Multilayer networks

Traditional social network analysis often reduces homophily—the tendency of similar individuals to connect—to a single parameter, neglecting nuanced biases within and across groups. We propose an exponential family model that incorporates both local homophily (strong ties within cliques) and global homophily (weaker ties across communities), using a maximum entropy approach to analyze their effects on network dynamics under percolation. This framework decomposes homophily into finer levels, revealing how these interactions shape the spread of information, diseases, and innovation. Testing on diverse datasets, the model highlights how varying homophily patterns influence percolation thresholds and the effectiveness of interventions, offering valuable insights for public health strategies, social media information flow, and targeted mitigation efforts.

Network science provides a powerful framework for modeling complex systems, where the intricate interplay between structure and dynamics often leads to the emergence of complex behaviors such as synchronization and collective motion. Random walks, as one of the most studied stochastic processes, play a central role in exploring this interplay. However, traditional models often assume independent random walkers, overlooking real-world constraints such as finite carrying capacities at nodes. Addressing this limitation, recent studies introduced nonlinear diffusion processes that account for node capacity limits, enabling the inference of network structure through localized measurements and inverse problem-solving. In this work, we extend these nonlinear diffusion models to multigraphs, where nodes are connected by multiple types of links, each carrying distinct attributes. Examples of such systems include air transport networks categorized by airlines or social networks differentiated by interaction platforms. We show how the degree distribution of an entire multigraph can be reconstructed by combining knowledge of one link type with stationary density measurements from a single node. Through simulations on diverse multigraph topologies, including Erdős-Rényi, Watts-Strogatz, and scale-free networks, we evaluate the reconstruction accuracy and robustness of the proposed approach. Our findings demonstrate the capability to accurately infer key structural properties, such as degree distribution and moments, even under varying levels of sparsity and topology. This study strengthens the connection between network dynamics and topology, offering a novel framework for structural inference in multigraphs with limited information.

Each year, the CDC hosts the FluSight Forecast Challenge, where over 40 teams contribute to the flu forecasts. To create an ensemble forecast, the CDC takes the median of each quantile prediction across all models, assuming each provides statistically independent information. However, this assumption may not always hold, as models may share analytical frameworks, code, data, or calibrate on the same target variables (e.g. flu season peaks). The focus is to isolate sources of independent error and identify clusters of similar models to better understand ensemble performance and limitations.Using methodologies from climate forecasting, we first quantify the “effective number” of independent models by isolating independent noise from predictions. Our findings reveal that the effective number of models providing unique information is around 6—far fewer than the total number of models—indicating significant redundancy in the FluSight ensemble. This emphasizes a significant limitation in the current ensemble approach, where non-independent contributions may inflate the perceived diversity of forecasts.To further explore model dependencies, we apply a multilayer network clustering approach, combining similarity measures and multilayer community detection to cluster models with shared error patterns. Synthetic data experiments validate the pipeline’s robustness, correctly identifying ground truth groupings with independent, group-specific, and correlated noise. When applied to FluSight models, we observe temporal inconsistencies in groupings, likely driven by updates to individual models throughout the flu season.Our results highlight the need to address model interdependencies in epidemic forecasting. By quantifying the effective number of independent models and providing tools to isolate independent error, we offer a framework for improving ensemble reliability. These insights are essential for enhancing forecast accuracy and supporting public health decision-making.

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In this study, we analyze 19,563 patent abstracts, extracting approximately 100,000 keywords with the objective of constructing a comprehensive keyword co-occurrence network. The keywords were categorized into seven predefined tags: efficacy, mechanism, ingredient/substance, natural, formulation/product, technique/manufacturing, and characteristics. This enabled a detailed exploration of the technological domains within K-Beauty.This study addresses the aforementioned limitations by employing a multi-layer network analysis, a novel approach that integrates the seven defined tags and thus represents a significant advancement in the field of cosmetic patents. Centrality analysis is the foundation of our methodology, identifying influential keywords that define key technological areas. The degree centrality metric identifies common keywords such as 'conditioner', 'toner' and 'cream' that represent the formulation/product. Betweenness centrality identifies keywords such as 'anti-inflammatory', 'antioxidant', 'anti-wrinkle' and 'whitening', which are related to efficacy.A temporal analysis of the keyword network also reveals shifts in the focus of innovation, such as the transition from "whitening" to "anti-aging" and the growth of natural ingredients over time. The introduction of a multi-layered tagging framework to large-scale patent analysis provides a unique perspective on the evolution of the K-beauty technology landscape.The findings contribute to both the academic understanding of network science applications and the practical realm of R\&D planning, patent strategy, and technology forecasting. This research establishes a new standard for the utilization of LLMs and multi-layer network analysis in large-scale patent studies, exemplifying their efficacy in elucidating technological trends and innovation pathways within the cosmetics industry.