Video game retail chain GamesStop confirmed to the BBC on Sunday that it is making a $56bn (£41bn) unsolicited takeover offer for e-commerce firm eBay. GameStop's chief executive Ryan Cohen told the Wall Street Journal that he sees potential to make eBay a much bigger rival to Amazon, worth hundreds of billions of dollars. Cohen said his company has built a stake of around 5% in eBay and that the cash and stock takeover offer would value eBay at $125 a share, around 20% higher than its closing price on Friday. The BBC has contacted eBay for comment. Cohen also said that GameStop has a commitment letter from TD Bank to provide around $20bn in debt to help finance the deal. There is nobody who is more qualified, based on my experience, to run the eBay business, added Cohen, who is also the co-founder of online pet-products retailer Chewy.

Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an information-geometric framework that reinterprets the diffusion sampling trajectory as a parametric curve on a Riemannian manifold. Our key observation is that the Fisher-Rao metric provides a principled measure of the intrinsic distance. By analyzing this metric, we derive the Drift Variation Score (DVS), a geometry-aware indicator that quantifies the instantaneous rate of distributional change. Unlike prior heuristic-based adaptive samplers, our DVS solver enforces a constant informational speed on the statistical manifold, automatically maintaining a uniform rate of distributional change along the sampling trajectory. This equal arc-length strategy ensures that each discretization step contributes equally to the information speed. Theoretical analysis verifies that DVS characterizes the local stiffness of the sampling dynamics in the Fisher-Rao sense. Experimental results on molecule and social network generation show that DVS significantly improves structural fidelity and sampling efficiency. Code is at https://github.com/kunzhan/DVS

Online Conformal Prediction (CP) struggles to balance temporal adaptability and structural stability. Feedback-driven methods (e.g., Adaptive Conformal Inference (ACI)) suffer from systemic marginal under-coverage and high interval variance during abrupt shifts, while temporally discounted Bayesian CP suffers from severe structural lag and uncalibrated interval bloat. We propose State-Adaptive Bayesian Conformal Prediction (SA-BCP) to achieve optimal spatio-temporal decoupling. By gating long-term temporal inertia with spatial kernel-density evidence, SA-BCP proactively expands intervals for recognized historical regimes while maintaining tight efficiency during stable states. We rigorously prove this mechanism's optimality, identifying a minimax bias-variance tradeoff governed by an evidence threshold $K$. Extensive benchmarks on volatile financial datasets (2016--2026), including AMD, Gold, and GBP/USD, demonstrate that SA-BCP consistently minimizes the strictly proper Winkler score across diverse confidence levels. Specifically, SA-BCP resolves the systematic under-coverage inherent to ACI variants while simultaneously reducing the uncalibrated interval bloat of Bayesian CP by 10\% to 37\% under high-confidence requests. By elegantly navigating this tradeoff, SA-BCP achieves an optimal balance between conditional reliability and predictive efficiency.

Riemannian neural networks have proven effective in solving a variety of machine learning tasks. The key to their success lies in the development of principled Riemannian analogs of fundamental building blocks in deep neural networks (DNNs). Among those, Riemannian batch normalization (BN) layers have shown to enhance training stability and improve accuracy. In this paper, we propose BN layers for neural networks on complex domains. The proposed layers have close connections with existing Riemannian BN layers. We derive essential components for practical implementations of BN layers on some complex domains which are less studied in previous works, e.g., the Siegel disk domain. We conduct experiments on radar clutter classification, node classification, and action recognition demonstrating the efficacy of our method.

Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings. While Nesterov acceleration is well understood for full-gradient and coordinate-based methods, obtaining accelerated methods for general subspace sketches that use only projected-gradient information and can improve over full-dimensional Nesterov acceleration in oracle complexity is technically nontrivial. We develop randomized-subspace Nesterov accelerated gradient methods for smooth convex and smooth strongly convex optimization under matrix smoothness and generic sketch moment assumptions. The key technical ingredient is a three-sequence formulation tailored to matrix smoothness, which recovers the corresponding classical Nesterov methods in the full-dimensional case. The resulting theory establishes accelerated oracle-complexity guarantees and makes explicit how matrix smoothness and the sketch distribution enter the complexity. It also provides a unified basis for comparing sketch families and identifying when randomized-subspace acceleration improves over full-dimensional Nesterov acceleration in oracle complexity.

The UAE says it will integrate agentic AI across half of its government operations within two years, making one of the most aggressive moves in the global AI race.

Game Theory: Who gets to go to the 2026 World Cup? Who actually gets to go to the World Cup? With US President Donald Trump's strict immigration policies, some fans may never make it past the American border. Because while teams qualify on merit, passports don't. Al Jazeera's Samantha Johnson explains. The Masters: Golf's segregated past Are Iran's athletes political pawns?

The Iran war has strengthened Ukraine in surprising ways. Could a ceasefire with Russia be closer? When Ukrainian President Volodymyr Zelensky, serious-faced and clad in black, strolled down a lilac carpet in Saudi Arabia in March, it marked a moment in the US-Israeli war in Iran. In a post on X, he said his visit was to strengthen the protection of lives. Zelensky, who carries the weight of Ukraine's own war with Russia on his shoulders, has been seizing the moment, flying to the Gulf to publicly showcase the international value and marketability of Kyiv's learned-on-the-battlefield military nous in drone warfare. Ukraine says it has now signed deals with Saudi Arabia, the UAE and Qatar - all hit by Iranian missiles and drones in recent weeks - to share drone expertise and technology, tightening alliances and benefitting from business - and it hopes defence deals - with wealthy US-allied countries.

'They're going to come for me': Ex-FBI deputy director reveals he's'living in fear' as he issues astonishing warning House Republican makes shock claim about Trump assassination attempt being'an inside job' Truth about'budget Ozempic' supplement that'eradicates hunger': Where to get it, precisely how to take it, how fast you'll lose weight... and embarrassing side effects to know Family of woman abducted as a newborn describe fresh tragedy involving her'twin' brother... as kidnap victim reveals she is pregnant and shocking name she plans to give baby Horror in Portland as'disgruntled former employee' crashes into athletics club in car'packed with EXPLOSIVES' 'She's spiralling badly': How Meghan and Harry have burned ALL their bridges as insiders reveal spectacular fallout with Anna Wintour and Kardashians, money woes - and'problems' that are worse than anyone realises McDonald's phases out free refills with patronizing sign as customers rage'we understand we'll eat elsewhere' I had agonising acid reflux every day - but then overnight it stopped thanks to something you can buy in any supermarket. Family suffers unimaginable second tragedy as Kansas State freshman, 19, dies in frat house fall 13 years after his sister's death I was abused by expat millionaires in a Dubai hotel and left with horrific injuries. Alleged JPMorgan sex slave scandal makes me think of my female bosses... and the shocking office nickname one brazen colleague earned: KENNEDY Moment Italian waiter shows off his football skills - only to backheel ball into wine glass that smashes in customer's face Gunfire erupts outside Chris Brown's LA mansion amid Rihanna assault legal drama What Hollywood insiders are saying about those Harry Styles sexuality rumors after shock Zoe Kravitz engagement... as friends finally address the'Larry' gossip Health experts are calling for AI chatbot addiction to be recognised as a mental illness, as the number of supposed cases climbs. On online forums, more and more teenagers and young adults are now saying they feel'addicted' to their AI companions and struggle to kick the habit. These young users spend hours every day roleplaying complex fantasies, venting their frustrations, and seeking emotional connection with digital companions.

Activists sailed to Gaza to deliver aid, but were met with drone attacks and imprisonment. "All of this preparation, all of this work--it's actually come together and we're sailing east, finally," said Dane Hunter. Get your news from a source that's not owned and controlled by oligarchs. Last fall, hundreds of activists from all over the world crowded onto several dozen boats and set sail for Gaza. They thought that by sharing their journey through social media, they could capture the world's attention.