8 citations · 19 across the 6 of their papers we have counts for
6 papers
Simplicial Complex Representation Learning
Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou +2
Simplicial complexes form an important class of topological spaces that are frequently used in many application areas such as computer-aided design, computer graphics, and simulati…
Persistent Homology and Graphs Representation Learning
Mustafa Hajij, Ghada Zamzmi, Xuanting Cai
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically,…
A cellular basis for the generalized Temperly-Lieb Algebra and Mahler Measure
Xuanting Cai, Robert G. Todd
Just as the Temperley-Lieb algebra is a good place to compute the Jones polynomial, the Kauffman bracket skein algebra of a disk with colored points on the boundary, each with…
On the Turaev-Viro endomorphism, and the colored Jones polynomial
Xuanting Cai, Patrick M. Gilmer
By applying a variant of the TQFT constructed by Blanchet, Habegger, Masbaum, and Vogel, and using a construction of Ohtsuki, we define a module endomorphism for each knot K by usi…
Bilinear Forms on Skein Modules and Steps in Dyck Paths
Xuanting Cai, Toufik Mansour
We use Jones-Wenzl idempotents to construct bases for the relative Kauffman bracket skein module of a square with n points colored 1 and one point colored h. We consider a natural…
A Gram Determinant For Lickorish's Bilinear Form
Xuanting Cai
We use the Jones-Wenzl idempotents to construct a basis of Temperley-Lieb algebra TL_n. This allows a short calculation for a Gram determinant of Lickorish's bilinear form on the T…