Tootfinder

Integrated Noise and Safety Management in UAM via A Unified Reinforcement Learning Framework
Surya Murthy, Zhenyu Gao, John-Paul Clarke, Ufuk Topcu
https://arxiv.org/abs/2508.16440

Integrated Noise and Safety Management in UAM via A Unified Reinforcement Learning Framework
Urban Air Mobility (UAM) envisions the widespread use of small aerial vehicles to transform transportation in dense urban environments. However, UAM faces critical operational challenges, particularly the balance between minimizing noise exposure and maintaining safe separation in low-altitude urban airspace, two objectives that are often addressed separately. We propose a reinforcement learning (RL)-based air traffic management system that integrates both noise and safety considerations within…

Borderline regularity in singular free boundary problems
Dami\~ao J. Ara\'ujo, Aelson Sobral, Eduardo V. Teixeira, Jos\'e Miguel Urbano
https://arxiv.org/abs/2508.14736 …

Borderline regularity in singular free boundary problems
In this paper, we investigate the borderline regularity of local minimizers of energy functionals under minimal assumptions on the potential term $σ$. When $σ$ is merely bounded and measurable, we show that sign-changing minimizers are Log-Lipschitz continuous, which represents the optimal regularity in this general setting. In the one-phase case, however, we establish gradient bounds for minimizers along their free boundaries, revealing a structural gain in regularity. Most notably, we prove…

Bicriteria Polygon Aggregation with Arbitrary Shapes
Lotte Blank, David Eppstein, Jan-Henrik Haunert, Herman Haverkort, Benedikt Kolbe, Philip Mayer, Petra Mutzel, Alexander Naumann, Jonas Sauer
https://arxiv.org/abs/2507.11212

Bicriteria Polygon Aggregation with Arbitrary Shapes
We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the regions. This problem has applications in cartographic map generalization and urban analytics. Here, the polygons represent building footprints and the clusters may represent urban areas. Previous approaches forced the boundaries of the regions to come from a…

Thresholds of Queen covers
Tirthankar Adhikari, Harman Agrawal, Anjali Bhagat, Ankita Dargad, Sahana Jahagirdar, Prem Kant, Urban Larsson, Sahil Wagh
https://arxiv.org/abs/2508.02545

Thresholds of Queen covers
We study optimal configurations of Queens on a square chessboard, defined as those covering the maximum number of squares. For a fixed number of Queens, $q$, we prove the existence of two thresholds in board size: a non-attacking threshold beyond which all optimal configurations are pairwise non-attacking, and a stabilizing threshold beyond which the set of optimal configurations becomes constant. Related studies on Queen domination, such as Tarnai and Gáspár (2007), focus on minimizing the n…