A Mos Food Services employee places an order via a microphone at an artificial intelligence drive-thru facility, which was unveiled to members of the media in Yoshikawa City, Saitama Prefecture, on Wednesday. The Japanese hamburger chain aims to improve store management efficiency by automating part of customer interaction with conversational AI amid a serious labor shortage. The company plans to introduce the new AI system at multiple outlets in fiscal 2026, which begins in April. In a media demonstration held at a store in the city of Yoshikawa, Saitama Prefecture, a Mos Food employee acting as a customer spoke into a microphone to place a drive-thru order. The AI system took the order after making suggestions such as, We recommend a limited-time avocado burger. Once the system is introduced, store employees will prepare food based on customer orders transmitted from the AI system.

River of waste'visible for miles' dumped at mountain beauty spot A farmer says she is devastated by a disgusting river of fly-tipped waste dumped down the side of a mountain. Katie Davies, whose family has owned land on Bwlch Mountain in Treorchy for 90 years, said the clean up could cost thousands of pounds and could also harm her sheep which graze on the land. Travel blogger Nathan Dixon, who captured drone footage showing the scale of the discarded waste, said the mess could be seen from three to five miles away, adding that it sticks out like a sore thumb. Rhondda Cynon Taf council said it always took action to hold those responsible for fly-tipping to account, while Natural Resources Wales (NRW) said fly-tipping was a serious crime. Davies, who runs small family business Nantymoel farm which produces Welsh beef and lamb, said the mess keeps me up at night.

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Could Ukraine hold a presidential election right now? Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? 'Ukraine is running out of men, money and time' At least three people have been reported killed after Russian forces struck the southeastern Ukrainian city of Zaporizhzhia, Governor Ivan Fedorov announced on the Telegram messaging app. Russian strikes also destroyed several private houses and cars, and left nearly 1,500 households without electricity, the governor said.

Computing $\log\det(A)$ for large symmetric positive definite matrices arises in Gaussian process inference and Bayesian model comparison. Standard methods combine matrix-vector products with polynomial approximations. We study a different model: access to trace powers $p_k = \tr(A^k)$, natural when matrix powers are available. Classical moment-based approximations Taylor-expand $\log(λ)$ around the arithmetic mean. This requires $|λ- \AM| < \AM$ and diverges when $κ> 4$. We work instead with the moment-generating function $M(t) = \E[X^t]$ for normalized eigenvalues $X = λ/\AM$. Since $M'(0) = \E[\log X]$, the log-determinant becomes $\log\det(A) = n(\log \AM + M'(0))$ -- the problem reduces to estimating a derivative at $t = 0$. Trace powers give $M(k)$ at positive integers, but interpolating $M(t)$ directly is ill-conditioned due to exponential growth. The transform $K(t) = \log M(t)$ compresses this range. Normalization by $\AM$ ensures $K(0) = K(1) = 0$. With these anchors fixed, we interpolate $K$ through $m+1$ consecutive integers and differentiate to estimate $K'(0)$. However, this local interpolation cannot capture arbitrary spectral features. We prove a fundamental limit: no continuous estimator using finitely many positive moments can be uniformly accurate over unbounded conditioning. Positive moments downweight the spectral tail; $K'(0) = \E[\log X]$ is tail-sensitive. This motivates guaranteed bounds. From the same traces we derive upper bounds on $(\det A)^{1/n}$. Given a spectral floor $r \leq λ_{\min}$, we obtain moment-constrained lower bounds, yielding a provable interval for $\log\det(A)$. A gap diagnostic indicates when to trust the point estimate and when to report bounds. All estimators and bounds cost $O(m)$, independent of $n$. For $m \in \{4, \ldots, 8\}$, this is effectively constant time.

Large language models (LLMs) are increasingly used in economics as predictive tools--both to generate synthetic responses in place of human subjects (Horton, 2023; Anthis et al., 2025), and to forecast economic outcomes directly (Hewitt et al., 2024a; Faria-e Castro and Leibovici, 2024; Chan-Lau et al., 2025). Their appeal in these roles is obvious: A pretrained LLM embeds a vast amount of information and can be deployed at negligible cost, often in settings where collecting new, domain-specific human data would be expensive or infeasible. What remains unclear is how to assess the quality of these predictions. This paper proposes a measure that quantifies the domain-specific value of LLMs in an interpretable unit: the amount of human data they substitute for. Specifically, we ask how much human data would be required for a conventional model trained on that data to match the predictive performance of the pretrained LLM in that domain.

Fairness-aware machine learning has recently attracted various communities to mitigate discrimination against certain societal groups in data-driven tasks. For fair supervised learning, particularly in pre-processing, there have been two main categories: data fairness and task-tailored fairness. The former directly finds an intermediate distribution among the groups, independent of the type of the downstream model, so a learned downstream classification/regression model returns similar predictive scores to individuals inputting the same covariates irrespective of their sensitive attributes. The latter explicitly takes the supervised learning task into account when constructing the pre-processing map. In this work, we study algorithmic fairness for supervised learning and argue that the data fairness approaches impose overly strong regularization from the perspective of the HGR correlation. This motivates us to devise a novel pre-processing approach tailored to supervised learning. We account for the trade-off between fairness and utility in obtaining the pre-processing map. Then we study the behavior of arbitrary downstream supervised models learned on the transformed data to find sufficient conditions to guarantee their fairness improvement and utility preservation. To our knowledge, no prior work in the branch of task-tailored methods has theoretically investigated downstream guarantees when using pre-processed data. We further evaluate our framework through comparison studies based on tabular and image data sets, showing the superiority of our framework which preserves consistent trade-offs among multiple downstream models compared to recent competing models. Particularly for computer vision data, we see our method alters only necessary semantic features related to the central machine learning task to achieve fairness.

Machine learning systems appear stochastic but are deterministically random, as seeded pseudorandom number generators produce identical realisations across repeated executions. Standard evaluation practice typically treats runs across alternatives as independent and does not exploit shared sources of randomness. This paper analyses the statistical structure of comparative evaluation under shared random seeds. Under this design, competing systems are evaluated using identical seeds, inducing matched stochastic realisations and yielding strict variance reduction whenever outcomes are positively correlated at the seed level. We demonstrate these effects using an extended learning-based multi-agent economic simulator, where paired evaluation exposes systematic differences in aggregate and distributional outcomes that remain statistically inconclusive under independent evaluation at fixed budgets.

Elon Musk has suggested he could buy Ryanair and called for its chief executive to be fired amid a deepening spat between the pair. The budget airline on Tuesday branded the Tesla chief executive an idiot, and used the extraordinary row to promote its January sale. Musk and Ryanair boss Michael O'Leary have been trading insults over the past week after O'Leary rejected the idea of using Musk's Starlink technology to provide wi-fi on flights. The two are among the world's most outspoken business chiefs, with Musk the world's richest man with an estimated net worth of $769bn (£573bn), and O'Leary running Europe's busiest airline. A statement on Ryanair's X account on Tuesday evening said: Perhaps Musk needs a break?? Ryanair is launching a Great Idiots seat sale especially for Elon and any other idiots on'X'.

Scientists discover how a vitamin A byproduct may weaken immune responses against cancer, potentially explaining why some immunotherapies fail in patients.