… This result concerns Lipschitz functions on triangulable, … d is any p-stable distance on
finitely presented n-parameter … multiparameter persistence landscapes are 1-Lipschitz stable …

… are built to handle a one-parameter family of persistence diagrams. While this collection of
methods includes multiparameter persistence 45 … to Lipschitz functions), the Betti curves are at …

… , however, are based on kernels. This paper presents persistence indicator functions (PIFs), …
In this paper, we describe a summarizing function for persistence diagrams, the . were …

… In this paper, we are concerned with estimating the persistence intensity function and a …
As we show below in Theorem 3.1,L∞-consistency for the persistence intensity function is a …

… have more regularity (eg Lipschitz or Hölder) under additional assumptions. Section 5.2 states
a very concise law of large for persistence … For any ε > 0, there exists a L-Lipschitz function …

In Topological Data Analysis, a common way of quantifying the shape of data is to use a
persistence diagram (PD). PDs are multisets of points in R2 computed using tools of algebraic …

… It is well known that metric regularity is persistent with respect to small Lipschitz perturbation
(cf. [2, Theorem 3.3]), ie, if \(F:X\rightrightarrows Y\) is a closed multifunction and is metrically …

… with respect to property P (or Pstable), if for every value of h … on positive parameters by using
the Lipschitz-type inequality. … Discrete and continuous fractional persistence problems-the …

… are used to make inferences about the shape of data. A popular topological summary is the
persistence … a notion of global probability density function for persistence diagrams that fully …

… by the choice of filtrations and persistence signatures (respectively the input and output
of PH), and in particular, that PH features are often not robust to noise in a classification task. …