Belarus and Russia's show of firepower appears to be a message to Europe In a large field 45 miles (72km) from Belarus' capital Minsk, a battle is raging. There are giant explosions as Sukhoi-34 bombers drop guided bombs. Helicopter gunships join the attack, while surveillance drones sweep overhead to view the damage. Together with other international media we've been brought to the Borisovsky training ground where Belarusian and Russian forces are taking part in joint manoeuvres. Military attachés, too, from a variety of embassies are observing the drill from a viewing platform.

The 77th Primetime Emmy Awards have taken place in Los Angeles on Sunday night, with shows The Studio, The Pit and Adolescence dominating the awards. Owen Cooper became the youngest ever male Emmy winner at 15-years-old, for his breakout role in the Netflix miniseries Adolescence. Seth Rogan's comedy series The Studio scooped up four Emmys, while The Pitt beat out the likes of Severance and The White Lotus to win Best Drama. 'No doubt' Russia will cross Nato border if Ukraine falls, former US VP says Former US Vice-President Mike Pence calls for security guarantees in Ukraine to help deliver "just and lasting peace". The US House Oversight Committee has released new surveillance footage recorded hours before the convicted paedophile's death.

How is Russia replenishing its military? What is a'coalition of the willing'? How China forgot promises and'debts' to Ukraine How are Europe, the US pulling apart on Ukraine? Despite Russian drone strikes, Kharkiv's factories stand firm for Ukraine's security Russian forces killed two people in Ukraine's Kherson, including a 49-year-old woman who was found dead in the rubble of her home, authorities said, a day after Russian attacks killed six people across the country. Ukrainian President Volodymyr Zelenskyy said that Ukrainian soldiers were advancing in the border areas of the northern Sumy region, and said Russian forces had suffered significant losses in the Donetsk and Kharkiv regions along the 1,000km (620-mile) front line.

Modern machine learning often requires training with large batch size, distributed data, and massively parallel compute hardware (like mobile and other edge devices or distributed data centers). Communication becomes a major bottleneck in such settings but methods like Local Stochastic Gradient Descent (Local SGD) show great promise in reducing this additional communication overhead. Local SGD consists of three parts: a local optimization process, an aggregation mechanism, and an outer optimizer that uses the aggregated updates from the nodes to produce a new model. While there exists an extensive literature on understanding the impact of hyperparameters in the local optimization process, the choice of outer optimizer and its hyperparameters is less clear. We study the role of the outer optimizer in Local SGD, and prove new convergence guarantees for the algorithm. In particular, we show that tuning the outer learning rate allows us to (a) trade off between optimization error and stochastic gradient noise variance, and (b) make up for ill-tuning of the inner learning rate. Our theory suggests that the outer learning rate should sometimes be set to values greater than $1$. We extend our results to settings where we use momentum in the outer optimizer, and we show a similar role for the momentum-adjusted outer learning rate. We also study acceleration in the outer optimizer and show that it improves the convergence rate as a function of the number of communication rounds, improving upon the convergence rate of prior algorithms that apply acceleration locally. Finally, we also introduce a novel data-dependent analysis of Local SGD that yields further insights on outer learning rate tuning. We conduct comprehensive experiments with standard language models and various outer optimizers to validate our theory.

Graph Neural Networks (GNNs) are widely used in learning on graph-structured data, yet a principled understanding of why they succeed or fail remains elusive. While prior works have examined architectural limitations such as over-smoothing and over-squashing, these do not explain what enables GNNs to extract meaningful representations or why performance varies drastically between similar architectures. These questions are related to the role of generalisation: the ability of a model to make accurate predictions on unlabelled data. Although several works have derived generalisation error bounds for GNNs, these are typically loose, restricted to a single architecture, and offer limited insight into what governs generalisation in practice. In this work, we take a different approach by deriving the exact generalisation error for GNNs in a transductive fixed-design setting through the lens of signal processing. From this viewpoint, GNNs can be interpreted as graph filter operators that act on node features via the graph structure. By focusing on linear GNNs while allowing non-linearity in the graph filters, we derive the first exact generalisation error for a broad range of GNNs, including convolutional, PageRank-based, and attention-based models. The exact characterisation of the generalisation error reveals that only the aligned information between node features and graph structure contributes to generalisation. Furthermore, we quantify the effect of homophily on generalisation. Our work provides a framework that explains when and why GNNs can effectively leverage structural and feature information, offering practical guidance for model selection.

We propose an efficient algorithm for tensor PCA based on counting a specific family of weighted hypergraphs. For the order-$p$ tensor PCA problem where $p \geq 3$ is a fixed integer, we show that when the signal-to-noise ratio is $λn^{-\frac{p}{4}}$ where $λ=Ω(1)$, our algorithm succeeds and runs in time $n^{C+o(1)}$ where $C=C(λ)$ is a constant depending on $λ$. This algorithm improves a poly-logarithmic factor compared to previous algorithms based on the Sum-of-Squares hierarchy \cite{HSS15} or based on the Kikuchi hierarchy in statistical physics \cite{WEM19}. Furthermore, our result shows a smooth tradeoff between the signal-to-noise ratio and the computational cost in this problem, thereby confirming a conjecture posed in \cite{KWB22}.

In the aftermath of disasters, many institutions worldwide face challenges in continually monitoring changes in disaster risk, limiting the ability of key decision-makers to assess progress towards the UN Sendai Framework for Disaster Risk Reduction 2015-2030. While numerous efforts have substantially advanced the large-scale modeling of hazard and exposure through Earth observation and data-driven methods, progress remains limited in modeling another equally important yet challenging element of the risk equation: physical vulnerability. To address this gap, we introduce Graph Categorical Structured Variational Autoencoder (GraphCSVAE), a novel probabilistic data-driven framework for modeling physical vulnerability by integrating deep learning, graph representation, and categorical probabilistic inference, using time-series satellite-derived datasets and prior expert belief systems. We introduce a weakly supervised first-order transition matrix that reflects the changes in the spatiotemporal distribution of physical vulnerability in two disaster-stricken and socioeconomically disadvantaged areas: (1) the cyclone-impacted coastal Khurushkul community in Bangladesh and (2) the mudslide-affected city of Freetown in Sierra Leone. Our work reveals post-disaster regional dynamics in physical vulnerability, offering valuable insights into localized spatiotemporal auditing and sustainable strategies for post-disaster risk reduction.

Efficient hospital management systems (HMS) are critical worldwide to address challenges such as overcrowding, limited resources, and poor availability of urgent health care. Existing methods often lack the ability to provide accurate, real-time medical advice, particularly for irregular inputs and underrepresented languages. To overcome these limitations, this study proposes an approach that fine-tunes large language models (LLMs) for Arabic medical text generation. The system is designed to assist patients by providing accurate medical advice, diagnoses, drug recommendations, and treatment plans based on user input. The research methodology required the collection of a unique dataset from social media platforms, capturing real-world medical conversations between patients and doctors. The dataset, which includes patient complaints together with medical advice, was properly cleaned and preprocessed to account for multiple Arabic dialects. Fine-tuning state-of-the-art generative models, such as Mistral-7B-Instruct-v0.2, LLaMA-2-7B, and GPT-2 Medium, optimized the system's ability to generate reliable medical text. Results from evaluations indicate that the fine-tuned Mistral-7B model outperformed the other models, achieving average BERT (Bidirectional Encoder Representations from Transformers) Score values in precision, recall, and F1-scores of 68.5\%, 69.08\%, and 68.5\%, respectively. Comparative benchmarking and qualitative assessments validate the system's ability to produce coherent and relevant medical replies to informal input. This study highlights the potential of generative artificial intelligence (AI) in advancing HMS, offering a scalable and adaptable solution for global healthcare challenges, especially in linguistically and culturally diverse environments.

HGTV's Erin Napier erupts at fans after being slammed for refusing to'celebrate' Charlie Kirk's death Truth about America's murder hotspots... as map reveals surprising cities Trump may send National Guard City of vanishing children: Dark truth behind the THOUSANDS of missing kids in Rust Belt town... and the underworld they are plunged into Monkees musician Bobby Hart who wrote the band's theme and Last Train To Clarksville dies at 86 I didn't air any dirty laundry in public - my conscience is clear, says Prince Harry during visit to Ukraine: Duke reveals he wants to spend more time in the UK in the next year as'the focus really has to be on my dad' FBI tried to hide trans identity of Charlie Kirk suspect's lover after his chilling four-word response to investigators I've been lying to my husband about the thing he loves most. If I come clean, he'll be humiliated: DEAR JANE My HOA from hell fined me $1,000 per day for the pettiest issue imaginable inside my $600k home... then I realized they were spying on me Teen arrested'destroying' Charlie Kirk memorial as chilling copycat fantasy exposed Hollywood insiders lay bare'intimidation' tactics by woke celebrities branded worse than the Ku Klux Klan: 'Everyone is living in fear' NFL fans left in disbelief as Russell Wilson launches'mind blowing' touchdown pass for New York Giants Islanders claim they know the sinister truth about Amelia Earhart... and demand the proof is finally released Urgent warning as toxic fumes on major airlines' flights cause devastating brain injuries I dropped from a size 20 to a size 12 in five months - these'healthy' foods were making me overweight Who are the shortest actresses in Hollywood? Emotional Tucker Carlson reveals'close call' on his life as he breaks silence on Charlie Kirk: 'We're in a civil war' People are just realizing that they're pronouncing the name of America's biggest holiday wrong The three-word phrase to get people to listen'instantly,' according to a public speaking expert Capturing people's attention during a presentation, or in any crowded room, is often half the battle, and one many fail to win. Now, a public speaking expert has shared a three-word phrase he claimed will get people listening to you'instantly.' John Bowe, a speech trainer, said that starting with'Imagine this scenario...' will have the room perk up and pay attention. 'It works every time,' Bowe wrote for CNBC, breaking down how each word is highly engaging.

Grok claimed the location was Trafalgar Square. Grok claimed the location was Trafalgar Square. Musk's Grok AI bot falsely suggests police misrepresented footage of far-right rally in London The Metropolitan police has had to counter false suggestions by the artificial intelligence on Elon Musk's X platform that the force passed off footage from 2020 as being from Saturday's far-right rally in the city. The claim by the chatbot Grok was in answer to an X user's query about where and when footage of police clashing with crowds was filmed. Police seek man who called for Keir Starmer to be'assassinated' at far-right rally Grok, which has had a track record of giving false and misleading answers, replied: "This footage appears to be from an anti-lockdown protest in London's Trafalgar Square on 26 September 2020, during clashes between demonstrators and police over Covid restrictions."