21 citations · 22 across the 7 of their papers we have counts for
8 papers
The Volume Exchange Metric
Enrique Alvarado, Joseph Jung, Jeremy Mason +2
The volume exchange metric between cell structures embedded in Euclidean space is introduced. Intuitively, it measures the minimum amount of volume that must be swept out to contin…
Box Filtration
Enrique Alvarado, Prashant Gupta, Bala Krishnamoorthy
We define a new framework that unifies the filtration and mapper approaches from TDA, and present efficient algorithms to compute it. Termed the box filtration of a PCD, we grow bo…
Partial Plateau's Problem with -mass
Enrique Alvarado, Qinglan Xia
Classically, Plateau's problem asks to find a surface of the least area with a given boundary . In this article, we investigate a version of Plateau's problem, where the boundar…
Geometry of a Set and its Random covers
Enrique Alvarado, Bala Krishnamoorthy, Kevin R. Vixie
Let be a bounded open subset of . We study the following questions: For i.i.d. samples drawn uniformly from , what is the probability that $\…
Representations of Energy Landscapes by Sublevelset Persistent Homology: An Example With n-Alkanes
Joshua Mirth, Yanqin Zhai, Johnathan Bush +8
Encoding the complex features of an energy landscape is a challenging task, and often chemists pursue the most salient features (minima and barriers) along a highly reduced space,…
The Maximum Distance Problem and Minimal Spanning Trees
Enrique G. Alvarado, Bala Krishnamoorthy, Kevin R. Vixie
Given a compact and , the maximum distance problem seeks a compact and connected subset of of smallest one dimensional Hausdorff meas…
A Lower Bound for the Reach of Flat Norm Minimizers
Enrique G. Alvarado, Kevin R. Vixie
We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in .
On the Measure of the Midpoints of the Cantor Set in
Enrique Alvarado, Yunfeng Hu
In this paper, we are going to discuss the following problem: Let be a fixed set in . And let and he two subsets in such that for any i…