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Data integration is a powerful tool for facilitating a comprehensive and generalizable understanding of microbial communities and their association with outcomes of interest. However, integrating data sets from different studies remains a challenging problem because of severe batch effects, unobserved confounding variables, and high heterogeneity across data sets. We propose a new data integration method called MetaDICT, which initially estimates the batch effects by weighting methods in causal inference literature and then refines the estimation via novel shared dictionary learning. Compared with existing methods, MetaDICT can better avoid the overcorrection of batch effects and preserve biological variation when there exist unobserved confounding variables, data sets are highly heterogeneous across studies, or the batch is completely confounded with some covariates. Furthermore, MetaDICT can generate comparable embedding at both taxa and sample levels that can be used to unravel the hidden structure of the integrated data and improve the integrative analysis. Applications to synthetic and real microbiome data sets demonstrate the robustness and effectiveness of MetaDICT in integrative analysis. Using MetaDICT, we characterize microbial interaction, identify generalizable microbial signatures, and enhance the accuracy of outcome prediction in two real integrative studies, including an integrative analysis of colorectal cancer metagenomics studies and a meta-analysis of immunotherapy microbiome studies. 

Abstract Recent advances in whole-cell modeling enable the computational tracking of the temporal evolution of thousands of molecular species across genomic, transcriptomic, proteomic, and metabolomic layers. These models provide a complementary perspective for studying cellular dynamics, offering continuous, system-wide observations that are difficult to obtain from experimental technologies, which are often destructive and yield only static measurements from limited modalities. While whole-cell models generate multi-omic simulation trajectories with high temporal resolution, analyzing and interpreting such complex data remains a major challenge that limits their potential to elucidate cellular dynamics. To address this challenge, we propose COTree, a statistical framework that learns integrated multi-omic representations and constructs a trajectory principal tree to summarize cellular progression patterns. COTree enables a broad range of downstream analyses, including cell classification, fate prediction, developmental time detection, and driver species identification, that provide new insights into how cells develop and differentiate. To demonstrate its practical utility, we apply COTree to a multi-omic trajectory dataset generated from the whole-cell model of JCVI-Syn3A, revealing cell types, characterizing long-term cellular dynamics, and identifying key driver species associated with cell death and replication. 

𝐵 site ordered 5⁢𝑑2 double perovskites (𝐴2⁢𝐵⁢𝐵′⁢O6,𝐵′=5⁢𝑑2) display a remarkable range of physical properties upon variation of the chosen 𝐵 and 𝐵′ site ions. This sensitivity to chemical substitution reflects the delicate balance and profound impact of strong electronic correlation and spin-orbit coupling in such systems. We present rhenium 𝐿2 and 𝐿3 resonant inelastic x-ray scattering (RIXS) measurements of two such physically dissimilar materials, Mott-insultating Ba2⁢Y⁢Re⁢O6 and semiconducting Sr2⁢Cr⁢Re⁢O6. Despite these differences, our RIXS results reveal similar energy scales of Hund's (𝐽𝐻) and spin-orbit coupling (𝜁) in the two materials, with both systems firmly in the intermediate Hund's coupling regime where 𝐽𝐻/𝜁∼1. However, there are clear differences in their RIXS spectra. The conductive character of Sr2⁢Cr⁢Re⁢O6 broadens and obfuscates the atomic transitions within an electron-hole continuum, while the insulating character of Ba2⁢Y⁢Re⁢O6 results in sharp atomic excitations. This contrast in their RIXS spectra despite their similar energy scales reflects a difference in the itinerancy-promoting hopping integral and illustrates the impact of the local crystal environment in double perovskites. Finally, 𝐿2 and 𝐿3 edge analyses of the atomic excitations in Ba2⁢Y⁢Re⁢O6 reveal that the ordering of the low lying excited states is inverted compared to previous reports, such that the appropriate energy scales of Hund's and spin-orbit coupling are significantly modified. We present exact diagonalization calculations of the RIXS spectra at both edges which show good agreement with our results for new energy scales of 𝜁=0.290⁢(5)⁢eV and 𝐽𝐻=0.38⁢(2)⁢eV [𝐽𝐻/𝜁=1.30⁢(5)].