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QEC and EAQEC Codes from Hermitian Sums and Hulls of Cyclic Codes over $\mathbb{F}_2 \times (\mathbb{F}_2+v\mathbb{F}_2)$
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Comprehensive Ab Initio Quantum Computations of CO$_{\rm 2}$-H$_{\rm 2}$ and CO$_{\rm 2}$-He Collisional Properties
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The Grothendieck Constant is Less Than $\frac{\pi}{2 \log (1+ \sqrt{2})} - 10^{-5}$
Computer Science > Data Structures and Algorithms [Submitted on 2 Jun 2026] Title:The Grothendieck Constant is Less Than $\fracπ{2 \log (1+ \sqrt{2})} - 10^{-5}$ View PDF HTML (experimental)Abstract:We prove that the Grothendieck constant $K_G < $\frac{\pi}{2 \log (1+ \sqrt{2})} - 10^{-5}$. This improves on the work of braverman et.
The Grothendieck Constant is Less Than $\frac{\pi}{2 \log (1+ \sqrt{2})} - 10^{-5}$
Computer Science > Data Structures and Algorithms [Submitted on 2 Jun 2026 (v1), last revised 6 Jun 2026 (this version, v2)] Title:The Grothendieck Constant is Less Than $\fracπ{2 \log (1+ \sqrt{2})} - 10^{-5}$ View PDF HTML (experimental)Abstract:We prove that the Grothendieck constant $K_G 0$. Submission history From: Pravesh K Kothari [view email][v1] Tue, 2 Jun 2026 17:59:53 UTC (829 KB)
Betti Numbers and Higher Weight Spectra of Reed-Muller Codes $RM_q(2,2)$
arXiv:2408.02548v3 Announce Type: replace-cross Abstract: We determine all the Betti numbers of the $q$-ary second order Reed-Muller codes of length $q^2$, and also of the elongations of matroids associated to these codes. We then use it to determine the higher weight spectra of these codes. As a special case, we recover some results of Kaplan and Matei about counting certain curves over finite fields with prescribed rational intersection points.
Reliable Viscosity Calculation from High-Pressure Equilibrium Molecular Dynamics: Case Study of 2,2,4-Trimethylhexane
Announce Type: replace Abstract: Viscosity is a fundamental property of liquid lubricants, yet it is challenging to determine accurately, especially at high pressures. Although equilibrium molecular dynamics (EMD) simulations are a promising alternative to resource-intensive experiments, practical challenges remain in assessing the sufficiency of simulation time and in controlling uncertainties in the Green-Kubo formalism due to the finite amount of trajectory data. In this work, we extend...
Characterization and chromatic number of triangle-free graphs with diameter 2
arXiv:2606.03267v1 Announce Type: cross Abstract: In this paper, we consider triangle-free graphs with diameter 2. If a triangle-free graph $G$ with diameter 2 is not isomorphic to a star, then the radius of $G$ is also 2, where such a graph is also called a $2$-self-centered graph. [A characterization for 2-self-centered graphs, Discuss.
The next Nintendo sports game for Switch 2 features thumb wrestling
The next Nintendo sports game for Switch 2 features thumb wrestling Nintendo Switch Sports Resort features 12 activities and it's coming to Switch 2 on October 22. As revealed during Tuesday's Nintendo Direct, the company is bringing its long-running series of sports sim games to Switch 2 with a new entry called Nintendo Switch Sports Resort. The follow-up to 2022's Nintendo Switch Sports features a dozen sports that you can play yourself or with family and friends via Joy-Con 2 motion controls.
WSL 2 is getting faster Windows file system access
WSL 2 is getting faster Windows file system access From DrvFs in WSL 1 to Plan 9 to virtiofs, cross-OS file access in WSL 2 has improved with each generation. A new change gives each virtio device its own dedicated DMA pool, removing the last major contention point on the virtiofs path. If your workflow crosses the Windows/Linux boundary, file I/O performance in WSL 2 has been getting steadily better.
Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography
Announce Type: replace-cross Abstract: In this work we study quantitative existence results for genus-$2$ curves over $\mathbb{Q}$ whose Jacobians have Mordell--Weil rank at least $1$ or $2$, ordering the curves by the naive height of their integral Weierstrass models. We use geometric techniques to show that asymptotically the Jacobians of almost all integral models with two rational points at infinity have rank $r \geq Since there are $\asymp X^{\frac{13}{2}}$ such models among the $X^7$...