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Lorenz Hilfiker

Publications and source records attributed to Lorenz Hilfiker.

2 recordsLinked to original sources

Graph Neural Networks for Source Detection: A Review and Benchmark Study

The source detection problem arises when an epidemic process unfolds over a contact network, and the objective is to identify its point of origin, i.e., the source node. Research on this problem began with the seminal work of Shah and Zaman in 2010, who formally defined it and introduced the notion of rumor centrality. With the emergence of Graph Neural Networks (GNNs), several studies have proposed GNN-based approaches to source detection. However, there is room to strengthen methodological clarity and reproducibility across these works. As a result, it remains unclear whether GNNs truly outperform more traditional source detection methods across comparable settings. In this paper, we first systematically review existing GNN-based methods for source detection, clearly outlining the specific settings each addresses and the architectures they employ. We then reproduce and benchmark four representative GNN architectures against a diverse set of traditional and MLP-based baselines under controlled, comparable conditions. We also investigate key questions surrounding this problem, including how detectability evolves over time, how performance scales with training set size, and how sensitive methods are to uncertainty in observation timing and epidemic parameters. Our experiments show that GNNs substantially outperform all other methods we test across a variety of network topologies. Although we initially set out to challenge the notion of GNNs as a solution to source detection, our results instead demonstrate their remarkable effectiveness for this task. To ensure full reproducibility, we release all code and data on GitHub. Finally, we argue that epidemic source detection constitutes a natural and attractive benchmark task for evaluating GNN architectures.

cs.SI↗

Existence and uniqueness of solutions to Y-systems and TBA equations

We consider Y-system functional equations of the form $$ Y_n(x+i)Y_n(x-i)=\prod_{m=1}^N (1+Y_m(x))^{G_{nm}}$$ and the corresponding nonlinear integral equations of the Thermodynamic Bethe Ansatz. We prove an existence and uniqueness result for solutions of these equations, subject to appropriate conditions on the analytical properties of the $Y_n$, in particular the absence of zeros in a strip around the real axis. The matrix $G_{nm}$ must have non-negative real entries, and be irreducible and diagonalisable over $\mathbb{R}$ with spectral radius less than 2. This includes the adjacency matrices of finite Dynkin diagrams, but covers much more as we do not require $G_{nm}$ to be integers. Our results specialise to the constant Y-system, proving existence and uniqueness of a strictly positive solution in that case.

math-ph↗