To mitigate the bias exhibited by machine learning models, fairness criteria can be
integrated into the training process to ensure fair treatment across all demographics, but it …

The Čech and Rips constructions of persistent homology are stable with respect to
perturbations of the input data. However, neither is robust to outliers, and both can be …

Abstract Topological Data Analysis (TDA) is a discipline that applies algebraic topology
techniques to analyze complex, multi-dimensional data. Although it is a relatively new field …

Abstract The Delaunay filtration D.(X) of a point cloud X⊂ ℝd is a central tool of
computational topology. Its use is justified by the topological equivalence of D.(X) and the …

For a finite set of balls of radius r, the k-fold cover is the space covered by at least k balls.
Fixing the ball centers and varying the radius, we obtain a nested sequence of spaces that is …

Given a finite set A⊂ R d, let Cov r, k denote the set of all points within distance r to at least k
points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow …

As a step towards establishing homotopy-theoretic foundations for topological data analysis
(TDA), we introduce and study homotopy interleavings between filtered topological spaces …

The alpha complex is a fundamental data structure from computational geometry, which
encodes the topological type of a union of balls B (x; r)⊂ R m for x∈ S, including a weighted …

We study the size of Sheehy's subdivision bifiltrations, up to homotopy. We focus in
particular on the subdivision-Rips bifiltration $\mathcal {SR}(X) $ of a metric space $ X $, the …

Motivated by applications in the sciences, we study finite chromatic sets in Euclidean space
from a topological perspective. Based on the persistent homology for images, kernels and …