Finnish police have launched a criminal investigation into suspected breaches of environmental law at the construction site of a planned Google data centre in northern Finland. The project is part of a $15bn deal announced last month by Alphabet's Google to invest in artificial intelligence (AI) infrastructure in Finland, which the US company described as its largest investment in Europe. "We are investigating whether the company's operations have breached the Water Act and resulted in environmental damage," Detective Superintendent Kari Pakanen told the Reuters news agency on Thursday, adding that a guilty finding could lead to a corporate fine. Pakanen declined to say whether any individuals could become a target of the investigation, and a Google spokesperson said the company would cooperate with the police investigation and continue to focus on maintaining compliance at its sites. Videos and photographs showing the scale of the forest clearance at the site of the data centre, and Google's initial reluctance to address the issue in the days after the news broke, have prompted widespread anger in Finland, where there is a high level of respect for the natural environment among the public.

Google has been ordered to temporarily stop work on two datacentres in Finland after failing to do the necessary environmental impact assessments on its construction sites. The planned datacentres in Muhos and Kajanni are part of a €13bn (£11bn) project across multiple sites in northern Finland by the technology company amid huge demand for space to house online infrastructure. It comes after it emerged that Tuike Finland Oy, the company representing Google, had felled 330 hectares (815 acres) of forest in Muhos without completing an environmental impact assessment (EIA). In Kajaani, the company has reportedly been logging across just under 200 hectares (494 acres) of land. The Finnish Association for Nature Conservation said the sites had been reduced to "sand", blaming the oversights on the "overheated" market for new datacentres.

Finland completed a 124-mile border fence along its frontier with Russia to counter hybrid warfare tactics, including the weaponization of migration to destabilize border security.

Google will buy up to half the electricity produced by one of Finland's nuclear power plants as part of a record €13bn (£11bn; $15bn) investment in the country's AI infrastructure, the company announced. The US tech giant said the package would fund three new data centres, expand an existing site and support energy projects to power growing demand for AI services. This is Google's largest single investment in Europe and a testament to Finland's leadership in responsibly building AI infrastructure, the company said on Wednesday. Google's decision is a clear testament to our strengths, Finland's Prime Minister Petteri Orpo said in a statement. As part of the deal, Google signed a 22-year contract with Finnish utility Fortum to buy up to 50% of the output from the Loviisa nuclear power plant.

Survival analysis is central to clinical decision-making, yet reliable time-to-event models require large, diverse cohorts that are rarely available at a single institution, while privacy regulations restrict the centralization of patient data. Federated learning (FL) offers a privacy-preserving alternative by training shared models without exchanging raw data, but its effectiveness for survival modeling under realistic, heterogeneous conditions remains insufficiently understood. This paper presents a systematic, multi-model evaluation of federated survival analysis on a cross-institutional breast cancer cohort with naturally heterogeneous distributed clients. Three representative survival models, the Cox Proportional Hazards model, DeepSurv, and Random Survival Forest (RSF), are compared across centralized, local, and federated training, and three federated optimization strategies (FedAvg, FedProx, and FedAdam) are assessed for the gradient-based models. Results show that FL consistently outperforms local training and approaches, and occasionally exceeds, centralized performance, while RSF offers the best overall balance of discrimination, calibration, and robustness across heterogeneous clients. We further find that performance depends on the diversity of client distributions, and that FedAvg and FedProx are stronger and more stable than FedAdam. Based on these findings, we derive practical, decision-oriented guidelines mapping data, privacy, interpretability, and resource constraints to recommended model and training-paradigm choices for federated survival modeling in healthcare.

We propose a flexible framework for modeling the predictive distributions of nonlinear, possibly multivariate time series. Our approach expresses a general predictive distribution in an appropriate generative representation that is based on a folklore result from measure theoretic probability. This representation provides a direct simulation-based approximation to the predictive distribution, enabling straightforward computation of forecasts for the conditional mean and variance, fan charts, value at risk, expected shortfall, joint tail risks, and other quantities of interest. We estimate this generative representation using a version of conditional generative adversarial networks and provide a formal statistical analysis of estimation under weak temporal dependence. Specifically, estimation is expressed as a particular minimax problem and we establish consistency of its approximate solutions in Hausdorff distance. The empirical relevance of the approach is illustrated using applications to equity returns, realized variance, and realized covariances. The proposed method is also computationally manageable, with estimation in our applications taking approximately one minute on a standard laptop.

We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces. We show that the covariance operator of a weak second-order Radon probability measure on such a space is uniquely determined by a positive definite function. In the Gaussian case, we characterize those positive definite functions that arise from covariance operators in terms of $γ$-radonifying operators. Building on these results, we extend the classical Driscoll theorem to the Banach space setting.

We prove that no reinforcement learning policy with confidence-gated autonomy can simultaneously achieve maximum helpfulness, optimal calibration, and full autonomy under rational oversight, whenever some tasks exceed the agent's reliable competence: the Behavioral Credibility Trilemma. The impossibility is geometric -- adding any non-affine autonomy incentive to a strictly proper scoring rule destroys strict properness, so an agent rewarded for both calibrated confidence and autonomous action systematically inflates its reported confidence on tasks below the principal's approval threshold. The Behavioral Perturbation Lemma quantifies the inflation (scaling as $w_A/(2 w_C)$ for the Brier score) and shows detection requires $Ω(1/Δ^2)$ observations. We prove the principal's optimal oversight rule is necessarily non-affine, making the impossibility unconditional and optimizer-independent across log-concave-density policy families. We formalize the Confidence-Gated Decision Problem, map existing methods onto the trilemma, and identify two constructive resolution pathways (commitment, domain separation). A 540-configuration Best-of-N experiment tests five pre-registered hypotheses, all strongly confirmed (effect sizes $d = 1.10$ to $5.32$), and adds a descriptive analysis of the achievable-$(H, C, A)$ surface geometry showing a plateau-truncated frontier consistent with the predicted inflation saturation.

What are Russia's gains from the Iran war? 'We are not losers; we are winners' Finland has stood down its defence forces after sounding an alarm over suspected drone activities in its airspace. The authorities said on Friday that suspected drone activity above the Helsinki region no longer posed a threat and that the situation was returning to normal hours after launching an emergency response, including the launch of fighter jets and closure of the capital's airport. The Helsinki City Rescue Department had warned the nearly 2 million inhabitants of Finland's Uusimaa region to stay indoors starting about 4am local time (1:00 GMT), as fighter jets were scrambled. Helsinki's airport was also closed for about three hours. Later, President Alexander Stubb wrote on X that authorities had "demonstrated their readiness and capacity to react", adding that the country was now facing "no direct military threat". Kimmo Kohvakka, director general for rescue services at the Ministry of the Interior, called the response a "precautionary measure" and said "daily life can continue."