An estimated 5 million Italians are in need of mental health support but are unable to afford it. An estimated 5 million Italians are in need of mental health support but are unable to afford it. My friends in Italy are using AI therapists. But is that so bad, when a stigma surrounds mental health? State provision for psychological health services is lamentable.

To survive, this isolated population of only 2,000 whales needs to be smart about mates. Breakthroughs, discoveries, and DIY tips sent six days a week. Among marine mammals, beluga whales () are particularly difficult to study in their icy habitat. To better understand and protect this endangered species, scientists must piece together bits of their lives from fragments, including one of the most important behaviors of any species--mating. One small population of beluga whales living in southwest Alaska's Bristol Bay appears to have a surprising strategy.

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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.

All UK children could be offered screening for type 1 diabetes using a simple finger-prick blood test, say researchers who have been running a large study. Currently, many young people go undiagnosed and risk developing a life-threatening complication called diabetic ketoacidosis that needs urgent hospital treatment. Identifying diabetes earlier could help avoid this and mean treatments to control problematic blood sugar levels can be given sooner. Some 17,000 children aged three to 13 have already been checked as part of the ELSA (Early Surveillance for Autoimmune diabetes) study, funded by diabetes charities. Imogen, who is 12 and from the West Midlands, is one of those found to have diabetes thanks to the screening.

The 2025 Nature Photography Contest features a playful fox and a muscly horse. Crowned in Dust and Shadow A young male lion steps through a cloud of dust lifted by his own movement and caught in the back light. The night around him stays silent, but the glow reveals every contour of rising strength. Breakthroughs, discoveries, and DIY tips sent six days a week. While our world is filled with brilliant colors, seeing it in monochrome can be striking.

We study low-rank tensor-product B-spline (TPBS) models for regression tasks and investigate Dirichlet energy as a measure of smoothness. We show that TPBS models admit a closed-form expression for the Dirichlet energy, and reveal scenarios where perfect interpolation is possible with exponentially small Dirichlet energy. This renders global Dirichlet energy-based regularization ineffective. To address this limitation, we propose a novel regularization strategy based on local Dirichlet energies defined on small hypercubes centered at the training points. Leveraging pretrained TPBS models, we also introduce two estimators for inference from incomplete samples. Comparative experiments with neural networks demonstrate that TPBS models outperform neural networks in the overfitting regime for most datasets, and maintain competitive performance otherwise. Overall, TPBS models exhibit greater robustness to overfitting and consistently benefit from regularization, while neural networks are more sensitive to overfitting and less effective in leveraging regularization.

Healthcare sector indices consolidate the economic health of pharmaceutical, biotechnology, and healthcare service firms. The short-term movements in these indices are closely intertwined with capital allocation decisions affecting research and development investment, drug availability, and long-term health outcomes. This research investigates whether historical open-high-low-close (OHLC) index data contain sufficient information for predicting the directional movement of the opening index on the subsequent trading day. The problem is formulated as a supervised classification task involving a one-step-ahead rolling window. A diverse feature set is constructed, comprising original prices, volatility-based technical indicators, and a novel class of nowcasting features derived from mutual OHLC ratios. The framework is evaluated on data from healthcare indices in the U.S. and Indian markets over a five-year period spanning multiple economic phases, including the COVID-19 pandemic. The results demonstrate robust predictive performance, with accuracy exceeding 0.8 and Matthews correlation coefficients above 0.6. Notably, the proposed nowcasting features have emerged as a key determinant of the market movement. We have employed the Shapley-based explainability paradigm to further elucidate the contribution of the features: outcomes reveal the dominant role of the nowcasting features, followed by a more moderate contribution of original prices. This research offers a societal utility: the proposed features and model for short-term forecasting of healthcare indices can reduce information asymmetry and support a more stable and equitable health economy.

Self-Organizing Maps provide topology-preserving projections of high-dimensional data and have been widely used for visualization, clustering, and vector quantization. In this work, we show that the activation pattern of a SOM - the squared distances to its prototypes - can be inverted to recover the exact input under mild geometric conditions. This follows from a classical fact in Euclidean distance geometry: a point in $D$ dimensions is uniquely determined by its distances to $D{+}1$ affinely independent references. We derive the corresponding linear system and characterize the conditions under which the inversion is well-posed. Building upon this mechanism, we introduce the Manifold-Aware Unified SOM Inversion and Control (MUSIC) update rule, which enables controlled, semantically meaningful trajectories in latent space. MUSIC modifies squared distances to selected prototypes while preserving others, resulting in a deterministic geometric flow aligned with the SOM's piecewise-linear structure. Tikhonov regularization stabilizes the update rule and ensures smooth motion on high-dimensional datasets. Unlike variational or probabilistic generative models, MUSIC does not rely on sampling, latent priors, or encoder-decoder architectures. If no perturbation is applied, inversion recovers the exact input; when a target cluster or prototype is specified, MUSIC produces coherent semantic variations while remaining on the data manifold. This leads to a new perspective on data augmentation and controllable latent exploration based solely on prototype geometry. We validate the approach using synthetic Gaussian mixtures, the MNIST and the Faces in the Wild dataset. Across all settings, MUSIC produces smooth, interpretable trajectories that reveal the underlying geometry of the learned manifold, illustrating the advantages of SOM-based inversion over unsupervised clustering.

Orthogonal and 1-Lipschitz neural network layers are essential building blocks in robust deep learning architectures, crucial for certified adversarial robustness, stable generative models, and reliable recurrent networks. Despite significant advancements, existing implementations remain fragmented, limited, and computationally demanding. To address these issues, we introduce Orthogonium , a unified, efficient, and comprehensive PyTorch library providing orthogonal and 1-Lipschitz layers. Orthogonium provides access to standard convolution features-including support for strides, dilation, grouping, and transposed-while maintaining strict mathematical guarantees. Its optimized implementations reduce overhead on large scale benchmarks such as ImageNet. Moreover, rigorous testing within the library has uncovered critical errors in existing implementations, emphasizing the importance of standardized and reliable tools. Orthogonium thus significantly lowers adoption barriers, enabling scalable experimentation and integration across diverse applications requiring orthogonality and robust Lipschitz constraints. Orthogonium is available at https://github.com/deel-ai/orthogonium.