Tootfinder

Localized and weighted versions of extremal problems
Binlong Li, Bo Ning
https://arxiv.org/abs/2509.17055 https://arxiv.org/pdf/2509.17055

Localized and weighted versions of extremal problems
Malec and Tompkins (EUJC, 2023) considered the localized versions of Turán-type problems, and proved a localized theorem on Erdős-Gallai Theorem on paths. Zhao and Zhang (JGT, 2025) gave a long proof of a localized version of Erdős-Gallai Theorem on cycles. In this paper, we consider several types of generalization of Turán-type problems, that is, localized versions, weighted versions, and generalized Turán-type problems, and their connectedness. We first present very short proofs for re…

Enhancing the NAO: Extending Capabilities of Legacy Robots for Long-Term Research
Austin Wilson, Sahar Kapasi, Zane Greene, Alexis E. Block
https://arxiv.org/abs/2509.17760 http…

Enhancing the NAO: Extending Capabilities of Legacy Robots for Long-Term Research
Many research groups face challenges when legacy (unsupported) robotic platforms lose manufacturer support and cannot accommodate modern sensing, speech, and interaction capabilities. We present the Enhanced NAO, a revitalized version of Aldebaran's NAO robot that uses upgraded microphones, RGB-D and thermal cameras, and additional compute resources in a fully self-contained package. This system combines cloud and local models for perception and dialogue, while preserving the NAO's expressive b…

PyG 2.0: Scalable Learning on Real World Graphs
Matthias Fey, Jinu Sunil, Akihiro Nitta, Rishi Puri, Manan Shah, Bla\v{z} Stojanovi\v{c}, Ramona Bendias, Alexandria Barghi, Vid Kocijan, Zecheng Zhang, Xinwei He, Jan Eric Lenssen, Jure Leskovec
https://arxiv.org/abs/2507.16991

PyG 2.0: Scalable Learning on Real World Graphs
PyG (PyTorch Geometric) has evolved significantly since its initial release, establishing itself as a leading framework for Graph Neural Networks. In this paper, we present Pyg 2.0 (and its subsequent minor versions), a comprehensive update that introduces substantial improvements in scalability and real-world application capabilities. We detail the framework's enhanced architecture, including support for heterogeneous and temporal graphs, scalable feature/graph stores, and various optimization…

NPO radio1 heeft AIVD expert op bezoek:
Bovendien "gebeurt" er de afgelopen tientallen jaren "veel minder" vanuit linksextremisme, gaat Hanselman verder. Bij de aanstaande ministerraad zal Den Haag de motie van FvD om Antifa als terroristische organisatie te bestempelen overwegen.
Maar Hanselman verwacht niet dat het erdoorheen zal komen, mede door de rellen in Den Haag van vorig weekend. "[...] Ik denk dat de rechtse partijen nu een beetje op moeten pass…

Waarom heeft politiek het zo druk met Antifa? 'Iedereen die enigszins links is op één grote hoop gooien'

De Tweede Kamer volgde Trump en bracht een motie om Antifa als 'terroristische organisatie' te bestempelen. Maar het gaat in werkelijkheid om een antifascistische beweging, niet een organisatie. Wat betekent het dan om deze beweging wel van een terroristisch label te voorzien? "Ik denk dat de rechtse partijen nu een beetje op moeten passen", zegt Berrie Hanselman, voormalig analist bij de AIVD, bij Spraakmakers.

Neue direkte Gespräche zwischen Ukraine und Russland begonnen
Die Ukraine und Russland haben in Istanbul neue direkte Gespräche begonnen. Die Verhandlungsführer beider Seiten seien zu einem bilateralen Treffen zusammengekommen, hieß es aus russischen Delegationskreisen.
Der Kreml hatte im Vorfeld bereits die Erwartungen gedämpft: Die Gespräche würden "sehr schwierig", sagte Kreml-Sprecher Sprecher Dmitri Peskow.
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Ukraine-Liveblog: ++ Unterhändler aus Kiew und Moskau zusammengekommen ++
Unterhändler aus Kiew und Moskau sind zu bilateralen Gesprächen in der Türkei zusammengekommen. Israel und die Ukraine wollen gemeinsam gegen die Bedrohung aus dem Iran vorgehen - vor allem mit Blick auf Verteidigungstechnologien.

A Unifying Framework for Semiring-Based Constraint Logic Programming With Negation (full version)
Jeroen Spaans, Jesse Heyninck
https://arxiv.org/abs/2507.16067

A Unifying Framework for Semiring-Based Constraint Logic Programming With Negation (full version)
Constraint Logic Programming (CLP) is a logic programming formalism used to solve problems requiring the consideration of constraints, like resource allocation and automated planning and scheduling. It has previously been extended in various directions, for example to support fuzzy constraint satisfaction, uncertainty, or negation, with different notions of semiring being used as a unifying abstraction for these generalizations. None of these extensions have studied clauses with negation allowe…

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Singleton algorithms for the Constraint Satisfaction Problem
Dmitriy Zhuk
https://arxiv.org/abs/2509.18434 https://arxiv.org/pdf/2509.18434

Singleton algorithms for the Constraint Satisfaction Problem
A natural strengthening of an algorithm for the (promise) constraint satisfaction problem is its singleton version: we first fix a constraint to some tuple from the constraint relation, then run the algorithm, and remove the tuple from the constraint if the answer is negative. We characterize the power of the singleton versions of standard universal algorithms for the (promise) CSP over a fixed template in terms of the existence of a minion homomorphism. Using the Hales-Jewett theorem, we show …

Edge version of the inducibility via the entropy method
Yichen Wang, Xiamiao Zhao, Mei Lu
https://arxiv.org/abs/2509.17502 https://arxiv.org/pdf/2509.17502…

Edge version of the inducibility via the entropy method
The inducibility of a graph $H$ is about the maximum number of induced copies of $H$ in a graph on $n$ vertices. We consider its edge version, that is, the maximum number of induced copies of $H$ in a graph with $m$ edges. Let $c(G,H)$ be the number of induced copies of $H$ in $G$ and $ρ(H,m) = \max \{c(G,H) \mid |E(G)| = m\}$. For any graph $H$, we prove that $ρ(H,m) = Θ(m^{α_f(H)})$ where $α_f(H)$ is the fractional independence number of $H$. Therefore, we now focus on the cons…

Colour-biased Hamilton cycles in dense graphs and random graphs
Natalie Behague, Debsoumya Chakraborti, Jared Le\'on
https://arxiv.org/abs/2509.18012 https://

Colour-biased Hamilton cycles in dense graphs and random graphs
A classical result of Dirac says that every $n$-vertex graph with minimum degree at least $\frac{n}{2}$ contains a Hamilton cycle. A `discrepancy' version of Dirac's theorem was shown by Balogh--Csaba--Jing--Pluhár, Freschi--Hyde--Lada--Treglown, and Gishboliner--Krivelevich--Michaeli as follows. Every $r$-colouring of the edge set of every $n$-vertex graph with minimum degree at least $(\frac{1}{2} + \frac{1}{2r} + o(1))n$ contains a Hamilton cycle where one of the colours appears at least $(…