DIFFERENTIAL MODULES AND THEOREM OF HUKUHARA–TURRITTIN

Author(s):  
Yasutaka Sibuya
Keyword(s):  
2020 ◽  
Vol 15 ◽  
Author(s):  
Jujuan Zhuang ◽  
Shuang Dai ◽  
Lijun Zhang ◽  
Pan Gao ◽  
Yingmin Han ◽  
...  

Background: Breast cancer is a complex disease with high prevalence in women, the molecular mechanisms of which are still unclear at present. Most transcriptomic studies on breast cancer focus on differential expression of each gene between tumor and the adjacent normal tissues, while the other perturbations induced by breast cancer including the gene regulation variations, the changes of gene modules and the pathways, which might be critical to the diagnosis, treatment and prognosis of breast cancer are more or less ignored. Objective: We presented a complete process to study breast cancer from multiple perspectives, including differential expression analysis, constructing gene co-expression networks, modular differential connectivity analysis, differential gene connectivity analysis, gene function enrichment analysis key driver analysis. In addition, we prioritized the related anti-cancer drugs based on enrichment analysis between differential expression genes and drug perturbation signatures. Methods: The RNA expression profiles of 1109 breast cancer tissue and 113 non-tumor tissues were downloaded from The Cancer Genome Atlas (TCGA) database. Differential expression of RNAs was identified using the “DESeq2” bioconductor package in R, and gene co-expression networks was constructed using the weighted gene co-expression network analysis (WGCNA). To compare the module changes and gene co-expression variations between tumor and the adjacent normal tissues, modular differential connectivity (MDC) analysis and differential gene connectivity analysis (DGCA) were performed. Results: Top differential genes like MMP11 and COL10A1 were known to be associated with breast cancer. And we found 23 modules in the tumor network had significantly different co-expression patterns. The top differential modules were enriched in Goterms related to breast cancer like MHC protein complex, leukocyte activation, regulation of defense response and so on. In addition, key genes like UBE2T driving the top differential modules were significantly correlated with the patients’ survival. Finally, we predicted some potential breast cancer drugs, such as Eribulin, Taxane, Cisplatin and Oxaliplatin. Conclusion: As an indication, this framework might be useful in understanding the molecular pathogenesis of diseases like breast cancer and inferring useful drugs for personalized medication


2010 ◽  
Vol 9 (3) ◽  
pp. 669-671 ◽  
Author(s):  
Kiran S. Kedlaya ◽  
Liang Xiao

The statement of Theorem 2.7.6 in the indicated paper is incorrect. For instance, if m = 0 (i.e., the base field K contains no additional derivations), it is inconsistent with Theorem 2.7.4 due to the distinction between intrinsic and extrinsic generic radii of convergence. Theorems 2.7.12 and 2.7.13 are incorrect for similar reasons.


1985 ◽  
Vol 15 (1) ◽  
pp. 141-143
Author(s):  
Mitsuo Kanemitsu ◽  
Ken-ichi Yoshida
Keyword(s):  

1981 ◽  
Vol 83 ◽  
pp. 107-121 ◽  
Author(s):  
Norio Yamauchi

Let k be a field and A a noetherian k-algebra. In this note, we shall study the universal finite module of differentials of A over k, which is denoted by Dk(A). When the characteristic of k is zero, detailed results have been obtained by Scheja and Storch [8]. So we shall treat the positive characteristic case. In § 1, we shall study differential modules of a local ring over subfields. We obtain a criterion of regularity (Theorem (1.14)). In § 2, we shall study the formal fibres and regular locus of A with Dk(A). Our main result is Theorem (2.1) which shows that, if Dk(A) exists, then A is a universally catenary G-ring under a certain assumption. In the local case, this is a generalization of Matsumura’s theorem ([5] Theorem 15), where regularity of A is assumed.


Author(s):  
Jiaqun Wei

We show that a differential module is Gorenstein projective (injective, respectively) if and only if its underlying module is Gorenstein projective (injective, respectively). We then relate the Ringel–Zhang theorem on differential modules to the Avramov–Buchweitz–Iyengar notion of projective class of differential modules and prove that for a ring R there is a bijective correspondence between projectively stable objects of split differential modules of projective class not more than 1 and R-modules of projective dimension not more than 1, and this is given by the homology functor H and stable syzygy functor ΩD. The correspondence sends indecomposable objects to indecomposable objects. In particular, we obtain that for a hereditary ring R there is a bijective correspondence between objects of the projectively stable category of Gorenstein projective differential modules and the category of all R-modules given by the homology functor and the stable syzygy functor. This gives an extended version of the Ringel–Zhang theorem.


2017 ◽  
Vol 12 (1) ◽  
pp. 443-451
Author(s):  
Bing Kong ◽  
Yu-Wu Ma ◽  
De-Xue Li ◽  
Xi-Jiang Liu ◽  
Yong-Guang Xu

AbstractBackgroundWe aim to identify sevoflurane-induced modules and pathways in patients following coronary artery bypass graft (CABG) surgery, and to further elucidate the molecular mechanisms of the cardioprotective effects of sevoflurane.MethodsDifferential co-expression network (DCN) was constructed. Candidate modules were identified via three steps: selection of seed genes, search of modules using snowball sampling, and refinement of modules. Afterwards, the significance of the candidate modules was assessed. Ultimately, pathway analyses for genes in differential modules were implemented to illuminate the biological processes.ResultsOverall, 122 genes were identified to serve as seed genes. From every seed gene, we extracted 122 modules and the mean node size in a module was 3. By setting the classification accuracy cutoff at 0.9 and the number of nodes in a module at 5, 7 candidate modules were identified, including module 80, 82, 82, 84, 85, 86 and 89. Based on the random permutation test, we found that these 7 candidate modules were all differential ones. Moreover, pathway analysis showed that genes in the differential modules 80, 82, and 85 were all enriched in the pathway of chemokine receptors bind chemokines.ConclusionSevoflurane might exert cardioprotective functions in patients following CABG, partially through regulating the pathway of chemokine receptors bind chemokines.


2017 ◽  
Vol 16 (2) ◽  
pp. 1047-1054 ◽  
Author(s):  
Bin Liu ◽  
Zhi Zhang ◽  
E-Nuo Dai ◽  
Jia-Xin Tian ◽  
Jiang-Ze Xin ◽  
...  
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document