The Euler characteristic transform (ECT) is a simple to define yet powerful representation of
shape. The idea is to encode an embedded shape by tracking how the Euler characteristic …

Persistent homology is a tool that can be employed to summarize the shape of data by
quantifying homological features. When the data is an object in $\mathbb {R}^ d $, the …

Persistent homology has been an important tool in topological and geometrical data
analysis to study the shape of data. However, its ability to differentiate between various …

Abstract In Topological Data Analysis, filtered chain complexes enter the persistence
pipeline between the initial filtering of data and the final persistence invariants extraction. It …

We introduce the notion of Orthogonal M\" obius Inversion, a custom-made analog to M\"
obius inversion on the poset of intervals $\mathsf {Int}(P) $ of a linear poset $ P $. This …

Given a geometric simplicial complex, the uncountable set of (augmented) persistence
diagrams corresponding to lower-star filtrations taken with respect to all possible directions …

One perspective for studying the foundations of Topological Data Analysis (TDA) involves
investigating it through the lens of algebraic combinatorics. Mobius inversion stands out as …