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Product units in gated recurrent units improve nuclear-mass prediction
arXiv:2606.06866v1 Announce Type: new Abstract: The prediction of masses of atomic nuclei using machine learning can complement theoretical models and advance the exploration of poorly known domains of the nuclear chart. We propose a machine learning technique based on gated recurrent units (GRU), which have demonstrated competitive performance in nuclear-mass prediction by exploiting long-term dependencies. By integrating multiplicative interactions and product-unit transformations within...
Napoli sign Hojlund from Man United after loan spell
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Language Models Compare Quantities Using Number-specific and Unit-specific Heuristics
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Multilingual Multi-Speaker Unit Vocoders: A Systematic Analysis of Discrete Speech Representations
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Thai consumer watchdog to file civil suit against Volvo Cars' Thai unit, official says
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Optimizing Explicit Unit-Distance Lower-Bound Certificates
arXiv:2606.03419v2 Announce Type: replace-cross Abstract: The 2026 disproof of Erd\H{o}s's unit-distance conjecture and Sawin's subsequent explicit quantitative refinement show that the maximum number $u(n)$ of unit distances among $n$ planar points can exceed $n^{1+\varepsilon}$ for a fixed positive $\varepsilon$. Sawin's explicit bound gives more than $n^{1.014}$ unit distances for arbitrarily large $n$ and exposes integer parameters whose choice is not fully optimized. This report starts...
Ella Toone weighs up Manchester United future after tough campaign
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Ella Toone weighs up Manchester United future after tough campaign
‘Right now, I’m a Manchester United player’ says strikerToone back in England camp after injury absencesElla Toone has said she will have to decide “what’s best for me” as she weighs up her long-term future with one year remaining on her Manchester United contract. The England midfielder, speaking before Friday’s crucial Women’s World Cup qualifier in Spain, was asked about her club future and implied she would hold discussions with United this summer.
Optimizing Explicit Unit-Distance Lower-Bound Certificates
arXiv:2606.03419v1 Announce Type: cross Abstract: The 2026 disproof of Erd\H{o}s's unit-distance conjecture and Sawin's subsequent explicit quantitative refinement show that the maximum number $u(n)$ of unit distances among $n$ planar points can exceed $n^{1+\varepsilon}$ for a fixed positive $\varepsilon$. Sawin's explicit bound gives more than $n^{1.014}$ unit distances for arbitrarily large $n$ and exposes finite parameters whose choice is not fully optimized. This report formulates the...
Optimizing Explicit Unit-Distance Lower-Bound Certificates
arXiv:2606.03419v3 Announce Type: replace-cross Abstract: The 2026 disproof of Erd\H{o}s's unit-distance conjecture and Sawin's quantitative refinement show that the maximum number $u(n)$ of unit distances among $n$ planar points can exceed $n^{1+\varepsilon}$ for a fixed positive $\varepsilon$. Sawin's explicit bound gives more than $n^{1.014}$ unit distances for arbitrarily large $n$ and exposes integer parameters whose choice is not fully optimized. This report starts from Sawin's...