What is in the 28-point US plan for Ukraine? 'Ukraine is running out of men, money and time' Can the US get all sides to end the war? Why is Europe opposing Trump's peace plan? How can Ukraine rebuild China ties scarred by Russia's war? Back in the 1990s, China's nascent capitalism triggered demand for Ukrainian steel slabs and iron ore, corn and sunflower oil.

The second season of Fallout - Prime Video's mega-hit based on the popular video game series - has landed. Set in a post-apocalyptic future where Earth has been ravaged by nuclear war, the first series was a commercial and critical hit, impressing long-time fans and viewers who'd never played before. Its surprising success had a huge impact on Bethesda Softworks, the developer of its source material, bringing back lapsed players and creating new ones along the way. Key creatives from the company have told BBC Newsbeat about working with the show's producers, and what the success of the programme means for the future of the games. The first season of Fallout arrived at a turning point for Hollywood video game adaptations.

Drone attacks kill over 100 civilians across war-torn Sudan's Kordofan At least 104 civilians have been killed in drone attacks across Sudan's Kordofan region as fighting between rival military factions reached deadly new heights in the brutal civil war deep into its third year. The attacks have battered the central region since early December, right up to Friday, following the capture of a significant army base by the paramilitary Rapid Support Forces (RSF) in Babnusa after a week of intense fighting. Sudan's RSF trying to hide atrocities: Report The deadliest attack was reported from a kindergarten and a hospital in Kalogi, South Kordofan, where 89 people were killed, including 43 children and eight women. United Nations human rights chief Volker Turk said he was "alarmed by the further intensification in hostilities" and warned that targeting medical facilities violates international humanitarian law. Six Bangladeshi peacekeepers serving with the UN mission were killed when drones hit their base in Kadugli, South Kordofan's capital, on December 13.

Dutch company employees work on a semiconductor lithography tool in Veldhoven, Netherlands, April 2019. Dutch company employees work on a semiconductor lithography tool in Veldhoven, Netherlands, April 2019. This is Europe's secret weapon against Trump: it could burst his AI bubble T he unthinkable has happened. The US is Europe's adversary. The stark, profound betrayal contained in the Trump administration's national security strategy should stop any further denial and dithering in Europe's capitals.

What is in the 28-point US plan for Ukraine? 'Ukraine is running out of men, money and time' Can the US get all sides to end the war? Why is Europe opposing Trump's peace plan? Kyiv Mayor Vitalii Klitschko said explosions were heard in the Ukrainian capital and warned people to stay in shelters late on Tuesday night as air defences worked to repel a Russian attack. Russian forces launched a "massive" drone attack on Ukraine's Sumy region, targeting energy infrastructure and causing electricity blackouts, Governor Oleh Hryhorov said on Telegram late on Tuesday night.

A BBC investigation has uncovered claims that essay cheating remains widespread at UK universities despite the introduction of a law designed to stop it. Since April 2022, it has been illegal to provide essays for students in post-16 education in England. But so far there have been no prosecutions. The BBC has spoken to a former lecturer who describes essay cheating as an open secret and to a businessman who claims to have made millions from selling model answer essays to university students. Universities UK, which represents 141 institutions, said there were severe penalties for students caught submitting work that was not their own.

In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on SINDy-type algorithms. STLS is an algorithm to solve the $\ell_0$ sparse least-squares problem, which relies on splitting to efficiently solve the least-squares portion while handling the sparse term via proximal methods. It produces coefficient vectors whose components depend on both the projected reconstruction errors, here referred to as the scores, and the mutual coherence of dictionary terms. The first contribution of this work is a theoretical analysis of the score and dictionary-selection strategy. This could be understood in both the original and weak SINDy regime. Second, numerical experiments on ordinary and partial differential equations highlight the effectiveness of score-based screening, improving both accuracy and interpretability in dynamical system identification. These results suggest that integrating score-guided methods to refine the dictionary more accurately may help SINDy users in some cases to enhance their robustness for data-driven discovery of governing equations.

Amortized Bayesian inference (ABI) offers fast, scalable approximations to posterior densities by training neural surrogates on data simulated from the statistical model. However, ABI methods are highly sensitive to model misspecification: when observed data fall outside the training distribution (generative scope of the statistical models), neural surrogates can behave unpredictably. This makes it a challenge in a model comparison setting, where multiple statistical models are considered, of which at least some are misspecified. Recent work on self-consistency (SC) provides a promising remedy to this issue, accessible even for empirical data (without ground-truth labels). In this work, we investigate how SC can improve amortized model comparison conceptualized in four different ways. Across two synthetic and two real-world case studies, we find that approaches for model comparison that estimate marginal likelihoods through approximate parameter posteriors consistently outperform methods that directly approximate model evidence or posterior model probabilities. SC training improves robustness when the likelihood is available, even under severe model misspecification. The benefits of SC for methods without access of analytic likelihoods are more limited and inconsistent. Our results suggest practical guidance for reliable amortized Bayesian model comparison: prefer parameter posterior-based methods and augment them with SC training on empirical datasets to mitigate extrapolation bias under model misspecification.

Former chancellor George Osborne is joining artificial intelligence (AI) giant OpenAI. He will lead its OpenAI for Countries programme, which is aimed at helping governments increase their AI capacity. Announcing his new London-based role, Osborne said it was a privilege to be joining the company. I recently asked myself the question: what's the most exciting and promising company in the world right now? The answer I believe is OpenAI, he said on X.

Negotiations over a technology deal between the UK and US have stalled due to stumbling blocks in wider trade negotiations between the two sides. The Technology Prosperity Deal - which was billed as historic when it was unveiled during US President Donald Trump's state visit in September - saw both countries pledge to co-operate in areas such as AI. However, talks on the agreement are now being held up because of US concerns about what it considers to be wider UK trade barriers. A government spokesperson said our special relationship with the US remains strong and the UK is firmly committed to ensuring the Tech Prosperity Deal delivers opportunity for hardworking people in both countries. The New York Times - which first reported the story - said there were broader disagreements between the two sides, including over digital regulations and food safety rules.