Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intricate geometries often result in prohibitively expensive representations for traditional numerical methods and lead to difficult optimization landscapes for machine learning-based approaches. In this work, we introduce an enhanced Finite Expression Method (FEX) designed to address these challenges with improved accuracy, interpretability, and computational efficiency. The proposed framework incorporates three key innovations: a symbolic spectral composition module that enables FEX to learn and represent multiscale oscillatory behavior; a redesigned linear input layer that significantly expands the expressivity of the model; and an eigenvalue formulation that extends FEX to a new class of problems involving eigenvalue PDEs. Through extensive numerical experiments, we demonstrate that FEX accurately resolves oscillatory PDEs on domains containing multiple holes of varying shapes and sizes. Compared with existing neural network-based solvers, FEX achieves substantially higher accuracy while yielding interpretable, closed-form solutions that expose the underlying structure of the problem. These advantages, often absent in conventional finite element, finite difference, and black-box neural approaches, highlight FEX as a powerful and transparent framework for solving complex PDEs.

Graph Neural Networks (GNNs) have revolutionized the field of graph learning by learning expressive graph representations from massive graph data. As a common pattern to train powerful GNNs, the "pre-training, adaptation" scheme first pre-trains GNNs over unlabeled graph data and subsequently adapts them to specific downstream tasks. In the adaptation phase, graph prompting is an effective strategy that modifies input graph data with learnable prompts while keeping pre-trained GNN models frozen. Typically, existing graph prompting studies mainly focus on *feature-oriented* methods that apply graph prompts to node features or hidden representations. However, these studies often achieve suboptimal performance, as they consistently overlook the potential of *topology-oriented* prompting, which adapts pre-trained GNNs by modifying the graph topology. In this study, we conduct a pioneering investigation of graph prompting in terms of graph topology. We propose the first **Graph** **T**opology-**O**riented **P**rompting (GraphTOP) framework to effectively adapt pre-trained GNN models for downstream tasks. More specifically, we reformulate topology-oriented prompting as an edge rewiring problem within multi-hop local subgraphs and relax it into the continuous probability space through reparameterization while ensuring tight relaxation and preserving graph sparsity. Extensive experiments on five graph datasets under four pre-training strategies demonstrate that our proposed GraphTOP outshines six baselines on multiple node classification datasets. Our code is available at https://github.com/xbfu/GraphTOP.

High-temperature superconductors are essential for next-generation energy and quantum technologies, yet their performance is often limited by the critical current density ($J_c$), which is strongly influenced by microstructural defects. Optimizing $J_c$ through defect engineering is challenging due to the complex interplay of defect type, density, and spatial correlation. Here we present an integrated workflow that combines reinforcement learning (RL) with time-dependent Ginzburg-Landau (TDGL) simulations to autonomously identify optimal defect configurations that maximize $J_c$. In our framework, TDGL simulations generate current-voltage characteristics to evaluate $J_c$, which serves as the reward signal that guides the RL agent to iteratively refine defect configurations. We find that the agent discovers optimal defect densities and correlations in two-dimensional thin-film geometries, enhancing vortex pinning and $J_c$ relative to the pristine thin-film, approaching 60\% of theoretical depairing limit with up to 15-fold enhancement compared to random initialization. This RL-driven approach provides a scalable strategy for defect engineering, with broad implications for advancing HTS applications in fusion magnets, particle accelerators, and other high-field technologies.

Forecasting on widely used benchmark time series data (e.g., ETT, Electricity, Taxi, and Exchange Rate, etc.) has favored smooth, seasonal series, but network telemetry time series -- traffic measurements at service, IP, or subnet granularity -- are instead highly bursty and intermittent, with heavy-tailed bursts and highly variable inactive periods. These properties place the latter in the statistical regimes made famous and popularized more than 20 years ago by B.~Mandelbrot. Yet forecasting such time series with modern-day AI architectures remains underexplored. We introduce NetBurst, an event-centric framework that reformulates forecasting as predicting when bursts occur and how large they are, using quantile-based codebooks and dual autoregressors. Across large-scale sets of production network telemetry time series and compared to strong baselines, such as Chronos, NetBurst reduces Mean Average Scaled Error (MASE) by 13--605x on service-level time series while preserving burstiness and producing embeddings that cluster 5x more cleanly than Chronos. In effect, our work highlights the benefits that modern AI can reap from leveraging Mandelbrot's pioneering studies for forecasting in bursty, intermittent, and heavy-tailed regimes, where its operational value for high-stakes decision making is of paramount interest.

Social media enables data-driven analysis of public opinion on contested issues. Target-Stance Extraction (TSE) is the task of identifying the target discussed in a document and the document's stance towards that target. Many works classify stance towards a given target in a multilingual setting, but all prior work in TSE is English-only. This work introduces the first multilingual TSE benchmark, spanning Catalan, Estonian, French, Italian, Mandarin, and Spanish corpora. It manages to extend the original TSE pipeline to a multilingual setting without requiring separate models for each language. Our model pipeline achieves a modest F1 score of 12.78, underscoring the increased difficulty of the multilingual task relative to English-only setups and highlighting target prediction as the primary bottleneck. We are also the first to demonstrate the sensitivity of TSE's F1 score to different target verbalizations. Together these serve as a much-needed baseline for resources, algorithms, and evaluation criteria in multilingual TSE.

Wide-bandgap (WBG) technologies offer unprecedented improvements in power system efficiency, size, and performance, but also introduce unique sensor corruption and cybersecurity risks in industrial control systems (ICS), particularly due to high-frequency noise and sophisticated cyber-physical threats. This proof-of-concept (PoC) study demonstrates the adaptation of a noise-driven physically unclonable function (PUF) and machine learning (ML)-assisted anomaly detection framework to the demanding environment of WBG-based ICS sensor pathways. By extracting entropy from unavoidable WBG switching noise (up to 100 kHz) as a PUF source, and simultaneously using this noise as a real-time threat indicator, the proposed system unites hardware-level authentication and anomaly detection. Our approach integrates hybrid machine learning (ML) models with adaptive Bayesian filtering, providing robust and low-latency detection capabilities resilient to both natural electromagnetic interference (EMI) and active adversarial manipulation. Through detailed simulations of WBG modules under benign and attack scenarios--including EMI injection, signal tampering, and node impersonation--we achieve 95% detection accuracy and sub-millisecond processing latency. These results demonstrate the feasibility of physics-driven, dual-use noise exploitation as a scalable ICS defense primitive. Our findings lay the groundwork for next-generation security strategies that leverage inherent device characteristics, bridging hardware and artificial intelligence (AI) for enhanced protection of critical ICS infrastructure.

Cooperative systems often remain in persistently suboptimal yet stable states. This paper explains such "rational stagnation" as an equilibrium sustained by a rational adversary whose utility follows the principle of potential loss, $u_{D} = U_{ideal} - U_{actual}$. Starting from the Prisoner's Dilemma, we show that the transformation $u_{i}' = a\,u_{i} + b\,u_{j}$ and the ratio of mutual recognition $w = b/a$ generate a fragile cooperation band $[w_{\min},\,w_{\max}]$ where both (C,C) and (D,D) are equilibria. Extending to a dynamic model with stochastic cooperative payoffs $R_{t}$ and intervention costs $(C_{c},\,C_{m})$, a Bellman-style analysis yields three strategic regimes: immediate destruction, rational stagnation, and intervention abandonment. The appendix further generalizes the utility to a reference-dependent nonlinear form and proves its stability under reference shifts, ensuring robustness of the framework. Applications to social-media algorithms and political trust illustrate how adversarial rationality can deliberately preserve fragility.

The Swadesh approach for determining the temporal separation between two languages relies on the stochastic process of words replacement (when a complete new word emerges to represent a given concept). It is well known that the basic assumptions of the Swadesh approach are often unrealistic due to various contamination phenomena and misjudgments (horizontal transfers, variations over time and space of the replacement rate, incorrect assessments of cognacy relationships, presence of synonyms, and so on). All of this means that the results cannot be completely correct. More importantly, even in the unrealistic case that all basic assumptions are satisfied, simple mathematics places limits on the accuracy of estimating the temporal separation between two languages. These limits, which are purely probabilistic in nature and which are often neglected in lexicostatistical studies, are analyzed in detail in this article. Furthermore, in this work we highlight that the evolution of a language's lexicon is also driven by another stochastic process: gradual lexical modification of words. We show that this process equally also represents a major contribution to the reshaping of the vocabulary of languages over the centuries and we also show, from a purely probabilistic perspective, that taking into account this second random process significantly increases the precision in determining the temporal separation between two languages.

We measure LLMs' output error at pairwise text comparison, noting the probability of error in their preferences. Our method does not rely on the ground truth and supports two scenarios: (i) uniform error rate regardless of the order of comparison, estimated with two comparisons for each text pair with either text placed first; (ii) binary positional bias assuming distinct error rates for the two orders of comparison, estimated with repeated comparisons between the texts. The Copeland counting constructs a ranking over the compared texts from pairwise preferences; the ranking reveals the poor scalability of LLM-based pairwise comparison and helps yield the estimates for LLMs' error rates. We apply the method to six LLMs (ChatGPT, Claude, DeepSeek, Gemini, Grok, Qwen) with five types of text input and obtain consistent estimates of LLMs' error. In general, the measured two positional bias terms are similar, close to the uniform error. Considering both the error rates and the robustness to the variation of prompts, Claude obtained the most desirable performance in this experiment. Our model outperforms the biased Bradley-Terry model and the commutativity score in indicating LLMs' error at this task.

Wide-angle tail (WAT) and narrow-angle tail (NAT) radio active galactic nuclei (RAGNs) are key tracers of dense environments in galaxy groups and clusters, yet no machine-learning classifier of bent RAGNs has been trained using both unlabeled data and purely visually inspected labels. We release the RGC Python package, which includes two newly preprocessed labeled datasets of 639 WATs and NATs derived from a publicly available catalog of visually inspected sources, along with a semi-supervised RGC model that leverages 20,000 unlabeled RAGNs. The two labeled datasets in RGC were preprocessed using PyBDSF which retains spurious sources, and Photutils which removes them. The RGC model integrates the self-supervised framework BYOL (Bootstrap YOur Latent) with the supervised E2CNN (E2-equivariant Convolutional Neural Network) to form a semi-supervised binary classifier. The RGC model, when trained and evaluated on a dataset devoid of spurious sources, reaches peak performance, attaining an accuracy of 88.88% along with F1-scores of 0.90 for WATs and 0.85 for NATs. The model's attention patterns amid class imbalance suggest that this work can serve as a stepping stone toward developing physics-informed foundation models capable of identifying a broad range of AGN physical properties.