10 papers
LEAP: Local ECT-Based Learnable Positional Encodings for Graphs
Juan Amboage, Ernst Röell, Patrick Schnider +1
Graph neural networks (GNNs) largely rely on the message-passing paradigm, where nodes iteratively aggregate information from their neighbors. Yet, standard message passing neural…
Bowties and Hourglasses: Intersections of Double-Wedges (or Stabbing and Avoiding Line Segments)
Daniel Bertschinger, Henry Förster, Fabian Klute +3
We study the common intersection of arrangements of double-wedges. We consider arrangements where double-wedges may be either bowties (which do not contain a vertical line) or hour…
Garment numbers of bi-colored point sets in the plane
Oswin Aichholzer, Helena Bergold, Simon D. Fink +3
We consider colored variants of a class of geometric-combinatorial questions on -gons and empty -gons that have been started around 1935 by ErdÅs and Szekeres. In our settin…
Splitting Sandwiches Unevenly via Unique Sink Orientations and Rainbow Arrangements
Michaela Borzechowski, Sebastian Haslebacher, Hung P. Hoang +2
The famous Ham-Sandwich theorem states that any point sets in can be simultaneously bisected by a single hyperplane. The -Ham-Sandwich theorem gives a suffic…
AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithm
Marius Huber, Sara Kalisnik, Patrick Schnider
We present AuToMATo, a novel clustering algorithm based on persistent homology. While AuToMATo is not parameter-free per se, we provide default choices for its parameters that make…
Flagifying the Dowker Complex
Marius Huber, Patrick Schnider
The Dowker complex is a simplicial complex capturing the topological interplay between two finite sets and under some relation .…