Subgroup analyses within randomized controlled trials are often underpowered due to limited sample sizes. We address this challenge by leveraging trial participants outside the subgroup of interest to augment estimation within the subgroup. Specifically, we study two Targeted Maximum Likelihood Estimators (TMLEs) that borrow information from non-subgroup participants within the same trial: a TMLE with pooled regression (TMLE-PR) and an Adaptive Targeted Maximum Likelihood Estimator (A-TMLE). Both estimators enable information sharing without relying on any external real-world data, thereby capitalizing on key strengths of the trial: most importantly, the protection against bias afforded by the randomized treatment, but also harmonized data collection, and consistent treatment and outcome definitions. The general strategy proposed here directly advances the priorities of key regulatory agencies, including the FDA, by improving the precision of subgroup-specific treatment effect estimates without introducing external sources of bias, thereby facilitating rigorous inference to support equitable labeling, access, and post-market evaluation. In a case study based on analysis of data from a cardiovascular outcome trial (LEADER, NCT01179048), we estimate the risk reduction of major adverse cardiac events (MACE) under liraglutide treatment among Black and Asian subgroups -- each comprising less than 10\% of the trial population -- using the proposed estimators that borrow information from the remainder of the trial. Using A-TMLE, in particular, we find estimated absolute MACE risk reductions of 1.6, 1.5, and 1.5 percentage points among Asian participants and 2.1, 2.0, and 2.1 percentage points among Black participants at 365, 540, and 730 days, respectively, with 95\% confidence intervals excluding the null at each time point.

We consider the problem of testing properties of graphs underlying high-dimensional graphical models. We adopt the model of covariance queries introduced by Lugosi, Truszkowski, Velona, and Zwiernik (2021). We study the case when the underlying graph is a tree. The main results of the paper show that, while reconstructing the entire tree may be costly, certain global structural properties can be tested efficiently. In particular, we design randomized tests for global structural properties that use a sub-quadratic number of queries. We develop testing procedures for several fundamental properties, including the number of leaves, the maximum degree, the typical distance, and the diameter of the tree. For each property, we obtain explicit query complexity bounds that depend on the target threshold and tolerance parameters.

Neural network surrogate models have emerged as a promising approach to model solution fields for a wide variety of boundary value problems encountered in physical modeling. Stochastic problems represent an area of particularly high interest because of the potential to significantly reduce the repeated evaluation of expensive forward models via traditional numerical solvers when conducting parametric analysis. However, many studies found in the literature primarily focus on the ability of neural network surrogate models to represent deterministic samples or mean field solutions and largely overlook surrogate model performance at the tails of the distribution. The present study examines in detail the ability of neural network surrogate models to capture the full distribution of solution fields over the entire probability space, while emphasis is placed at the tails of the distribution. Serving as a canonical problem is the heat conduction equation with a highly stochastic source term, inducing extremely large variation in the thermal solution field. Comparisons are made between a classic feed-forward fully connected network and a Deep Operator Network architecture, using both data-driven and physics-informed loss functions. Results show that the worst-case prediction errors are an order of magnitude larger than the mean field error, highlighting the importance of the outlier samples. The large errors associated with extreme samples result from the networks having to extrapolate beyond the bounds of the training data. A method for identifying these samples is presented along with a discussion of potential approaches to account of their errors. Among the models considered, the fully connected neural network trained using a weak form residual loss performs best in handling these extrapolated inputs, achieving the highest prediction accuracy for the numerically produced datasets.

What would make the UK a better place to live? People across the UK are being urged to share their vision for how their community and country's future should look, as part of a major new research project. The National Conversation is being launched with voice notes submitted by high-profile figures, including former footballer Gary Lineker, Chief Rabbi Sir Ephraim Mirvis, and broadcaster Mariella Frostrup. Participants will be asked to complete a survey carried out by researchers from the University of Oxford and leave a 60-second voice note. AI models will then be used to analyse thousands of responses to map what could bring us together.

Inside the'kill-zone' on Ukraine's front line, where new weapons have transformed war After 225 days stuck in a front-line foxhole, the Ukrainian infantryman's muscles were so weak he could barely walk. His commanders had tried five times to swap him with another soldier - but they could never reach him. Rotating soldiers on the front line in eastern Ukraine is extremely difficult because of the constant threat of drones. This area near Kostyantynivka is currently one of the most dangerous hotspots and the Ukrainian military admits that Russian forces have reached its outskirts. Known as Kenya, the infantryman took two days to walk 11km (6.8 miles) to get back to his brigade, avoiding mines and hiding from drones to get out.

ISIS shadow commander Abu-Bilal al-Minuki was killed in a precision strike in Nigeria after human intelligence penetrated defenses that had shielded him for years, analyst says.

Bulgarian pop star Dara was met by a crowd of fans in Sofia airport on Sunday, celebrating her historic Eurovision win. The 27-year-old's tune Bangaranga won Bulgaria its first ever title in the song contest. Thank you for being here, she told fans as she arrived in the Bulgarian capital, Sofia, before adding I cannot wait to dip my toes in this atmosphere. Russia launched one of the biggest air strikes on Kyiv since the start of the war with several apartment blocks hit. Why is the Princess of Wales in Italy this week?

Nothing to see here: Cowboys quarterback Dak Prescott and his ex's bridesmaid are just friends Can't sleep, Japanese bear-fighting robo-wolves will eat me and a gorilla trade captivates the nation A replica of KITT from'Knight Rider' got a traffic ticket in another state despite being in a museum Jena Sims covers her butt with a bow at the SI Swimsuit party, the NFL saves us from Romo & is Star Wars dead? Taylor Sheridan shocks'Yellowstone' fans with new spinoff series, provides viewers with dark ride Early reviews for new'Star Wars' movie are generally horrific, but does anyone even care at this point? Retired Navy admiral makes bombshell claim about UFOs and'non-human intelligence' controlling them Mother's Day chaos at a steakhouse includes knives thrown at waiters and a touching mother-daughter arrest Japanese bear-fightin' robo-wolves are pure unleaded nightmare fuel but they're working Jennifer Lopez's dress holds on for dear life at her Netflix event, Trump powers through some wine & Kay Adams Trump warns Iran'clock is ticking' amid Strait of Hormuz tensions Sen. John Kennedy reacts to Bill Cassidy's primary loss in Louisiana Peter Doocy gives BEHIND-THE-SCENES look at Trump's China visit Speaker Johnson says Trump admin'laid the groundwork' for new China deal Sen. Bill Cassidy ousted in Louisiana primary by Trump-backed opponent Donald Trump rejects Xi Jinping's offer on Iran conflict Senate Republicans narrowly block Democrats' effort to end Iran conflict Cignetti reflected on his time at Alabama under Nick Saban, describing the intensity of a program where every day felt like 4th and 1. Footage from a high-speed chase in Wisconsin earlier this month shows the fleeing driver going airborne and jumping his car over another. It's one of the most insane dashcam videos you'll ever see. The Fond du Lac County Sheriff's Office released the now-viral footage of the arrest, which took place on Saturday morning, May 9. A fleeing driver goes airborne and flies his car over another one during a high-speed police chase in Wisconsin.

No one wants to hang out with her': Why Meghan and Harry have been ditched by A-list friends as insiders reveal Oprah's merciless snub, why the Clooneys now want nothing to do with them - and how SHE'S the problem Truth about Kate Middleton's past before Prince William... we Americans see this for what it is: KENNEDY I was on track to make $1 million... then I quit my job and moved into an off-grid tiny home with no running water or electricity Professional tasters decide best and worst fast food cheeseburger - do you agree? Hamptons cancer cluster: Rates are spiking in summer enclave of New York's wealthy elite... and doctors think they know the tragic reason why Disturbing trove of images woke Los Angeles mayor Karen Bass doesn't want you to see: Filthy truth is so much worse than people think... Comedian replacing Stephen Colbert appears to take a swipe at his predecessor as he vows to avoid politics and'just be funny' Jordon Hudson blasts double standards over Mike Vrabel and Dianna Russini'affair' scandal: 'What is going on?' I've discovered my'nice' neighbor's dirty secret... what I caught him doing one night was far more disturbing than I realized: DEAR JANE SNL season finale cold open sees ghost of Jeffrey Epstein played by Will Ferrell'haunt' Trump as dark jokes leave viewers shocked Golf star becomes instant fan favorite after stopping to smoke a cigarette with crowd in the middle of the PGA Championship: 'Man of the people' New kind of penis enlargement surgery will add inches, claims the doctor set to offer it... but there is a gruesome detail that may make some think twice I saw a 40-year-old middle-class mom in a psychiatric ward after a single hit of this drug. Her symptoms were terrifying but it's so common now... here's what you must know: DR MAX PEMBERTON US airman returns home to every dog owner's nightmare as he finds his husky DEAD in garage after trusting pet sitter to take care of his beloved companion I'm an exorcist... Here's the chilling encounter that made me believe UFOs are the work of Satan A Catholic priest and exorcist who has encountered demons first-hand has revealed a chilling experience that led him to believe UFOs are actually the work of the devil. Father Carlos Martins, an Ontario-born priest who has performed exorcisms around the world, believes the UFO phenomenon is part of a larger spiritual deception designed to undermine Christianity and cast doubt on the Bible . The priest said a longtime friend who later converted to Christianity once witnessed a gigantic spacecraft hovering silently over a suburban park before it shot away'instantly to the speed of a bullet.'

Can't sleep, Japanese bear-fighting robo-wolves will eat me and a gorilla trade captivates the nation A replica of KITT from'Knight Rider' got a traffic ticket in another state despite being in a museum Jena Sims covers her butt with a bow at the SI Swimsuit party, the NFL saves us from Romo & is Star Wars dead? Taylor Sheridan shocks'Yellowstone' fans with new spinoff series, provides viewers with dark ride Early reviews for new'Star Wars' movie are generally horrific, but does anyone even care at this point? Retired Navy admiral makes bombshell claim about UFOs and'non-human intelligence' controlling them Mother's Day chaos at a steakhouse includes knives thrown at waiters and a touching mother-daughter arrest Japanese bear-fightin' robo-wolves are pure unleaded nightmare fuel but they're working Jennifer Lopez's dress holds on for dear life at her Netflix event, Trump powers through some wine & Kay Adams Eric Church's uses his guitar to deliver one of the most powerful addresses ever at UNC commencement Speaker Johnson says Trump admin'laid the groundwork' for new China deal Sen. Bill Cassidy ousted in Louisiana primary by Trump-backed opponent Donald Trump rejects Xi Jinping's offer on Iran conflict Senate Republicans narrowly block Democrats' effort to end Iran conflict General Jack Keane warns of China's ambitions on Taiwan Gen Z driving'spiritual revival' with increased church attendance Pastor says Trump's visit to Detroit church meant'everything' David Perdue discusses Trump's new China trade commitments amid renewed relations OutKick Nothing to see here: Cowboys quarterback Dak Prescott and his ex's bridesmaid are just friends Dan Dakich reacts to the bombshell new photos of Mike Vrabel and Dianna Russini in Arizona that officially debunk the girls trip narrative. Sometimes a relationship leads to marriage. Sometimes those marriages end in divorce.