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Abstract In microbiome analysis, researchers often seek to identify taxonomic features associated with an outcome of interest. However, microbiome features are intercorrelated and linked by phylogenetic relationships, making it challenging to assess the association between an individual feature and an outcome. This paper proposes a novel conditional association test, CAT, that can account for other features and phylogenetic relatedness when testing the association between a feature and an outcome. CAT adopts a permutation approach, measuring the importance of a feature in predicting the outcome by permuting operational taxonomic unit/amplicon sequence variant counts belonging to that feature from the data and quantifying how much the association with the outcome is weakened through the change in the coefficient of determination $$R^{2}$$. Compared with marginal association tests, it focuses on the added value of a feature in explaining outcome variation that is not captured by other features. By leveraging global tests including PERMANOVA and MiRKAT-based methods, CAT allows association testing for continuous, binary, categorical, count, survival, and correlated outcomes. We demonstrate through simulation studies that CAT can provide a direct quantification of feature importance that is distinct from that of marginal association tests, and illustrate CAT with applications to two real-world studies on the microbiome in melanoma patients: one examining the role of the microbiome in shaping immunotherapy response, and one investigating the association between the microbiome and survival outcomes. Our results illustrate the potential of CAT to inform the design of microbiome interventions aimed at improving clinical outcomes. 

As graph data grows increasingly complicated, training graph neural networks (GNNs) on large-scale datasets presents significant challenges, including computational resource constraints, data redundancy, and transmission inefficiencies. While existing graph condensation techniques have shown promise in addressing these issues, they are predominantly designed for single-label datasets, where each node is associated with a single class label. However, many real-world applications, such as social network analysis and bioinformatics, involve multi-label graph datasets, where one node can have various related labels. To deal with this problem, we extend traditional graph condensation approaches to accommodate multi-label datasets by introducing modifications to synthetic dataset initialization and condensing optimization. Through experiments on eight real-world multi-label graph datasets, we prove the effectiveness of our method. In the experiment, the GCond framework, combined with K-Center initialization and binary cross-entropy loss (BCELoss), generally achieves the best performance. This benchmark for multi-label graph condensation not only enhances the scalability and efficiency of GNNs for multi-label graph data but also offers substantial benefits for diverse real-world applications. Code is available at https://github.com/liangliang6v6/Multi-GC. 

Abstract SummaryAdvances in survival analysis have facilitated unprecedented flexibility in data modeling, yet there remains a lack of tools for illustrating the influence of continuous covariates on predicted survival outcomes. We propose the utilization of a colored contour plot to depict the predicted survival probabilities over time. Our approach is capable of supporting conventional models, including the Cox and Fine–Gray models. However, its capability shines when coupled with cutting-edge machine learning models such as random survival forests and deep neural networks. Availability and implementationWe provide a Shiny app at https://biostatistics.mdanderson.org/shinyapps/survivalContour/ and an R package available at https://github.com/YushuShi/survivalContour as implementations of this tool. 

Abstract The Green’s function of a bimaterial infinite domain with a plane interface is applied to thermal analysis of a spherical underground heat storage tank. The heat transfer from a spherical source is derived from the integral of the Green’s function over the spherical domain. Because the thermal conductivity of the tank is generally different from soil, the Eshelby’s equivalent inclusion method (EIM) is used to simulate the thermal conductivity mismatch of the tank from the soil. For simplicity, the ground with an approximately uniform temperature on the surface is simulated by a bimaterial infinite domain, which is perfectly conductive above the ground. The heat conduction in the ground is investigated for two scenarios: First, a steady-state uniform heat flux from surface into the ground is considered, and the heat flux is disturbed by the existence of the tank due to the conductivity mismatch. A prescribed temperature gradient, or an eigen-temperature gradient, is introduced to investigate the local temperature field in the neighborhood of the tank. Second, when a temperature difference exists between the water in the tank and soil, the heat transfer between the tank and soil depends on the tank size, conductivity, and temperature difference, which provide a guideline for heat exchange design for the tank size. The modeling framework can be extended to two-dimensional cases, periodic, or transient heat transfer problems for geothermal well operations. The corresponding Green’s functions are provided for those applications. 

Abstract The paper extends the recent work (JAM, 88, 061002, 2021) of the Eshelby's tensors for polynomial eigenstrains from a two dimensional (2D) to three dimensional (3D) domain, which provides the solution to the elastic field with continuously distributed eigenstrain on a polyhedral inclusion approximated by the Taylor series of polynomials. Similarly, the polynomial eigenstrain is expanded at the centroid of the polyhedral inclusion with uniform, linear and quadratic order terms, which provides tailorable accuracy of the elastic solutions of polyhedral inhomogeneity by using Eshelby's equivalent inclusion method. However, for both 2D and 3D cases, the stress distribution in the inhomogeneity exhibits a certain discrepancy from the finite element results at the neighborhood of the vertices due to the singularity of Eshelby's tensors, which makes it inaccurate to use the Taylor series of polynomials at the centroid to catch the eigenstrain at the vertices. This paper formulates the domain discretization with tetrahedral elements to accurately solve for eigenstrain distribution and predict the stress field. With the eigenstrain determined at each node, the elastic field can be predicted with the closed-form domain integral of Green's function. The parametric analysis shows the performance difference between the polynomial eigenstrain by the Taylor expansion at the centroid and the 𝐶0 continuous eigenstrain by particle discretization. Because the stress singularity is evaluated by the analytical form of the Eshelby's tensor, the elastic analysis is robust, stable and efficient.