Hamilton--Jacobi Reachability for Spacecraft Collision Avoidance

This article presents a Hamilton--Jacobi (HJ) reachability framework for a two--satellite collision avoidance problem operating in the same circular orbit, where relative motion is modeled in the radial--tangential--normal (RTN) frame using planar Hill--Clohessy--Wiltshire (HCW) dynamics. We define the target state space as unsafe relative configurations in the orbit plane corresponding to minimum separation requirements consistent with Federal Communications Commission (FCC) orbital standards. The interaction between spacecraft is formulated as a zero--sum differential game, where Player 1 is the controlled satellite and Player 2 is modeled as a bounded adversarial disturbance with unknown intent. We present the HJ formulation and compute backward reachable sets that characterize relative states from which collision cannot be avoided under worst-case disturbances, while states outside this set admit provably collision-free trajectories. These reachable sets are integrated with supervisory hybrid control logic to determine when evasive maneuvers must be initiated, enabling mathematically grounded safety guarantees for scalability.

Quantification of BERT Diagnosis Generalizability Across Medical Specialties Using Semantic Dataset Distance

Deep learning models in healthcare may fail to generalize on data from unseen corpora. Additionally, no quantitative metric exists to tell how existing models will perform on new data. Previous studies demonstrated that NLP models of medical notes generalize variably between institutions, but ignored other levels of healthcare organization. We measured SciBERT diagnosis sentiment classifier generalizability between medical specialties using EHR sentences from MIMIC-III. Models trained on one specialty performed better on internal test sets than mixed or external test sets (mean AUCs 0.92, 0.87, and 0.83, respectively; p = 0.016). When models are trained on more specialties, they have better test performances (p < 1e-4). Model performance on new corpora is directly correlated to the similarity between train and test sentence content (p < 1e-4). Future studies should assess additional axes of generalization to ensure deep learning models fulfil their intended purpose across institutions, specialties, and practices.