Synthetic control methods are commonly applied in empirical research to estimate the
effects of treatments or interventions on aggregate outcomes. A synthetic control estimator …

TetGen® is a C++ program for generating good quality tetrahedral meshes aimed to support
numerical methods and scientific computing [Hang Si] 1. The problem of quality tetrahedral …

Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

The Vietoris-Rips complex characterizes the topology of a point set. This complex is popular
in topological data analysis as its construction extends easily to higher dimensions. We …

Given the enormous scale and diverse distribution of 2D point cloud data, an adaptive
Hilbert curve insertion algorithm which has quasi-linear time complexity is proposed to …

TetGen is a program to generate tetrahedral meshes from 3d polyhedral domains. Its goal is
to generate good quality tetrahedral meshes suitable for various applications in scientific …

We give a provably correct algorithm to reconstruct ak-dimensional manifold embedded in d-
dimensional Euclidean space. Input to our algorithm is a point sample coming from an …

Scientific data is often in the form of a finite set of noisy points, sampled from an unknown
space, and embedded in a high-dimensional space. Topological data analysis focuses on …

We associate with each compact set X of Rn two real-valued functions cX and hX defined on
R+ which provide two measures of how much the set X fails to be convex at a given scale …

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 …