Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The persistence of outliers and clusters of arbitrary shape is inferred from the resulting hierarchy. We demonstrate the potential of the algorithm on selected datasets in which outliers play relevant roles, consisting of images, medical and economic data. These methods can provide meaningful clusters in situations in which other techniques fail to do so.

Pillay is an editorial fellow at TIME. Albania's new AI-generated minister Diella speaks during the parliamentary session for the voting of the new government of Albania, in Tirana on Sept. 18, 2025. Albania's new AI-generated minister Diella speaks during the parliamentary session for the voting of the new government of Albania, in Tirana on Sept. 18, 2025. Pillay is an editorial fellow at TIME. It's been three years since the launch of ChatGPT gave hundreds of millions of people access to a kind of digital genie in their pocket--and things have been getting stranger by the month. Besides billions of AI-generated emails and the technology's widespread disruption of education and cognitive work, in 2025, some people began to fall in love with their AIs.

Inside the former US embassy that's now one of the world's top luxury hotels - with 8 bars and restaurants and suites to book for £26,100 The world's most expensive cities for days out revealed, with London in the top 15 Going beyond the guidebook: Here are 10 must-try cultural and wildlife experiences in Australia's'Garden State' Fairy-tale villages, castle tours and dinner at Austria's oldest winery: These enchanting river cruises will take you to the heart of each picturesque port of call you visit Revealed: The world's best new luxury hotel is in the UK - and it has a huge pool and rooftop bar Travel expert reveals the'science-backed tool' to help overcome fear of flying Eurostar's'snow train' set to return this week for winter Could YOU pass France's new'civic examination' needed to live in the country? Try these sample questions and find out... Airline finds'lost' Boeing 737 a decade after it vanished'If you don't enjoy Benidorm, you've only got yourself to blame': Meet the British couple who have been to the Spanish hotspot more than 100 TIMES The'dangerous' destinations that are actually not scary - and why you should holiday there next Brit who moved to the world's most desirable place to live reveals the soaring unexpected costs of relocating A major UK city is set to get driverless trains next year as part of its rail modernisation project. In 2023, new trains were launched in Glasgow as part of the full-scale upgrade to improve the city's subway after more than 30 years. The renovations have continued and now, the Strathclyde Partnership for Transport (SPT) has announced Unattended Train Operation will be introduced to Glasgow. The modernisation project is in its'final stages,' Time Out reports, and the driverless subway trains are expected to be brought in next year.

Would artificial intelligence (AI) cut interest rates or adopt conservative monetary policy? Would it deregulate or opt for a more controlled economy? As AI use by economic policymakers, academics, and market participants grows exponentially, it is becoming critical to understand AI preferences over economic policy. However, these preferences are not yet systematically evaluated and remain a black box. This paper makes a conjoint experiment on leading large language models (LLMs) from OpenAI, Anthropic, and Google, asking them to evaluate economic policy under multi-factor constraints. The results are remarkably consistent across models: most LLMs exhibit a strong preference for high growth, low unemployment, and low inequality over traditional macroeconomic concerns such as low inflation and low public debt. Scenario-specific experiments show that LLMs are sensitive to context but still display strong preferences for low unemployment and low inequality even in monetary-policy settings. Numerical sensitivity tests reveal intuitive responses to quantitative changes but also uncover non-linear patterns such as loss aversion.

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of existing methodologies exploit various levels of approximations that lower accuracy and limit the flexibility of kernel and noise-model designs -- an unacceptable drawback at a time when expressive non-stationary kernels are on the rise in many fields. Here, we propose a methodology we term \emph{gp2Scale} that scales exact Gaussian processes to more than 10 million data points without relying on inducing points, kernel interpolation, or neighborhood-based approximations, and instead leveraging the existing capabilities of a GP: its kernel design. Highly flexible, compactly supported, and non-stationary kernels lead to the identification of naturally occurring sparse structure in the covariance matrix, which is then exploited for the calculations of the linear system solution and the log-determinant for training. We demonstrate our method's functionality on several real-world datasets and compare it with state-of-the-art approximation algorithms. Although we show superior approximation performance in many cases, the method's real power lies in its agnosticism toward arbitrary GP customizations -- core kernel design, noise, and mean functions -- and the type of input space, making it optimally suited for modern Gaussian process applications.

As Large Language Models (LLMs) become increasingly integrated into everyday life and information ecosystems, concerns about their implicit biases continue to persist. While prior work has primarily examined socio-demographic and left--right political dimensions, little attention has been paid to how LLMs align with broader geopolitical value systems, particularly the democracy--authoritarianism spectrum. In this paper, we propose a novel methodology to assess such alignment, combining (1) the F-scale, a psychometric tool for measuring authoritarian tendencies, (2) FavScore, a newly introduced metric for evaluating model favorability toward world leaders, and (3) role-model probing to assess which figures are cited as general role-models by LLMs. We find that LLMs generally favor democratic values and leaders, but exhibit increased favorability toward authoritarian figures when prompted in Mandarin. Further, models are found to often cite authoritarian figures as role models, even outside explicit political contexts. These results shed light on ways LLMs may reflect and potentially reinforce global political ideologies, highlighting the importance of evaluating bias beyond conventional socio-political axes. Our code is available at: https://github.com/irenestrauss/Democratic-Authoritarian-Bias-LLMs.

Pots, quadrants, confederation constraints, group position grids... the 2026 World Cup finals draw on Friday is not going to be a straightforward affair. There's a lot to unpack so we're going to explain it as simply as we can. Luckily, Fifa will have a computer to do most of the heavy lifting and make sure everything runs smoothly. Though as Uefa found out in 2021, sometimes technology does go wrong. Let's hope there will be no gremlins in Washington once the draw ceremony kicks off.

Abstract--Modern Intrusion Detection Systems (IDS) face severe challenges due to heterogeneous network traffic, evolving cyber threats, and pronounced data imbalance between benign and attack flows. While generative models have shown promise in data augmentation, existing approaches are limited to single modalities and fail to capture cross-domain dependencies. This paper introduces MAGE-ID (Multimodal Attack Generator for Intrusion Detection), a diffusion-based generative framework that couples tabular flow features with their transformed images through a unified latent prior . By jointly training Transformer-and CNN-based variational encoders with an EDM-style denoiser, MAGE-ID achieves balanced and coherent multimodal synthesis. Evaluations on CIC-IDS-2017 and NSL-KDD demonstrate significant improvements in fidelity, diversity, and downstream detection performance over T abSyn and T abDDPM, highlighting MAGE-ID's effectiveness for multimodal IDS augmentation.