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IntroductionOver the past decades, immune dysregulation has been consistently demonstrated being common charactoristics of endometriosis (EM) and Inflammatory Bowel Disease (IBD) in numerous studies. However, the underlying pathological mechanisms remain unknown. In this study, bioinformatics techniques were used to screen large-scale gene expression data for plausible correlations at the molecular level in order to identify common pathogenic pathways between EM and IBD.MethodsBased on the EM transcriptomic datasets GSE7305 and GSE23339, as well as the IBD transcriptomic datasets GSE87466 and GSE126124, differential gene analysis was performed using the limma package in the R environment. Co-expressed differentially expressed genes were identified, and a protein-protein interaction (PPI) network for the differentially expressed genes was constructed using the 11.5 version of the STRING database. The MCODE tool in Cytoscape facilitated filtering out protein interaction subnetworks. Key genes in the PPI network were identified through two topological analysis algorithms (MCC and Degree) from the CytoHubba plugin. Upset was used for visualization of these key genes. The diagnostic value of gene expression levels for these key genes was assessed using the Receiver Operating Characteristic (ROC) curve and Area Under the Curve (AUC) The CIBERSORT algorithm determined the infiltration status of 22 immune cell subtypes, exploring differences between EM and IBD patients in both control and disease groups. Finally, different gene expression trends shared by EM and IBD were input into CMap to identify small molecule compounds with potential therapeutic effects.Results113 differentially expressed genes (DEGs) that were co-expressed in EM and IBD have been identified, comprising 28 down-regulated genes and 86 up-regulated genes. The co-expression differential gene of EM and IBD in the functional enrichment analyses focused on immune response activation, circulating immunoglobulin-mediated humoral immune response and humoral immune response. Five hub genes (SERPING1、VCAM1、CLU、C3、CD55) were identified through the Protein-protein Interaction network and MCODE.High Area Under the Curve (AUC) values of Receiver Operating Characteristic (ROC) curves for 5hub genes indicate the predictive ability for disease occurrence.These hub genes could be used as potential biomarkers for the development of EM and IBD. Furthermore, the CMap database identified a total of 9 small molecule compounds (TTNPB、CAY-10577、PD-0325901 etc.) targeting therapeutic genes for EM and IBD.DiscussionOur research revealed common pathogenic mechanisms between EM and IBD, particularly emphasizing immune regulation and cell signalling, indicating the significance of immune factors in the occurence and progression of both diseases. By elucidating shared mechanisms, our study provides novel avenues for the prevention and treatment of EM and IBD.

Turbulent flows are chaotic and multi-scale dynamical systems, which have large numbers of degrees of freedom. Turbulent flows, however, can be modeled with a smaller number of degrees of freedom when using an appropriate coordinate system, which is the goal of dimensionality reduction via nonlinear autoencoders. Autoencoders are expressive tools, but they are difficult to interpret. This article aims to propose a method to aid the interpretability of autoencoders. First, we introduce the decoder decomposition, a post-processing method to connect the latent variables to the coherent structures of flows. Second, we apply the decoder decomposition to analyze the latent space of synthetic data of a two-dimensional unsteady wake past a cylinder. We find that the dimension of latent space has a significant impact on the interpretability of autoencoders. We identify the physical and spurious latent variables. Third, we apply the decoder decomposition to the latent space of wind-tunnel experimental data of a three-dimensional turbulent wake past a bluff body. We show that the reconstruction error is a function of both the latent space dimension and the decoder size, which are correlated. Finally, we apply the decoder decomposition to rank and select latent variables based on the coherent structures that they represent. This is useful to filter unwanted or spurious latent variables or to pinpoint specific coherent structures of interest. The ability to rank and select latent variables will help users design and interpret nonlinear autoencoders.