Persistent Laplacians are matrix operators that track how the shape and structure of data transform across scales and are popularly adopted in biology, physics, and machine learning. Their eigenvalues are concise descriptors of geometric and topological features in a filtration. Although earlier work established global algebraic stability for these operators, the precise change in a single eigenvalue when one simplex, such as a vertex, edge, or triangle, is added has remained unknown. This is important because downstream tools, including heat-kernel signatures and spectral neural networks, depend directly on these eigenvalues. We close this gap by proving a uniform Lipschitz bound: after inserting one simplex, every up-persistent Laplacian eigenvalue can vary by at most twice the Euclidean norm of that simplex's boundary, independent of filtration scale and complex size. This result delivers the first eigenvalue-level robustness guarantee for spectral topological data analysis. It guarantees that spectral features remain stable under local updates and enables reliable error control in dynamic data settings.

Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters. We introduce a boundary-weighted operator that rescales each edge according to how far its endpoints drift toward the graph's Gromov boundary. Using Busemann functions on delta-hyperbolic networks, we prove a closed-form upper bound on the operator's spectral norm: every signal loses a curvature-controlled fraction of its energy at each pass. The result delivers a parameter-free, lightweight filter whose stability follows directly from geometric first principles, offering a new analytic tool for graph signal processing on data with dense or hidden hierarchical structure.

Despite the superb performance in many tasks, large language models (LLMs) bear the risk of generating hallucination or even wrong answers when confronted with tasks that demand the accuracy of knowledge. The issue becomes even more noticeable when addressing logic queries that require multiple logic reasoning steps. On the other hand, knowledge graph (KG) based question answering methods are capable of accurately identifying the correct answers with the help of knowledge graph, yet its accuracy could quickly deteriorate when the knowledge graph itself is sparse and incomplete. It remains a critical challenge on how to integrate knowledge graph reasoning with LLMs in a mutually beneficial way so as to mitigate both the hallucination problem of LLMs as well as the incompleteness issue of knowledge graphs. In this paper, we propose 'Logic-Query-of-Thoughts' (LGOT) which is the first of its kind to combine LLMs with knowledge graph based logic query reasoning. LGOT seamlessly combines knowledge graph reasoning and LLMs, effectively breaking down complex logic queries into easy to answer subquestions. Through the utilization of both knowledge graph reasoning and LLMs, it successfully derives answers for each subquestion. By aggregating these results and selecting the highest quality candidate answers for each step, LGOT achieves accurate results to complex questions. Our experimental findings demonstrate substantial performance enhancements, with up to 20% improvement over ChatGPT.

This paper proposes an innovative Attention-GAN framework for enhancing cybersecurity, focusing on anomaly detection. In response to the challenges posed by the constantly evolving nature of cyber threats, the proposed approach aims to generate diverse and realistic synthetic attack scenarios, thereby enriching the dataset and improving threat identification. Integrating attention mechanisms with Generative Adversarial Networks (GANs) is a key feature of the proposed method. The attention mechanism enhances the model's ability to focus on relevant features, essential for detecting subtle and complex attack patterns. In addition, GANs address the issue of data scarcity by generating additional varied attack data, encompassing known and emerging threats. This dual approach ensures that the system remains relevant and effective against the continuously evolving cyberattacks. The KDD Cup and CICIDS2017 datasets were used to validate this model, which exhibited significant improvements in anomaly detection. It achieved an accuracy of 99.69% on the KDD dataset and 97.93% on the CICIDS2017 dataset, with precision, recall, and F1-scores above 97%, demonstrating its effectiveness in recognizing complex attack patterns. This study contributes significantly to cybersecurity by providing a scalable and adaptable solution for anomaly detection in the face of sophisticated and dynamic cyber threats. The exploration of GANs for data augmentation highlights a promising direction for future research, particularly in situations where data limitations restrict the development of cybersecurity systems. The attention-GAN framework has emerged as a pioneering approach, setting a new benchmark for advanced cyber-defense strategies.

Fox News correspondent Mike Tobin reports that severe weather disrupts travel plans ahead of the holidays on'Special Report.' FedEx and UPS announced mail delivery could be interrupted by the massive winter storm moving across the U.S. after key distribution hubs were blasted by the severe weather conditions. On Friday, FedEx posted a statement to its website warning those who used its Express service that the guaranteed delivery date of Dec. 26 may not be met after the Memphis and Indianapolis hubs experienced "substantial" weather disruptions. The shipping company said actions have been taken to lessen any impact on delivery, but the safety of its team members is the "number one priority." "We recognize the importance of deliveries this holiday weekend and are committed to providing service to the best of our ability by implementing contingency measures where it is safe and possible to do so," the statement read.

Nothing will make you believe that time is a deeply personal experience than seven days like those the WIRED transportation desk just lived through. No surprise, Elon Musk was at the center of it all. Between detailing his plans to tunnel under Los Angeles, the ongoing struggle to build the Tesla Model 3, and an epic Twitter tirade slamming the media, the high-profile CEO kept America's transportation reporters chained to their desks. Then on Thursday morning, the National Transportation Safety Board released its preliminary report on Uber's fatal self-driving crash in March, providing fresh details on what the car saw--and why it couldn't avoid killing pedestrian Elaine Herzberg. Plus, some good things happened.

CHICAGO – The driest Thanksgiving weekend in five years may have helped holiday shopping, despite an overall decline in foot traffic. But some shoppers just took notes in the hopes of finding an even better deal online. That's a consequence of Amazon continuing to squeeze prices, exacerbating the "showrooming" practice of people getting ideas at brick-and-mortar stores, then buying online. Heather Just and husband Dominic of Rockford, Illinois, brought their twin 11-year-old boys and 13-year-old son to the giant Water Tower Place on Chicago's Magnificent Mile on Saturday to see "what their eyes get big about." The excursion was more recon mission than shopping spree. "We're watching, we're watching," she told her sons, who focused their attention on a Nintendo Switch portable game console.