相关论文: Notes on an Elementary Proof for the Stability of …

This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.

We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…

This is essentially an expository note based on S. Paul's works on the stability of pairs. Its connection to K-stability will be also discussed.

This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.

We generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the setting of constructible persistence modules valued in a symmetric monoidal category. We call this the type A persistence diagram of a persistence…

To our knowledge, the analysis of convergence rates for persistence diagrams estimation from noisy signals has predominantly relied on lifting signal estimation results through sup-norm (or other functional norm) stability theorems. We…

In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistences module valued in any small abelian category.

The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bottleneck distance between diagrams and the $\infty$-norm of…

This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of solutions snapshots, what…

In this paper we obtain the stability theorem for the independence number of $G(n, r, 1)$ graphs. This result was previously stated in the paper of M. Pyaderkin but the proof there was incorrect. We introduce the correct proof of the key…

We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.

The present note sketches a theory of constructs.

In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…

The primary objective of this paper is to introduce Hyers-Ulam-type stability results for monotone, subadditive, and convex graphs. We consider their standard definitions in an approximate sense and demonstrate the existence of a…

This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…

This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…

The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…