6 papers
The KnotMosaics Package for SageMath
Mary Y. Deng, Allison K. Henrich, Sean H. Kawano +1
We introduce KnotMosaics, a SageMath package for constructing, visualizing, and analyzing knot mosaic diagrams. The package represents an n-mosaic as a matrix of standard tile labe…
Taming Wild Knots with Mosaics
Mary Y. Deng, Allison K. Henrich, Sean H. Kawano +1
Wild knots--knots with infinite knotting behavior--have resisted traditional methods of knot classification, making them more of a curiosity in topology than a subject of sustained…
Topological Signatures of ReLU Neural Network Activation Patterns
Vicente Bosca, Tatum Rask, Sunia Tanweer +2
This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the po…
A tropical framework for using Porteous formula
Andrew R. Tawfeek
Given a rational polyhedral space (a tropical cycle with boundary, in the sense of Mikhalkin--Rau), one can define tropical vector bundles on having real or tropical fibers…
-Brouwer degrees in Macaulay2
Nikita Borisov, Thomas Brazelton, Frenly Espino +6
We describe the Macaulay2 package "A1BrouwerDegrees" for computing local and global -Brouwer degrees and studying symmetric bilinear forms over the complex numbers, t…
On discrete gradient vector fields and Laplacians of simplicial complexes
Ivan Contreras, Andrew R. Tawfeek
Discrete Morse theory, a cell complex-analog to smooth Morse theory, has been developed over the past few decades since its original formulation by Robin Forman in 1998. In particu…