions too much. This property is called stability. In…
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
We construct stable configurations of n overlapping discs of radius r in a unit square, with r = O(1/n). By a result of Diaconis, Lebeau, and Michel, this result is best possible, up to a constant factor. A consequence is that the…