Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its behavior in high-dimensional regimes remains limited. In this paper, we study a data integration model in which two high-dimensional data matrices share a low-rank common latent structure while also containing individual-specific components. We analyze the singular vectors of the associated cross-covariance matrix using tools from random matrix theory and derive asymptotic characterizations of the alignment between estimated and true latent directions. These results provide a quantitative explanation of the reconstruction performance of the PLS variant based on Singular Value Decomposition (PLS-SVD) and identify regimes where the method exhibits counter-intuitive or limiting behavior. Building on this analysis, we compare PLS-SVD with principal component analysis applied separately to each dataset and show its asymptotic superiority in detecting the common latent subspace. Overall, our results offer a comprehensive theoretical understanding of high-dimensional PLS-SVD, clarifying both its advantages and fundamental limitations.

Spatial boundaries, such as ecological transitions or climatic regime interfaces, capture steep environmental gradients, and shifts in their structure can signal emerging environmental changes. Quantifying uncertainty in spatial boundary locations and formally testing for temporal shifts remains challenging, especially when boundaries are derived from noisy, gridded environmental data. We present a unified framework that combines heteroskedastic Gaussian process (GP) regression with a scaled Maximum Absolute Difference (MAD) Global Envelope Test (GET) to estimate spatial boundary curves and assess whether they evolve over time. The heteroskedastic GP provides a flexible probabilistic reconstruction of boundary lines, capturing spatially varying mean structure and location specific variability, while the test offers a rigorous hypothesis testing tool for detecting departures from expected boundary behaviors. Simulation studies show that the proposed method achieves the correct size under the null and high power for detecting local boundary shifts. Applying our framework to the Sahel Sahara transition zone, using annual Koppen Trewartha climate classifications from 1960 to 1989, we find no statistically significant decade scale changes in the arid and semi arid or semi arid and non arid interfaces. However, the method successfully identifies localized boundary shifts during the extreme drought years of 1983 and 1984, consistent with climate studies documenting regional anomalies in these interfaces during that period.

In this work, inspired by machine learning techniques, we propose a new Bayesian model for Small Area Estimation (SAE), the Fay-Herriot model with Spectral Clustering (FH-SC). Unlike traditional approaches, clustering in FH-SC is based on spectral clustering algorithms that utilize external covariates, rather than geographical or administrative criteria. A major advantage of the FH-SC model is its flexibility in integrating existing SAE approaches, with or without clustering random effects. To enable benchmarking, we leverage the theoretical framework of posterior projections for constrained Bayesian inference and derive closed form expressions for the new Rao-Blackwell (RB) estimators of the posterior mean under the FH-SC model. Additionally, we introduce a novel measure of uncertainty for the benchmarked estimator, the Conditional Posterior Mean Square Error (CPMSE), which is generalizable to other Bayesian SAE estimators. We conduct model-based and data-based simulation studies to evaluate the frequentist properties of the CPMSE. The proposed methodology is motivated by a real case study involving the estimation of the proportion of households with internet access in the municipalities of Colombia. Finally, we also illustrate the advantages of FH-SC over existing Bayesian and frequentist approaches through our case study.

California regulators are threatening to suspend Tesla's licence to sell its electric cars in the state early next year unless the car maker tones down its marketing tactics for its self-driving features after a judge concluded that the Elon Musk-led company has been misleading consumers about the technology's capabilities. The potential 30-day blackout of Tesla's sales in California in the United States is the primary punishment being recommended to the state's Department of Motor Vehicles in a decision released late on Tuesday. After presiding over five days of hearings held in Oakland, California, in July, Cox also recommended suspending Tesla's licence to manufacture cars at its plant in Fremont, California. But California regulators will not impose that part of the judge's proposed penalty. Tesla will have a 90-day window to make changes that more clearly convey the limits of its self-driving technology to avoid having its California sales licence suspended.

Nick Reiner's siblings Romy and Jake describe'unimaginable pain' as they break silence after brother's arrest and parents' murder The full story of Nick Reiner and these murders is so much more unbearable than everyone thinks. Even Hollywood wouldn't dare write it: MAUREEN CALLAHAN I saw Nick Reiner just hours before the murders. I've known the family for decades - he was always a weirdo... but what I spotted that night haunts me Tara Reid investigation into alleged drugging is CLOSED as police say there is'not enough evidence' Dilbert creator reveals he's paralyzed from waist down amid aggressive cancer battle he begged Trump to help with Dan Bongino set to QUIT Trump admin after FBI job'put strain on his marriage' When GUY ADAMS revealed his 10-week body transformation, it was so astonishing he was accused of faking it. MIT professor was shot dead in apartment building's HALLWAY as petrified neighbors describe finding his bloody body I knew Rob Reiner's monster son Nick his whole life: Family friend reveals his'grunting' and violent outbursts... how he always SMELLED... and sign everyone missed at age 11 Harry and Meghan are making Netflix adaptation of The Wedding Date after couple announced'first look' multi-year deal with streaming giant Baby-faced stepbrother considered a'suspect' in Anna Kepner's cruise ship murder breaks cover as FBI weighs charges Erika Kirk vs Candace Owens exposed: Insider reveals high-stakes secret meeting drama... and what comes next US car dealer charged with FRAUD after bankruptcy revealed depths of American's debt crisis Revealed: Exactly what a week of drinking is doing to you. HARRY WALLOP took heart, liver, brain and blood tests to find out the truth.

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.

This was the year that A.I.-generated content passed a kind of audiovisual Turing test, sometimes fooling us against our better judgment. The Turing test, a long-established tool for measuring machine intelligence, gauges the point at which a text-generating machine can fool a human into thinking it's not a robot. ChatGPT passed that benchmark earlier this year, inaugurating a new technological era, though not necessarily one of superhuman intelligence . More recently, however, artificial intelligence passed another threshold, a kind of Turing test for the eye: the images and videos that A.I. can produce are now sometimes indistinguishable from real ones. As new, image-friendly models were trained, refined, and released by companies including OpenAI, Meta, and Google, the online public gained the ability to instantly generate realistic A.I. content on any theme they could imagine, from superhero fan art and cute animals to scenes of violence and war.

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.