Tootfinder

A polynomial bound on the pathwidth of graphs edge-coverable by $k$ shortest paths
Julien Baste, Lucas De Meyer, Ugo Giocanti, Etienne Objois, Timoth\'e Picavet
https://arxiv.org/abs/2510.02901

A polynomial bound on the pathwidth of graphs edge-coverable by $k$ shortest paths
Dumas, Foucaud, Perez and Todinca (2024) recently proved that every graph whose edges can be covered by $k$ shortest paths has pathwidth at most $O(3^k)$. In this paper, we improve this upper bound on the pathwidth to a polynomial one; namely, we show that every graph whose edge set can be covered by $k$ shortest paths has pathwidth $O(k^4)$, answering a question from the same paper. Moreover, we prove that when $k\leq 3$, every such graph has pathwidth at most $k$ (and this bound is tight). Fi…

Adaptive Thresholds for Monitoring and Screening in Imbalanced Samples: Optimality and Boosting Sensitivity
Ansgar Steland
https://arxiv.org/abs/2510.08035 https://

Adaptive Thresholds for Monitoring and Screening in Imbalanced Samples: Optimality and Boosting Sensitivity
Suppose (standardized) measurements or statistics are monitored to raise an alarm when a threshold is exceeded. Often, the underlying population is heterogenous with respect to important discrete variables and thus samples may consist of imbalanced classes. We propose to use thresholds which depend on such covariates to boost the sensitivity for rare classes, which otherwise tend to be ignored. Under mild conditions, we identify optimal threshold functions and develop a feasible procedure for t…

CoPAD : Multi-source Trajectory Fusion and Cooperative Trajectory Prediction with Anchor-oriented Decoder in V2X Scenarios
Kangyu Wu, Jiaqi Qiao, Ya Zhang
https://arxiv.org/abs/2509.15984

CoPAD : Multi-source Trajectory Fusion and Cooperative Trajectory Prediction with Anchor-oriented Decoder in V2X Scenarios
Recently, data-driven trajectory prediction methods have achieved remarkable results, significantly advancing the development of autonomous driving. However, the instability of single-vehicle perception introduces certain limitations to trajectory prediction. In this paper, a novel lightweight framework for cooperative trajectory prediction, CoPAD, is proposed. This framework incorporates a fusion module based on the Hungarian algorithm and Kalman filtering, along with the Past Time Attention (…

fev-bench: A Realistic Benchmark for Time Series Forecasting
Oleksandr Shchur, Abdul Fatir Ansari, Caner Turkmen, Lorenzo Stella, Nick Erickson, Pablo Guerron, Michael Bohlke-Schneider, Yuyang Wang
https://arxiv.org/abs/2509.26468

fev-bench: A Realistic Benchmark for Time Series Forecasting
Benchmark quality is critical for meaningful evaluation and sustained progress in time series forecasting, particularly given the recent rise of pretrained models. Existing benchmarks often have narrow domain coverage or overlook important real-world settings, such as tasks with covariates. Additionally, their aggregation procedures often lack statistical rigor, making it unclear whether observed performance differences reflect true improvements or random variation. Many benchmarks also fail to…

Findings of the Third Automatic Minuting (AutoMin) Challenge
Kartik Shinde, Laurent Besacier, Ondrej Bojar, Thibaut Thonet, Tirthankar Ghosal
https://arxiv.org/abs/2509.13814 ht…

Findings of the Third Automatic Minuting (AutoMin) Challenge
This paper presents the third edition of AutoMin, a shared task on automatic meeting summarization into minutes. In 2025, AutoMin featured the main task of minuting, the creation of structured meeting minutes, as well as a new task: question answering (QA) based on meeting transcripts. The minuting task covered two languages, English and Czech, and two domains: project meetings and European Parliament sessions. The QA task focused solely on project meetings and was available in two settings: …

Planar ternary graphs, flag spheres, and Delannoy polynomials
Margaret Bayer, Richard Danner, Thiago Holleben, Marie Kramer, Yirong Yang
https://arxiv.org/abs/2509.21705 https:/…

Planar ternary graphs, flag spheres, and Delannoy polynomials
In 2022 Kim showed when a graph $G$ is ternary (without induced cycles of length divisible by three), its independence complex $\text{Ind}(G)$ is either contractible or homotopy equivalent to a sphere. In this paper, we show that when $\text{Ind}(G)$ is homotopy equivalent to a sphere of dimension $\dim \text{Ind}(G)$, the complex is Gorenstein. Equivalently, $G$ is a $1$-well-covered graph. This answers a question by Faridi and Holleben. We then focus on the independence complexes of Gorenst…