An expansive area of research focuses on discerning patterns of alterations in functional brain networks from the early stages of Alzheimer's disease, even at the subjective cognitive decline (SCD) stage. Here, we developed a novel hyperbolic MEG brain network embedding framework for transforming high-dimensional complex MEG brain networks into lower-dimensional hyperbolic representations. Using this model, we computed hyperbolic embeddings of the MEG brain networks of two distinct participant groups: individuals with SCD and healthy controls. We demonstrated that these embeddings preserve both local and global geometric information, presenting reduced distortion compared to rival models, even when brain networks are mapped into low-dimensional spaces. In addition, our findings showed that the hyperbolic embeddings encompass unique SCD-related information that improves the discriminatory power above and beyond that of connectivity features alone. Notably, we introduced a unique metric-the radius of the node embeddings-which effectively proxies the hierarchical organization of the brain. Using this metric, we identified subtle hierarchy organizational differences between the two participant groups, suggesting increased hierarchy in the dorsal attention, frontoparietal, and ventral attention subnetworks among the SCD group. Last, we assessed the correlation between these hierarchical variations and cognitive assessment scores, revealing associations with diminished performance across multiple cognitive evaluations in the SCD group. Overall, this study presents the first evaluation of hyperbolic embeddings of MEG brain networks, offering novel insights into brain organization, cognitive decline, and potential diagnostic avenues of Alzheimer's disease.

This paper presents Meta's Production Wide Area Network (WAN) Entitlement solution used by thousands of Meta's services to share the network safely and efficiently. We first introduce the Network Entitlement problem, i.e., how to share WAN bandwidth across services with flexibility and SLO guarantees. We present a new abstraction entitlement contract, which is stable, simple, and operationally friendly. The contract defines services' network quota and is set up between the network team and services teams to govern their obligations. Our framework includes two key parts: (1) an entitlement granting system that establishes an agile contract while achieving network efficiency and meeting long-term SLO guarantees, and (2) a large-scale distributed run-time enforcement system that enforces the contract on the production traffic. We demonstrate its effectiveness through extensive simulations and real-world end-to-end tests. The system has been deployed and operated for over two years in production. We hope that our years of experience provide a new angle to viewing WAN network sharing in production and will inspire follow-up research.