When you purchase through links in our articles, we may earn a small commission. It's not perfect, but it definitely surprised me The Mammotion Luba 3 AWD turns out to be a lot more capable than expected, handling a rough, awkward yard surprisingly well, even if the app and setup aren't always smooth. Before testing, I never gave robot lawn mowers the time of day. They just seemed like expensive gadgets for people who didn't want to deal with mowing. After a few weeks with the Mammotion Luba 3 AWD, that assumption didn't really hold up.

Karmelo Anthony's sobbing mother pleads with jurors to show'mercy' for her son as they prepare to sentence him for murder of Austin Metcalf, 17, that shocked America Caitlyn Jenner biographer and Robin Riker's ex William Hasley found dead on hiking trail at 78 Karmelo Anthony's mother sobs with shock as son is found guilty of murdering Austin Metcalf, 17, in stabbing that horrified America: Live updates Disgraceful texts'hot' teacher sent boy, 17, who she had illegal sex with where she moaned about her HUSBAND Everyone always said I cleared my throat a lot. But then I developed shoulder pain and doctors discovered the sinister cause... the world's deadliest cancer. Don't leave it too late like I did Leaked transcript of UNAIRED 60 Minutes interview exposes REAL reason'callous' CBS star Scott Pelley'deserved to be fired' Urgent recall for 1.1m vehicles over fears they could spontaneously CATCH FIRE even when parked Disturbing new death scene photos show tech whistleblower's haunting final moments... as forensic report casts doubt on suicide claims: 'Execution angle' 'Great' mom, 32, tried to gas herself and her three young kids to death after inviting them to'popcorn sleepover' in car, prosecutors allege The porn-fuelled fantasy middle-class husbands are desperate to try with their wives... and it almost always ends in divorce: JANA HOCKING Grim-faced former Louisiana mayor Misty Roberts arrives in court for sentencing after being found guilty of having sex with son's teenage friend John Oliver's private panic: Late-night curse spreads and host prepares for worst as insiders reveal his desperate'plan B'... and the industry whispers swirling about his fate Woke Vegas school compared boy to racist cross burner over pro-ICE stickers and expelled him... but did not punish pro-migrant students for class walkout, lawsuit alleges Medical student, 24, died by suicide in his white coat a day after he was suspended for alleged'inappropriate' behavior towards female patient, lawsuit alleges, as his heartbreaking goodbye note to parents is revealed Mother's final words before she was shot dead'by new husband' in front of her two young children All the backstage gossip from Miami Swim Week: Insider exposes'catty' VIP's diva demands... STEALING... and'morbidly embarrassing' celeb moment everyone is whispering about The brewing super El Niño will likely be the strongest ever recorded, new predictions suggest. The latest modelling from the European Centre for Medium-Range Weather Forecasts (ECMWF) shows that sea temperatures will be well above average later this year. Scientists measure the intensity of El Niño using the Niño 3.4 index, which records sea surface temperature anomalies between 5 degrees north and 5 degrees south latitude, and 120 degrees west and 170 degrees west longitude.

"The Lost Soldiers," "Homebound," "Once Upon a Time There Was Truth," and "My World Is Melting." The year is 1919, the midst of Bolshevik takeover in Ukraine, and twenty-eight Red Army soldiers have vanished into thin air, last seen at a bathhouse. Kolechko must track them down. He gets little help from the absurd locals, who range from obstinately useless to selfishly malicious. Kolechko is a kind of anti-Poirot--a fairly conventional man whose powers of detection lie not in a dazzling intuition but in a supernatural severed ear, which has a bug-like ability to pick up dialogue.

Is Elon Musk's SpaceX Really Worth $1.75 Trillion? The billionaire spent more than two decades creating a successful space company. Now he's pitching it as an A.I. play. Later this week, Elon Musk's SpaceX is expected to issue stock to investors in what is shaping up to be the biggest initial public offering ever. The company has said it will issue 555,555,555 shares at a price of $135, which would value it at about $1.75 trillion.

Why this year's World Cup ball may not fly as far A team of outside researchers has been studying how Adidas's redesigned soccer ball cuts through the air. Much is new about this month's upcoming FIFA World Cup tournament, which will be held in the US, Canada, and Mexico. It hosts more teams than ever before. It's the first to occur in three different host countries. And, like predecessor cups for over half a century, it will employ a soccer ball with a brand-new design. One group of researchers that has been testing the physics of World Cup balls for the past 20 years recently studied this new entry, called the Trionda.

South Korean President Lee Jae Myung is placing his hopes on former Naver Chief Executive Han Seong Sook to help better use the nation's tech expertise for future growth and ensure its benefits spread more widely through the economy. Han will become the country's second female premier, assuming her appointment is approved by the national assembly, elevating a former technology executive to one of the nation's highest political posts. The tapping of Han underscores Lee's commitment to shoring up future growth of the domestic economy and the need to leverage a wider range of industries. During her five years at the helm of Naver, a company sometimes called the Google of Korea, Han helped broaden its revenue streams beyond its search engine model to also draw on e-commerce, fintech and content generation. In a time of both misinformation and too much information, quality journalism is more crucial than ever. By subscribing, you can help us get the story right.

Predicting outputs that are located in non-Euclidean spaces, such as probability distributions, networks, and symmetric positive-definite matrices, is becoming increasingly important in modern data analysis, particularly when inputs are high-dimensional. We propose DeSI (Deep Single-Index Fréchet Regression), a semiparametric framework for regression with metric space-valued outputs and multivariate inputs that assumes a single-index structure for the conditional Fréchet mean. DeSI estimates an interpretable index direction, which quantifies the relative importance of inputs, using a deep neural network, and performs Fréchet regression along the resulting one-dimensional index in the target metric space. This structure mitigates the curse of dimensionality while retaining interpretability, which stands in contrast to standard deep neural networks. We establish theoretical guarantees for DeSI, including uniform approximation and convergence rates, and demonstrate its strong predictive performance through simulations on distributions, networks, and symmetric positive-definite matrices, as well as an application to compositional mood data from New Jersey.

We study the minimax estimation error for distributed covariance matrix estimation in the vertical-split (feature-split) setting, where two agents each observe different coordinates of $m$ i.i.d. sub-Gaussian samples and communicate a limited number of bits to a central server. While Rahmani et al. [2025] established nearly tight bounds for dense (unstructured) cross-covariance matrices, we investigate whether imposing elementwise $s$-sparsity on the cross-covariance $C_{21}$ can reduce the required communication and sample complexity. In contrast to the horizontal-split setting, where Braverman et al. [2016] showed that sparsity does not reduce communication cost for mean estimation, we prove that sparsity does help for cross-covariance estimation in the vertical split. Specifically, we establish minimax lower bounds showing that the communication budget per agent scales as $B_k = Ω(σ^4 d_k\, s' \log(d_1 d_2/s')/\varepsilon^2)$ and the sample complexity for cross-covariance estimation as $m = Ω(σ^4\, s' \log(d_1 d_2/s')/\varepsilon^2)$, where $s' = s \wedge d_{\min}$. For the $1$-sparse case, this yields an exponential improvement from $d_1 d_2$ to $\log(d_1 d_2)$ compared to the dense rate. Our lower bounds are established via Fano's method with an explicit sparse packing using a Varshamov--Gilbert-type argument for signed partial permutation matrices combined with the Conditional Strong Data Processing Inequality of Rahmani et al. [2025]. We show the bounds are tight with a matching achievable scheme, based on covering-net quantization and entry-wise hard thresholding, that attains the $s$-sparse lower bound up to polylogarithmic factors.

Decision-making in complex systems often requires understanding counterfactuals of general, potentially highdimensional, interventions with limited data. Collecting sufficient data for every counterfactual in complex systems may be near impossible due to cost or ethical reasons. With the recent growth in expressivity and power in generative modeling, generative models that can synthesize counterfactual outcomes under generalized interventions stand as a viable solution for supporting robust decision-making in real-world systems. In an ideal world, we may simply train a generative model with the data we have, and sample from the generator under the intervention of interest. Counterfactual generative modeling may fail with such an approach due to confounding bias. Correlations observed in the sampled data may be mistaken for true causal effects, yielding incorrect downstream decisions. For example, generating medical images under changes in intervention dose can help track disease progression and identify optimal dosing strategies. However, if the training data primarily consisted of those who were responsive to intervention (e.g., younger populations), then the generator would identify the ranges in the data as effective even if this does not hold for different populations (e.g.

Identifying most influential sets (MIS) - size-$k$ subsets whose removal maximally changes a target estimand - is typically infeasible because it requires searching over $\binom{n}{k}$ subsets. For estimands with linear-fractional leave-set-out effects, we show that MIS selection reduces to a one-parameter sequence of top-$k$ problems. Dinkelbach's method yields an algorithm with $\mathcal{O}(n)$ cost per iteration and finite termination. For fixed residualized inputs, the algorithm returns a globally optimal set for the univariate ratio objective, including the oracle-residualized partial linear model. With estimated nuisance functions, uniform denominator and generated-score stability imply approximation to the first-order oracle orthogonal-score objective; exact set recovery follows under a separation condition. Simulations and applications show that the method recovers exact MIS that were previously computationally inaccessible.