The proper class generated by weak supplements

We show that, for hereditary rings, the smallest proper classes containing respectively the classes of short exact sequences determined by small submodules, submodules that have supplements and weak supplement submodules coincide. Moreover, we show that this class can be obtained as a natural extension of the class determined by small submodules. We also study injective, projective, coinjective and coprojective objects of this class. We prove that it is coinjectively generated and its global dimension is at most 1. Finally, we describe this class for Dedekind domains in terms of supplement submodules.TUBITAK (107T709

DataSheet3_Typing characteristics of metabolism-related genes in osteoporosis.CSV

Objective: Osteoporosis is a common musculoskeletal disease. Fractures caused by osteoporosis place a huge burden on global healthcare. At present, the mechanism of metabolic-related etiological heterogeneity of osteoporosis has not been explored, and no research has been conducted to analyze the metabolic-related phenotype of osteoporosis. This study aimed to identify different types of osteoporosis metabolic correlates associated with underlying pathogenesis by machine learning.Methods: In this study, the gene expression profiles GSE56814 and GSE56815 of osteoporosis patients were downloaded from the GEO database, and unsupervised clustering analysis was used to identify osteoporosis metabolic gene subtypes and machine learning to screen osteoporosis metabolism-related characteristic genes. Meanwhile, multi-omics enrichment was performed using the online Proteomaps tool, and the results were validated using external datasets GSE35959 and GSE7429. Finally, the immune and stromal cell types of the signature genes were inferred by the xCell method.Results: Based on unsupervised cluster analysis, osteoporosis metabolic genotyping can be divided into three distinct subtypes: lipid and steroid metabolism subtypes, glycolysis-related subtypes, and polysaccharide subtypes. In addition, machine learning SVM identified 10 potentially metabolically related genes, GPR31, GATM, DDB2, ARMCX1, RPS6, BTBD3, ADAMTSL4, COQ6, B3GNT2, and CD9.Conclusion: Based on the clustering analysis of gene expression in patients with osteoporosis and machine learning, we identified different metabolism-related subtypes and characteristic genes of osteoporosis, which will help to provide new ideas for the metabolism-related pathogenesis of osteoporosis and provide a new direction for follow-up research.</p

Table1_Typing characteristics of metabolism-related genes in osteoporosis.XLSX

Objective: Osteoporosis is a common musculoskeletal disease. Fractures caused by osteoporosis place a huge burden on global healthcare. At present, the mechanism of metabolic-related etiological heterogeneity of osteoporosis has not been explored, and no research has been conducted to analyze the metabolic-related phenotype of osteoporosis. This study aimed to identify different types of osteoporosis metabolic correlates associated with underlying pathogenesis by machine learning.Methods: In this study, the gene expression profiles GSE56814 and GSE56815 of osteoporosis patients were downloaded from the GEO database, and unsupervised clustering analysis was used to identify osteoporosis metabolic gene subtypes and machine learning to screen osteoporosis metabolism-related characteristic genes. Meanwhile, multi-omics enrichment was performed using the online Proteomaps tool, and the results were validated using external datasets GSE35959 and GSE7429. Finally, the immune and stromal cell types of the signature genes were inferred by the xCell method.Results: Based on unsupervised cluster analysis, osteoporosis metabolic genotyping can be divided into three distinct subtypes: lipid and steroid metabolism subtypes, glycolysis-related subtypes, and polysaccharide subtypes. In addition, machine learning SVM identified 10 potentially metabolically related genes, GPR31, GATM, DDB2, ARMCX1, RPS6, BTBD3, ADAMTSL4, COQ6, B3GNT2, and CD9.Conclusion: Based on the clustering analysis of gene expression in patients with osteoporosis and machine learning, we identified different metabolism-related subtypes and characteristic genes of osteoporosis, which will help to provide new ideas for the metabolism-related pathogenesis of osteoporosis and provide a new direction for follow-up research.</p

DataSheet2_Typing characteristics of metabolism-related genes in osteoporosis.CSV

Objective: Osteoporosis is a common musculoskeletal disease. Fractures caused by osteoporosis place a huge burden on global healthcare. At present, the mechanism of metabolic-related etiological heterogeneity of osteoporosis has not been explored, and no research has been conducted to analyze the metabolic-related phenotype of osteoporosis. This study aimed to identify different types of osteoporosis metabolic correlates associated with underlying pathogenesis by machine learning.Methods: In this study, the gene expression profiles GSE56814 and GSE56815 of osteoporosis patients were downloaded from the GEO database, and unsupervised clustering analysis was used to identify osteoporosis metabolic gene subtypes and machine learning to screen osteoporosis metabolism-related characteristic genes. Meanwhile, multi-omics enrichment was performed using the online Proteomaps tool, and the results were validated using external datasets GSE35959 and GSE7429. Finally, the immune and stromal cell types of the signature genes were inferred by the xCell method.Results: Based on unsupervised cluster analysis, osteoporosis metabolic genotyping can be divided into three distinct subtypes: lipid and steroid metabolism subtypes, glycolysis-related subtypes, and polysaccharide subtypes. In addition, machine learning SVM identified 10 potentially metabolically related genes, GPR31, GATM, DDB2, ARMCX1, RPS6, BTBD3, ADAMTSL4, COQ6, B3GNT2, and CD9.Conclusion: Based on the clustering analysis of gene expression in patients with osteoporosis and machine learning, we identified different metabolism-related subtypes and characteristic genes of osteoporosis, which will help to provide new ideas for the metabolism-related pathogenesis of osteoporosis and provide a new direction for follow-up research.</p

DataSheet4_Typing characteristics of metabolism-related genes in osteoporosis.CSV

Objective: Osteoporosis is a common musculoskeletal disease. Fractures caused by osteoporosis place a huge burden on global healthcare. At present, the mechanism of metabolic-related etiological heterogeneity of osteoporosis has not been explored, and no research has been conducted to analyze the metabolic-related phenotype of osteoporosis. This study aimed to identify different types of osteoporosis metabolic correlates associated with underlying pathogenesis by machine learning.Methods: In this study, the gene expression profiles GSE56814 and GSE56815 of osteoporosis patients were downloaded from the GEO database, and unsupervised clustering analysis was used to identify osteoporosis metabolic gene subtypes and machine learning to screen osteoporosis metabolism-related characteristic genes. Meanwhile, multi-omics enrichment was performed using the online Proteomaps tool, and the results were validated using external datasets GSE35959 and GSE7429. Finally, the immune and stromal cell types of the signature genes were inferred by the xCell method.Results: Based on unsupervised cluster analysis, osteoporosis metabolic genotyping can be divided into three distinct subtypes: lipid and steroid metabolism subtypes, glycolysis-related subtypes, and polysaccharide subtypes. In addition, machine learning SVM identified 10 potentially metabolically related genes, GPR31, GATM, DDB2, ARMCX1, RPS6, BTBD3, ADAMTSL4, COQ6, B3GNT2, and CD9.Conclusion: Based on the clustering analysis of gene expression in patients with osteoporosis and machine learning, we identified different metabolism-related subtypes and characteristic genes of osteoporosis, which will help to provide new ideas for the metabolism-related pathogenesis of osteoporosis and provide a new direction for follow-up research.</p

DataSheet1_Typing characteristics of metabolism-related genes in osteoporosis.CSV

Objective: Osteoporosis is a common musculoskeletal disease. Fractures caused by osteoporosis place a huge burden on global healthcare. At present, the mechanism of metabolic-related etiological heterogeneity of osteoporosis has not been explored, and no research has been conducted to analyze the metabolic-related phenotype of osteoporosis. This study aimed to identify different types of osteoporosis metabolic correlates associated with underlying pathogenesis by machine learning.Methods: In this study, the gene expression profiles GSE56814 and GSE56815 of osteoporosis patients were downloaded from the GEO database, and unsupervised clustering analysis was used to identify osteoporosis metabolic gene subtypes and machine learning to screen osteoporosis metabolism-related characteristic genes. Meanwhile, multi-omics enrichment was performed using the online Proteomaps tool, and the results were validated using external datasets GSE35959 and GSE7429. Finally, the immune and stromal cell types of the signature genes were inferred by the xCell method.Results: Based on unsupervised cluster analysis, osteoporosis metabolic genotyping can be divided into three distinct subtypes: lipid and steroid metabolism subtypes, glycolysis-related subtypes, and polysaccharide subtypes. In addition, machine learning SVM identified 10 potentially metabolically related genes, GPR31, GATM, DDB2, ARMCX1, RPS6, BTBD3, ADAMTSL4, COQ6, B3GNT2, and CD9.Conclusion: Based on the clustering analysis of gene expression in patients with osteoporosis and machine learning, we identified different metabolism-related subtypes and characteristic genes of osteoporosis, which will help to provide new ideas for the metabolism-related pathogenesis of osteoporosis and provide a new direction for follow-up research.</p