Notably, most real-world homophilic and heterophilic graphs are comprised of a mixture of nodes in both homophilic and heterophilic structural patterns, exhibiting a structural disparity.

Our work naturally extends Word Mover's Distance (WMD) [

Neural Information Processing Systems http://nips.cc/

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.

Why is Israel still in southern Lebanon? A war to shape Lebanon's future How many countries has Israel attacked in 2025? Israel has attacked more countries than any other country this year. In 2025, Israel attacked at least six countries, including Palestine, Iran, Lebanon, Qatar, Syria, and Yemen. It also carried out strikes in Tunisian, Maltese and Greek territorial waters on aid flotillas heading for Gaza.

Quantifying predictive uncertainty is essential for safe and trustworthy real-world AI deployment. Yet, fully nonparametric estimation of conditional distributions remains challenging for multivariate targets. We propose Tomographic Quantile Forests (TQF), a nonparametric, uncertainty-aware, tree-based regression model for multivariate targets. TQF learns conditional quantiles of directional projections $\mathbf{n}^{\top}\mathbf{y}$ as functions of the input $\mathbf{x}$ and the unit direction $\mathbf{n}$. At inference, it aggregates quantiles across many directions and reconstructs the multivariate conditional distribution by minimizing the sliced Wasserstein distance via an efficient alternating scheme with convex subproblems. Unlike classical directional-quantile approaches that typically produce only convex quantile regions and require training separate models for different directions, TQF covers all directions with a single model without imposing convexity restrictions. We evaluate TQF on synthetic and real-world datasets, and release the source code on GitHub.

We present an approach to denoising spatial transcriptomics images that is particularly effective for uncovering cell identities in the regime of ultra-low sequencing depths, and also allows for interpolation of gene expression. The method -- Spatial Transcriptomics via Adaptive Regularization and Kernels (STARK) -- augments kernel ridge regression with an incrementally adaptive graph Laplacian regularizer. In each iteration, we (1) perform kernel ridge regression with a fixed graph to update the image, and (2) update the graph based on the new image. The kernel ridge regression step involves reducing the infinite dimensional problem on a space of images to finite dimensions via a modified representer theorem. Starting with a purely spatial graph, and updating it as we improve our image makes the graph more robust to noise in low sequencing depth regimes. We show that the aforementioned approach optimizes a block-convex objective through an alternating minimization scheme wherein the sub-problems have closed form expressions that are easily computed. This perspective allows us to prove convergence of the iterates to a stationary point of this non-convex objective. Statistically, such stationary points converge to the ground truth with rate $\mathcal{O}(R^{-1/2})$ where $R$ is the number of reads. In numerical experiments on real spatial transcriptomics data, the denoising performance of STARK, evaluated in terms of label transfer accuracy, shows consistent improvement over the competing methods tested.

Large language models (LLMs) have shown strong performance in data-rich domains such as programming, but their reliability in engineering tasks remains limited. Circuit analysis -- requiring multimodal understanding and precise mathematical reasoning -- highlights these challenges. Although Gemini 2.5 Pro improves diagram interpretation and analog-circuit reasoning, it still struggles to consistently produce correct solutions when given both text and circuit diagrams. At the same time, engineering education needs scalable AI tools capable of generating accurate solutions for tasks such as automated homework feedback and question-answering. This paper presents an enhanced, end-to-end circuit problem solver built on Gemini 2.5 Pro. We first benchmark Gemini on a representative set of undergraduate circuit problems and identify two major failure modes: 1) circuit-recognition hallucinations, particularly incorrect source polarity detection, and 2) reasoning-process hallucinations, such as incorrect current directions. To address recognition errors, we integrate a fine-tuned YOLO detector and OpenCV processing to isolate voltage and current sources, enabling Gemini to re-identify source polarities from cropped images with near-perfect accuracy. To reduce reasoning errors, we introduce an ngspice-based verification loop in which Gemini generates a .cir file, ngspice simulates the circuit, and discrepancies trigger iterative regeneration with optional human-in-the-loop review. Across 83 problems, the proposed pipeline achieves a 97.59% success rate (81 correct solutions), substantially outperforming Gemini 2.5 Pro's original 79.52% accuracy. This system extends LLM capabilities for multimodal engineering problem-solving and supports the creation of high-quality educational datasets and AI-powered instructional tools.