Tootfinder

Computing Non-Obtuse Triangulations with Few Steiner Points
Mikkel Abrahamsen, Florestan Brunck, Jacobus Conradi, Benedikt Kolbe, Andr\'e Nusser
https://arxiv.org/abs/2505.23375

Computing Non-Obtuse Triangulations with Few Steiner Points
We present the winning implementation of the Seventh Computational Geometry Challenge (CG:SHOP 2025). The task in this challenge was to find non-obtuse triangulations for given planar regions, respecting a given set of constraints consisting of extra vertices and edges that must be part of the triangulation. The goal was to minimize the number of introduced Steiner points. Our approach is to maintain a constrained Delaunay triangulation, for which we repeatedly remove, relocate, or add Steiner …

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Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach
Matthieu Bonnivard, Elie Bretin, Antoine Lemenant, Eve Machefert
https://arxiv.org/abs/2506.22273

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach
This work focuses on a phase field approximation of Plateau's problem. Inspired by Reifenberg's point of view, we introduce a model that combines the Ambrosio-Torterelli energy with a geodesic distance term, which can be considered as a generalization of the approach developed by Bonnivard, Lemenant and Santambrogio to approximate solutions to Steiner's problem. First, we present a Gamma-convergence analysis of this model in the simple case of a single curve located on the edge of a cylinder. I…

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Optimal Approximations for the Requirement Cut Problem on Sparse Graph Classes
We study the Requirement Cut problem, a generalization of numerous classical graph partitioning problems including Multicut, Multiway Cut, $k$-Cut, and Steiner Multicut among others. Given a graph with edge costs, terminal groups $(S_1, ..., S_g)$ and integer requirements $(r_1,... , r_g)$; the goal is to compute a minimum-cost edge cut that separates each group $S_i$ into at least $r_i$ connected components. Despite many efforts, the best known approximation for Requirement Cut yields a double…

Some sharp bounds on the average Steiner (k, l)-eccentricity for trees
Cheng Zeng, Gengji Li
https://arxiv.org/abs/2506.17915 https://

Some sharp bounds on the average Steiner (k, l)-eccentricity for trees
In this paper we introduce some transformations for trees that do not increase the average Steiner $(k,l)$-eccentricity for all $0\leq l\leq k\leq n$. Using these transformations, we obtain some sharp bounds on the average Steiner $(k,l)$-eccentricity for trees with some certain conditions, including given nodes, given diameter, given max degree and given leaves, and get the corresponding extremal trees as well.

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The ESPRESSO transmission spectrum of HD$\,$189733$\,$b : Extracting the planetary sodium and lithium signatures amid stellar contamination
D. Mounzer, W. Dethier, C. Lovis, V. Bourrier, A. Psaridi, H. Chakraborty, M. Lendl, R. Allart, J. V. Seidel, M. R. Zapatero Osorio, P. Molaro, M. Steiner, D. Ehrenreich, Y. Alibert, I. Carleo, S. Cristiani, J. I. Gonz\'alez Hern\'andez, C. J. A. P. Martins, E. Palle, J. Rodrigues, N. Santos, A. Sozzetti, A. Su\'arez Mascare\~no

The ESPRESSO transmission spectrum of HD$\,$189733$\,$b : Extracting the planetary sodium and lithium signatures amid stellar contamination
While transmission spectroscopy has allowed us to detect many atomic and molecular species in exoplanet atmospheres, the improvement in resolution and signal-to-noise ratio enabled us to become sensitive to planet-occulted line distortions (POLDs) in the spectrum that are induced by center-to-limb variations and the Rossiter-McLaughlin effect. POLDs can bias the interpretation of the transmission spectrum, and it is difficult to correct for them with stellar models. We analyzed two ESPRESSO tra…

Control of pedestal-top electron density using RMP and gas puff at KSTAR
Minseok Kim, S. K. Kim, A. Rothstein, P. Steiner, K. Erickson, Y. H. Lee, H. Han, Sang-hee Hahn, J. W. Juhn, B. Kim, R. Shousha, C. S. Byun, J. Butt, ChangMin Shin, J. Hwang, Minsoo Cha, Hiro Farre, S. M. Yang, Q. Hu, D. Eldon, N. C. Logan, A. Jalalvand, E. Kolemen
https://

Control of pedestal-top electron density using RMP and gas puff at KSTAR
We report the experimental results of controlling the pedestal-top electron density by applying resonant magnetic perturbation with the in-vessel control coils and the main gas puff in the 2024-2025 KSTAR experimental campaign. The density is reconstructed using a parametrized psi_N grid and the five channels of the line-averaged density measured by a two-colored interferometer. The reconstruction procedure is accelerated by deploying a multi-layer perceptron to run in about 120 microseconds an…

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A biophysical approach to the design of networks of communication systems
Rodrigo Almeida, Ana Filipa Valente, Rui Dil\~ao
https://arxiv.org/abs/2506.20572

A biophysical approach to the design of networks of communication systems
Inspired by the growth dynamics of the protist \textit{Physarum polycephalum}, we use a formalism that describes adaptive incompressible Hagen-Poiseuille flows on channel networks to identify graphs connecting different nodes within Euclidean space. These graphs are either suboptimal or optimal in terms of their length. Occasionally, we obtain graph tree configurations that are topologically equivalent to Steiner trees. This approach is employed to design communication systems, such as railway …

Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data
Xiong-Hui Cao, Feng-Kun Guo, Zhi-Hui Guo, Qu-Zhi Li
https://arxiv.org/abs/2506.10619

Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data
A comprehensive analysis of $πK\rightarrow πK$ and $ππ\rightarrow K\bar K$ amplitudes at large unphysical pion mass for all important partial waves is presented. A set of crossing-symmetric partial-wave hyperbolic dispersion relations is used to describe lattice QCD data at $m_π=391~$MeV. In the present analysis, the amplitudes for the $S$- and $P$-waves are formulated by combining the constraints of analyticity, unitarity, and crossing symmetry, fulfilling Roy-Steiner-type equations. We u…

SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction
Lukas Radl, Felix Windisch, Thomas Deixelberger, Jozef Hladky, Michael Steiner, Dieter Schmalstieg, Markus Steinberger
https://arxiv.org/abs/2506.19139

SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction
Recent advances in 3D Gaussian representations have significantly improved the quality and efficiency of image-based scene reconstruction. Their explicit nature facilitates real-time rendering and fast optimization, yet extracting accurate surfaces - particularly in large-scale, unbounded environments - remains a difficult task. Many existing methods rely on approximate depth estimates and global sorting heuristics, which can introduce artifacts and limit the fidelity of the reconstructed mesh.…

Vortex ring induced by a disk translating toward or away from a wall
Joanne Steiner, Cyprien Morize, Ivan Delbende, Alban Sauret, Philippe Gondret
https://arxiv.org/abs/2506.18597

Vortex ring induced by a disk translating toward or away from a wall
This study investigates the time evolution of vortex rings generated by the normal translation of a disk either toward or away from a wall. We systematically vary the control parameters, including the disk size, stroke length, travel time, and distance from the wall, to analyze their influence on vortex dynamics. Experiments are conducted with Particle Image Velocimetry, while numerical simulations are performed using the flow solver Basilisk. The circulation and core radius are used as primary…

Enumeration of subsets with closedness in finite fields of characteristic 2
Nithish Kumar R, Vadiraja Bhatta G. R., Prasanna Poojary
https://arxiv.org/abs/2506.20351

Enumeration of subsets with closedness in finite fields of characteristic 2
The additive closedness in the subset of an additive group is termed as r-value. The nature of closedness in different subsets of fixed size is observed as a spectrum of r-values. We enumerate r-values of subsets in finite fields of characteristic 2 and represent them as the spectrum of values. Based on these values the subsets can be further studied as partial Steiner triple systems, sum-free sets, Sidon sets, and Schure triples.

Symmetry in Serrin-type overdetermined problems
Daomin Cao, Juncheng Wei, Weicheng Zhan
https://arxiv.org/abs/2506.02423 https://arxi…

Symmetry in Serrin-type overdetermined problems
This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overdetermined problems with potentially degenerate ellipticity in nonsmooth bounded domains. Furthermore, analogous symmetry results are established for ring-shaped domains. The proof relies on continuous Steiner symmetrization, along with a carefully constructed approximation argument.