The EU has revealed details of a 20bn ( 17bn) plan to create new sites equipped with vast supercomputers in Europe to develop the next generation of artificial intelligence models, while opening the door to amending its landmark law that regulates the technology. Publishing a strategy to turn Europe into an "AI continent", the European Commission vice-president Henna Virkkunen said the technology was at the heart of making Europe more competitive, secure and technologically sovereign, adding: "The global race for AI is far from over." The EU is attempting to catch up with the US and China, which have taken a lead in pioneering the technology that increasingly powers shopping websites and self-driving cars, generates text, and is predicted to play a transformative role in healthcare, security and defence, and advanced manufacturing, among other sectors. The US has a commanding lead in AI, far ahead of China. A report from Stanford University this week said 40 "notable AI models" – meaning influential – were produced by institutions in the US in 2024, compared with 15 in China and three in Europe (all French).

Donald Trump signed four executive orders on Tuesday aimed at reviving coal, the dirtiest fossil fuel that has long been in decline, and which substantially contributes to planet-heating greenhouse gas emissions and pollution. Environmentalists expressed dismay at the news, saying that Trump was stuck in the past and wanted to make utility customers "pay more for yesterday's energy". The US president is using emergency authority to allow some older coal-fired power plants scheduled for retirement to keep producing electricity. The move, announced at a White House event on Tuesday afternoon, was described by White House officials as being in response to increased US power demand from growth in datacenters, artificial intelligence and electric cars. Trump, standing in front of a group of miners in hard hats, said he would sign an executive order "that slashes unnecessary regulations that targeted the beautiful, clean coal".

FIRST ON FOX: The Department of Energy, the Department of the Interior and the Environmental Protection Agency are set to announce a bevy of new actions Tuesday afternoon that will "unleash" coal energy following President Donald Trump's expected signature on an executive order reinvigorating "America's beautiful clean coal industry," Fox News Digital learned. "The American people need more energy, and the Department of Energy is helping to meet this demand by unleashing supply of affordable, reliable, secure energy sources -- including coal," Department of Energy Secretary Chris Wright said in a Tuesday statement provided to Fox News Digital. "Coal is essential for generating 24/7 electricity generation that powers American homes and businesses, but misguided policies from previous administrations have stifled this critical American industry," he said. "With President Trump's leadership, we are cutting the red tape and bringing back common sense." Trump is expected to sign an executive order Tuesday afternoon that will cut through red tape surrounding the coal industry, including directing the National Energy Dominance Council to designate coal as a "mineral," end a current pause to coal leasing on federal lands, promote coal and coal technology exports, and encourage the use of coal to power artificial intelligence initiatives, Fox News Digital learned of the upcoming executive order.

If you thought robot dogs were the coolest animatronic animals out there, prepare to think again. Kawasaki Heavy Industries, a company better known for its high-end motorcycles, has unveiled a hydrogen-powered, ride-on robo-horse. The bizarre device was unveiled at the Osaka Kansai Expo on April 4 as part of Kawasaki's'Impulse to Move' project. Dubbed the CORLEO, this two-seater quadruped is capable of galloping over almost any terrain. The company calls it a'revolutionary off-road personal mobility vehicle' which swaps out the familiar wheels for four robotic legs. To steer, all you need to do is move your body and the machine's AI vision will pick out the best route to take.

Three-dimensional digital reconstruction of porous media presents a fundamental challenge in geoscience, requiring simultaneous resolution of fine-scale pore structures while capturing representative elementary volumes. We introduce a computational framework that addresses this challenge through latent diffusion models operating within the EDM framework. Our approach reduces dimensionality via a custom variational autoencoder trained in binary geological volumes, improving efficiency and also enabling the generation of larger volumes than previously possible with diffusion models. A key innovation is our controlled unconditional sampling methodology, which enhances distribution coverage by first sampling target statistics from their empirical distributions, then generating samples conditioned on these values. Extensive testing on four distinct rock types demonstrates that conditioning on porosity - a readily computable statistic - is sufficient to ensure a consistent representation of multiple complex properties, including permeability, two-point correlation functions, and pore size distributions. The framework achieves better generation quality than pixel-space diffusion while enabling significantly larger volume reconstruction (256-cube voxels) with substantially reduced computational requirements, establishing a new state-of-the-art for digital rock physics applications.

Given two boundary distributions, the Schr\"odinger Bridge (SB) problem seeks the ``most likely`` random evolution between them with respect to a reference process. It has revealed rich connections to recent machine learning methods for generative modeling and distribution matching. While these methods perform well in Euclidean domains, they are not directly applicable to topological domains such as graphs and simplicial complexes, which are crucial for data defined over network entities, such as node signals and edge flows. In this work, we propose the Topological Schr\"odinger Bridge problem (TSBP) for matching signal distributions on a topological domain. We set the reference process to follow some linear tractable topology-aware stochastic dynamics such as topological heat diffusion. For the case of Gaussian boundary distributions, we derive a closed-form topological SB (TSB) in terms of its time-marginal and stochastic differential. In the general case, leveraging the well-known result, we show that the optimal process follows the forward-backward topological dynamics governed by some unknowns. Building on these results, we develop TSB-based models for matching topological signals by parameterizing the unknowns in the optimal process as (topological) neural networks and learning them through likelihood training. We validate the theoretical results and demonstrate the practical applications of TSB-based models on both synthetic and real-world networks, emphasizing the role of topology. Additionally, we discuss the connections of TSB-based models to other emerging models, and outline future directions for topological signal matching.

In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting of univariate and multivariate interval-valued time series, overlooking another important aspect: classification. In this paper, we introduce a classification approach that treats intervals as unified entities, applicable to both univariate and multivariate interval-valued time series. Specifically, we first extend the point-valued time series imaging methods to interval-valued scenarios using the $D_K$-distance, enabling the imaging of interval-valued time series. Then, we employ suitable deep learning model for classification on the obtained imaging dataset, aiming to achieve classification for interval-valued time series. In theory, we derived a sharper excess risk bound for deep multiclassifiers based on offset Rademacher complexity. Finally, we validate the superiority of the proposed method through comparisons with various existing point-valued time series classification methods in both simulation studies and real data applications.

Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches often do not generalize readily to a broader class of linear models. In this work, we propose a novel algorithmic framework for solving a general class of non-negative linear regression models with an entropy-regularized OT datafit term, based on Sinkhorn-like scaling iterations. Our framework accommodates convex penalty functions on the weights (e.g. squared-$\ell_2$ and $\ell_1$ norms), and admits additional convex loss terms between the transported marginal and target distribution (e.g. squared error or total variation). We derive simple multiplicative updates for common penalty and datafit terms. This method is suitable for large-scale problems due to its simplicity of implementation and straightforward parallelization.

Abstract--In this paper, we analyze the performance of the estimation of Laplacian matrices under general observatio n models. Laplacian matrix estimation involves structural c on-straints, including symmetry and null-space properties, a long with matrix sparsity. By exploiting a linear reparametriza tion that enforces the structural constraints, we derive closed -form matrix expressions for the Cram er-Rao Bound (CRB) specifically tailored to Laplacian matrix estimation. We further extend the derivation to the sparsity-constrained case, introduc ing two oracle CRBs that incorporate prior information of the suppo rt set, i.e. the locations of the nonzero entries in the Laplaci an matrix. We examine the properties and order relations betwe en the bounds, and provide the associated Slepian-Bangs formu la for the Gaussian case. We demonstrate the use of the new CRBs in three representative applications: (i) topology identi fication in power systems, (ii) graph filter identification in diffuse d models, and (iii) precision matrix estimation in Gaussian M arkov random fields under Laplacian constraints. The CRBs are eval - uated and compared with the mean-squared-errors (MSEs) of the constrained maximum likelihood estimator (CMLE), whic h integrates both equality and inequality constraints along with sparsity constraints, and of the oracle CMLE, which knows the locations of the nonzero entries of the Laplacian matrix . We perform this analysis for the applications of power syste m topology identification and graphical LASSO, and demonstra te that the MSEs of the estimators converge to the CRB and oracle CRB, given a sufficient number of measurements. Graph-structured data and signals arise in numerous applications, including power systems, communications, finance, social networks, and biological networks, for analysis and inference of networks [ 2 ], [ 3 ]. In this context, the Laplacian matrix, which captures node connectivity and edge weights, serves as a fundamental tool for clustering [ 4 ], modeling graph diffusion processes [ 5 ], [ 6 ], topology inference [ 6 ]-[ 12 ], anomaly detection [ 13 ], graph-based filtering [ 14 ]-[ 18 ], and analyzing smoothness on graphs [ 19 ]. M. Halihal and T. Routtenberg are with the School of Electric al and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel, e-mail: moradha@post.bgu.ac.il, tirzar@b gu.ac.il.

The Bayesian conjugate gradient method offers probabilistic solutions to linear systems but suffers from poor calibration, limiting its utility in uncertainty quantification tasks. Recent approaches leveraging postit-erations to construct priors have improved computational properties but failed to correct calibration issues. In this work, we propose a novel randomised postiteration strategy that enhances the calibration of the BayesCG posterior while preserving its favourable convergence characteristics. We present theoretical guarantees for the improved calibration, supported by results on the distribution of posterior errors. Numerical experiments demonstrate the efficacy of the method in both synthetic and inverse problem settings, showing enhanced uncertainty quantification and better propagation of uncertainties through computational pipelines.