H3: A Healthcare Three-Hop Index for Physician Referral Network Prediction

Accurate prediction of physician referral links is essential for optimizing care coordination and reducing fragmentation in healthcare delivery. However, existing computational methods, ranging from triadic closure heuristics to graph neural networks, fail to capture the intrinsic properties of physician referral networks, including sparsity, disassortative degree mixing, and hub-dominated topology. Here, we propose H3, a healthcare three-hop index that addresses these limitations by modeling indirect referral pathways through intermediate physicians, with degree-based normalization and a redundancy penalty to mitigate hub-mediated noise. Using Medicare Physician Shared Patient Patterns data, we evaluate H3 under two complementary prediction regimes: within-period prediction, which assesses recovery of contemporaneous referral links under sparse conditions, and cross-period prediction, which tests robustness to temporal shift as referral windows expand. Across both regimes, H3 consistently outperforms classical heuristics and deep learning-based baselines. Unlike black-box neural network approaches, H3 produces fully decomposable predictions traceable to specific intermediary physicians, offering a transparent and deployable solution for referral network completion.

Artificial Intelligence for Microbiology and Microbiome Research

Advancements in artificial intelligence (AI) have transformed many scientific fields, with microbiology and microbiome research now experiencing significant breakthroughs through machine learning and deep learning applications. This review provides a comprehensive overview of AI-driven approaches tailored for microbiology and microbiome studies, emphasizing both technical advancements and biological insights. We begin with an introduction to foundational AI techniques, including primary machine learning paradigms and various deep learning architectures, and offer guidance on choosing between machine learning and deep learning methods based on specific research goals. The primary section on application scenarios spans diverse research areas, from taxonomic profiling, functional annotation & prediction, microbe-X interactions, microbial ecology, metabolic modeling, precision nutrition, clinical microbiology, to prevention & therapeutics. Finally, we discuss challenges unique to this field, including the balance between interpretability and complexity, the "small n, large p" problem, and the critical need for standardized benchmarking datasets to validate and compare models. Together, this review underscores AI's transformative role in microbiology and microbiome research, paving the way for innovative methodologies and applications that enhance our understanding of microbial life and its impact on our planet and our health.