Moment Dame Helen Mirren is called an'evil Zionist b****' as she is accosted by pro-Palestine stranger on London street'Hell on Wheels' teen Mackenzie Shirilla's diva demands and disturbing obsession with fame revealed in prison calls with mom Girl, 14, was enjoying evening walk through her leafy Midwest neighborhood... then a stranger in a black car pulled up alongside her and horror ensued Scandalous underbelly of America's new high-stakes obsession: Secret backroom games, brazen cheating allegations... and savage public humiliations I know the devil, he's far more terrifying than in the movies... you can feel his power He became a MAGA star at Trump rallies dressed as the border wall... find out what happened to'Brick Suit Guy' in the free DC Insider newsletter Rich Christians in the'Hamptons of South' are turning on their new neighbor - beach-baptizer and MAGA convert Russell Brand Hugh Jackman's girlfriend Sutton Foster admits she feels'really alone' after she was pictured looking tense with actor and says'women shouldn't be pitted against one another' amid ongoing comparisons to his ex-wife Naomi Osaka doubles down with new French Open'fashion show', despite infuriating opponent, as she adds an ivory train to her'problematic' Eiffel Tower dress as part of £7.5m Nike deal Every man I date has the same vile bedroom kink... it's a total turn off, but I keep saying yes: DEAR JANE Russia's tactics in Ukraine reach a new hellish low as troops are forced to crawl for miles through underground pipes - with a life expectancy of ten minutes at the other end Our perfect summer body secrets: We've found the ultimate shortcut to the'after' photo... and the easy '30:30' diet that sparked a 22-pound transformation Triumphant Trump nominee's bold statement: Cheater Ken Paxton struts out in Margaritaville mode as secrets of his love nest with mistress are exposed Iran attacks US airbase after Trump condemns Tehran's peace plan and strikes regime drone site near Strait of Hormuz Kim Kardashian is introduced to Lewis Hamilton's mother Carmen Larbalestier as new couple dine out with their families in Los Angeles Trump's DHS chief rocked by wild rumor about his WIFE... as furious staff leak scandalous details about his life of luxury Meghan Markle adds luxury matchboxes to As Ever product range as she reveals'limited edition' item will be part of £190 candle set How I dropped from 17.5st to 10st WITHOUT getting loose, saggy skin. So many women struggle with unsightly wrinkles and flapping folds left by extreme weight loss. Here's how to avoid them Uber is making a major update to improve safety for millions of passengers in the UK. Riders will now be able to make audio recordings of their journey through the Uber app if they feel unsafe. Users can activate the feature either before or during the trip and start recording at any point with the press of a button.

It's part of Amazon's efforts to reach net-zero carbon across its operations in the coming years. Amazon Japan has started using the country's iconic bullet trains to move packages between facilities across different regions. The company said teaming up with Japan Railway is part of its efforts to cut both delivery times and carbon dioxide emissions. Japan's Shinkansen can reach speeds of up to 200 mph and can cut down travel times, say, from Tokyo to Osaka from around 8 hours to two-and-a-half hours. They also run on electricity delivered by an overhead electrical system. Back in 2019, the company launched an initiative that aims for net zero carbon emissions for deliveries.

Countries including Japan see the ability to control chips, data centers and AI models as directly related to national resilience in a landscape dominated by U.S. and Chinese technology. Sakura Internet's chief said the company may need to hike its capital spending by nearly seven times its initial plan to keep up with artificial intelligence demand in Japan. The data center operator is eyeing an allocation of as much as ¥20 billion to ¥30 billion ($125 million to $190 million) this fiscal year, founder and CEO Kunihiro Tanaka said. That's above the ¥4.4 billion in the Osaka-based company's official capital expenditure plan announced last month. "AI server usage rates are 80% to 90%," Tanaka, 48, said in an interview.

SoftBank will partner with South Korea's Cosmos Lab and DeltaX to enable mass production of large-scale battery cells from the fiscal year starting next April. SoftBank Group's mobile unit said it plans to begin large-scale battery cell manufacturing at its plant in Sakai, Osaka Prefecture, to address growing power demand for AI services. SoftBank Corp. will partner with South Korea's Cosmos Lab and DeltaX to enable mass production from the fiscal year starting next April, the company said in a statement Monday. The aim is to output energy storage systems at a scale of one gigawatt-hour per year, SoftBank said, which would make it one of the largest facilities in Japan, according to data from BloombergNEF. SoftBank could scale up to a capacity of several GWh, Bloomberg reported last month.

SoftBank Group's mobile unit plans to transform part of its factory in Osaka Prefecture into one of Japan's biggest production lines for large-scale batteries in an ambitious attempt at powering its own artificial intelligence data centers. SoftBank Corp. aims to bring that production online within the next five years, according to people familiar with the matter. They asked not to be named as deliberations remain private. After SoftBank executives mulled different purposes for the plant in the city of Sakai, including robotics manufacturing, they decided to pursue energy. The Tokyo-based group led by Masayoshi Son is one of the world's foremost supporters of AI, having committed hundreds of billions of dollars to investment in data centers, cloud services and bets on startups like OpenAI.

RoboCup is an international competition that promotes and advances robotics and AI through the challenges presented by its various leagues. We got the chance to sit down with Professor Manuela Veloso, one of RoboCup's founders, to find out more about how it all started, how the community has grown over the years, and the vision for the future. I think it would be very interesting to go right back to the beginning and hear how RoboCup got started. What was the initial idea, and how did it get set up? So we are talking about the mid-90s. In terms of the research in those days, it was the beginning of the internet and many AI and computer science researchers were focused on the internet, first on sophisticated search algorithms, on natural language understanding, on information retrieval, and then on software agents and machine learning applied to digital information. From what I recall, there was a smaller group of researchers who were interested in actual, physical robots, and in particular in AI and robotics.

Variational inference (VI) is a central tool in modern machine learning, used to approximate an intractable target density by optimising over a tractable family of distributions. As the variational family cannot typically represent the target exactly, guarantees on the quality of the resulting approximation are crucial for understanding which of its properties VI can faithfully capture. Recent work has identified instances in which symmetries of the target and the variational family enable the recovery of certain statistics, even under model misspecification. However, these guarantees are inherently problem-specific and offer little insight into the fundamental mechanism by which symmetry forces statistic recovery. In this paper, we overcome this limitation by developing a general theory of symmetry-induced statistic recovery in variational inference. First, we characterise when variational minimisers inherit the symmetries of the target and establish conditions under which these pin down identifiable statistics. Second, we unify existing results by showing that previously known statistic recovery guarantees in location-scale families arise as special cases of our theory. Third, we apply our framework to distributions on the sphere to obtain novel guarantees for directional statistics in von Mises-Fisher families. Together, these results provide a modular blueprint for deriving new recovery guarantees for VI in a broad range of symmetry settings.

Background: Single-cell RNA sequencing (scRNA-seq) enables gene expression profiling at cellular resolution but is inherently affected by sparsity caused by dropout events, where expressed genes are recorded as zeros due to technical limitations. These artifacts distort gene expression distributions and compromise downstream analyses. Numerous imputation methods have been proposed to recover latent transcriptional signals. These methods range from traditional statistical models to deep learning (DL)-based methods. However, their comparative performance remains unclear, as existing benchmarks evaluate only a limited subset of methods, datasets, and downstream analyses. Results: We present a comprehensive benchmark of 15 scRNA-seq imputation methods spanning 7 methodological categories, including traditional and DL-based methods. Methods are evaluated across 30 datasets from 10 experimental protocols on 6 downstream analyses. Results show that traditional methods, such as model-based, smoothing-based, and low-rank matrix-based methods, generally outperform DL-based methods, including diffusion-based, GAN-based, GNN-based, and autoencoder-based methods. In addition, strong performance in numerical gene expression recovery does not necessarily translate into improved biological interpretability in downstream analyses, including cell clustering, differential expression analysis, marker gene analysis, trajectory analysis, and cell type annotation. Furthermore, method performance varies substantially across datasets, protocols, and downstream analyses, with no single method consistently outperforming others. Conclusions: Our findings provide practical guidance for selecting imputation methods tailored to specific analytical objectives and underscore the importance of task-specific evaluation when assessing imputation performance in scRNA-seq data analysis.

Financial statement auditing is conducted under a risk-based evidence approach to obtain reasonable assurance. In practice, auditors often perform additional sampling or related procedures when an initial sample does not provide a sufficient basis for a conclusion. Across jurisdictions, current standards and practice manuals acknowledge such extensions, while the statistical design of sequential audit procedures has not been fully explored. This study formulates audit sampling with additional, sequentially collected items as a sequential testing problem for a finite population under sampling without replacement. We define null and alternative hypotheses in terms of a tolerable deviation rate, specify stopping and decision rules, and formulate exact sequential boundary conditions in terms of finite-population error probabilities. For practical implementation, we calibrate those boundaries by Monte Carlo simulation at least-favorable deviation rates. The exact design yields ex ante control of decision error probabilities, and the simulation-based implementation approximates that design while allowing the computation of expected stopping times. The framework is most naturally suited to attribute auditing and deviation-rate auditing, especially tests of controls, and it can be extended to one-sided, two-stage, and truncated designs.

We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric problem, particularly in multidimensional settings, since the covariance function is defined on a product domain and thus suffers from the curse of dimensionality. This motivates the use of adaptive estimators, such as deep learning estimators. However, existing theoretical results are largely limited to estimators with explicit analytic representations, and the properties of general learning-based estimators remain poorly understood. We establish an oracle inequality for a broad class of learning-based estimators that applies to both sparse and dense observation regimes in a unified manner, and derive convergence rates for deep learning estimators over several classes of covariance functions. The resulting rates suggest that structural adaptation can mitigate the curse of dimensionality, similarly to classical nonparametric regression. We further compare the convergence rates of learning-based estimators with several existing procedures. For a one-dimensional smoothness class, deep learning estimators are suboptimal, whereas local linear smoothing estimators achieve a faster rate. For a structured function class, however, deep learning estimators attain the minimax rate up to polylogarithmic factors, whereas local linear smoothing estimators are suboptimal. These results reveal a distinctive adaptivity-variance trade-off in covariance function estimation.