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An Upper Bound on Grothendieck's Constant
Announce Type: cross Abstract: We show that Grothendieck's real constant $K_G$ can be upper bounded by projecting vectors onto a random plane through the origin and thresholding a degree five Hermite polynomial. This resolves a conjecture of Braverman-Makarychev-Makarychev-Naor from 2011, who required an extra randomization step in their rounding scheme and proved $K_G<\frac{\pi}{2\log(1+\sqrt{2})}-10^{-500}$. As a corollary of our result, we prove the bound...
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.
Keir Starmer says those behind ‘unacceptable’ Belfast disorder ‘will feel full force of the law’ – UK politics live
PM says he ‘will not tolerate’ rioting and says people were targeted ‘because of their background’ after widespread unrest following knife attack videoAt the Reform UK press conference, the first question came from a GB News reporter who said that Suella Braverman, Reform’s education spokesperson, was home secretary when the Belfast knife attack suspect was granted leave to remain in the UK, and Robert Jenrick, Reform’s Treasury spokesperson, was an immigration minister. The reporter asked...
[Written Question] Schools: Safety
Question by: Suella Braverman Answering Body: Department for Education Question: To ask the Secretary of State for Education, what steps her Department is taking to ensure that inclusion policies do not compromise (a) the safety of teachers and (b) the learning environment for pupils.
Badenoch’s attack on equalities laws is less about Henry Nowak and more about taking on Reform
Badenoch’s attack on equalities laws is less about Henry Nowak and more about taking on Reform Kemi Badenoch is using the Henry Nowak murder to launch a new attack on equalities legislation but political editor David Maddox warns that the speech is more about taking on Reform than justice for the 18-year-old - Bookmark - CommentsGo to comments Kemi Badenoch’s speech today on the need to overhaul equalities legislation has been framed as a justified reaction to the horrendous Henry Nowak case...
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)
Failed asylum seekers vanishing due to 'unacceptable' errors, damning report finds
Failed asylum seekers vanishing due to 'unacceptable' errors, damning report finds A report by the cross-party Public Accounts Committee (PAC) has accused the Home Office of losing control of the asylum system and having no clear plan to get people out of hotels A scathing report has found "shocking and unacceptable" errors mean failed asylum seekers are vanishing without a trace. MPs voiced their alarm after the Home Office admitted it knows where the vast majority of those whose...
Information-Theoretic Bounds for Sparse Covariance Estimation in the Vertical-Split Distributed Model
Announce Type: new Abstract: We study the minimax estimation error for distributed covariance matrix estimation in the vertical-split (feature-split) setting, where two agents each observe different coordinates of $m$ i.i.d. and communicate a limited number of bits to a central server. [2025] established nearly tight bounds for dense (unstructured) cross-covariance matrices, we investigate whether imposing elementwise $s$-sparsity on the cross-covariance $C_{21}$ can reduce the required...