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Modeling extreme precipitation and temperature is vital for understanding the impacts of climate change, as hazards like intense rainfall and record-breaking temperatures can result in severe consequences, including floods, droughts, and wildfires. Gaining insight into the spatial variation and interactions between these extremes is critical for effective risk management, early warning systems, and informed policy-making. However, challenges such as the rarity of extreme events, spatial dependencies, and complex cross-variable interactions hinder accurate modeling. We introduce a novel framework for modeling spatial extremes, building upon spatial generalized extreme value (GEV) models. Our approach incorporates a dimension-reduced latent spatial process to improve scalability and flexibility, particularly in capturing asymmetry in cross-covariance structures. This Joint Latent Spatial GEV model (JLS-GEV) overcomes key limitations of existing methods by providing a more flexible framework for inter-variable dependencies. In addition to addressing event rarity, spatial dependence and cross-variable interactions, JLS-GEV supports nonstationary spatial behaviors and independently collected data sources, while maintaining practical fitting times through dimension reduction. We validate JLS-GEV through extensive simulation studies, demonstrating its superior performance in capturing spatial extremes compared to baseline modeling approaches. Application to real-world data on extreme precipitation and temperature in the southeastern United States highlights its practical utility. While primarily motivated by environmental challenges, this framework is broadly applicable to interdisciplinary studies of spatial extremes in interdependent natural processes. more...

In this paper we provide a generalization of the concept of cohesion as introduced recently by Berenhaut, Moore and Melvin [Proceedings of the National Academy of Sciences, 119 (4) (2022)]. The formulation presented builds on the technique of partitioned local depth by distilling two key probabilistic concepts: local relevance and support division. Earlier results are extended within the new context, and examples of applications to revealing communities in data with uncertainty are included. The work sheds light on the foundations of partitioned local depth, and extends the original ideas to enable probabilistic consideration of uncertain, variable and potentially conflicting information., Comment: Typos correct & clarifying comments, 19 pages, 6 figures more...

As the complexity and heterogeneity of a system grows, the challenge of specifying, documenting and synthesizing correct, machine-readable designs increases dramatically. Separation of the system into manageable parts is needed to support analysis at various levels of granularity so that the system is maintainable and adaptable over its life cycle. In this paper, we argue that operads provide an effective knowledge representation to address these challenges. Formal documentation of a syntactically correct design is built up during design synthesis, guided by semantic reasoning about design effectiveness. Throughout, the ability to decompose the system into parts and reconstitute the whole is maintained. We describe recent progress in effective modeling under this paradigm and directions for future work to systematically address scalability challenges for complex system design., Comment: 33 pages; 14 figures; revised presentation, esp. first three sections and removal of appendix; new style file more...