38 citations · 199 across the 44 of their papers we have counts for
5 papers · 1 filter
Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial
Jesse S F Levitt, Mustafa Hajij, Radmila Sazdanovic
We examine the structure and dimensionality of the Jones polynomial using manifold learning techniques. Our data set consists of more than 10 million knots up to 17 crossings and t…
Framed Knots
Mohamed Elhamdadi, Mustafa Hajij, Kyle Istvan
This article gives a foundational account of various characterizations of framed links in the -sphere.
Propagate and Pair: A Single-Pass Approach to Critical Point Pairing in Reeb Graphs
Junyi Tu, Mustafa Hajij, Paul Rosen
With the popularization of Topological Data Analysis, the Reeb graph has found new applications as a summarization technique in the analysis and visualization of large and complex…
TopoLines: Topological Smoothing for Line Charts
Paul Rosen, Ashley Suh, Christopher Salgado +1
Line charts are commonly used to visualize a series of data values. When the data are noisy, smoothing is applied to make the signal more apparent. Conventional methods used to smo…
Mesh Learning Using Persistent Homology on the Laplacian Eigenfunctions
Yunhao Zhang, Haowen Liu, Paul Rosen +1
We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst triangulated 2-manifolds. Our method relies on studying the lower-star filtrat…