7 papers
Homomorphism Indistinguishability Beyond Graphs: Relational Weisfeiler--Leman and Hypertree Width
Panagiotis Aivasiliotis, Andreas Göbel, Matthias Lanzinger +1
The Weisfeiler--Leman (WL) algorithm is one of the most influential heuristics for the graph isomorphism problem. The expressive power of WL has been extensively studied in the con…
Uniqueness, analyticity and mixing for Gibbs point processes via spectral gaps
Andreas Göbel, Matthew Jenssen, Marcus Michelen +3
A Gibbs point process models particles interacting in the continuum through a potential. Among the most classical examples is the hard-sphere model, where given an activity paramet…
Reemergence of the Epidemic Threshold in SIRS Infections on Connected Stars
Andreas Göbel, Nicolas Klodt, Martin S. Krejca
The SIRS process is a continuous-time process for how infections spread on a graph. In this model, each vertex is in one of the following three states: susceptible (to the infectio…
Temporal Exploration of Random Spanning Tree Models
Samuel Baguley, Andreas Göbel, Nicolas Klodt +3
The Temporal Graph Exploration problem (TEXP) takes as input a temporal graph, i.e., a sequence of graphs on the same vertex set, and asks for a walk of s…
Testing Thresholds and Spectral Properties of High-Dimensional Random Toroidal Graphs via Edgeworth-Style Expansions
Samuel Baguley, Andreas Göbel, Marcus Pappik +1
We study high-dimensional random geometric graphs (RGGs) of edge-density with vertices uniformly distributed on the -dimensional torus and edges inserted between sufficientl…
Gradually Declining Immunity Retains the Exponential Duration of Immunity-Free Diffusion
Andreas Göbel, Nicolas Klodt, Martin S. Krejca +1
Diffusion processes pervade numerous areas of AI, abstractly modeling the dynamics of exchanging, oftentimes volatile, information in networks. A central question is how long the i…