This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
目的探究基于癌症基因组图谱(the cancer genome atlas,TCGA)数据库生物信息学分析构建肾癌N6-甲基腺苷相关长链非编码RNA(long non-coding RNA,LncRNA)配对模型及其预后预测价值。方法从TCGA数据库中下载肾癌的RNA-sep转录组数据及相...目的探究基于癌症基因组图谱(the cancer genome atlas,TCGA)数据库生物信息学分析构建肾癌N6-甲基腺苷相关长链非编码RNA(long non-coding RNA,LncRNA)配对模型及其预后预测价值。方法从TCGA数据库中下载肾癌的RNA-sep转录组数据及相关临床信息,后通过Perl软件对转录组数据进行数据整理、分离LncRNA和信使RNA(messenger RNA,mRNA)。总共得到564例肾癌患者的肾癌组织和72例正常组织,最终纳入540例肾癌患者。使用caret将540例肾癌患者采用随机数据表法分为训练集组(n=275)和验证集组(n=265)。根据单因素和多因素COX回归分析建立N6-甲基腺苷相关LncRNA配对模型。以LASSO回归算法获取风险评估方程。根据该方程分别计算出风险评分,并以中位风险值最佳临界点将所有患者分为高风险组及低风险组。采用Kaplan-Meier生存分析对总体样本中高、低风险组患者的生存差异作出生存曲线图。利用Cluster Profiler软件包中对基因本体论(gene ontology,GO)和京都基因与基因组百库全书(Kyoto encyclopedia of genes and genomes,KEGG)进行通路富集分析。运用R软件分析N6-甲基腺苷相关LncRNA配对模型与免疫细胞浸润的关系。结果根据Kaplan-Meier生存分析显示,在训练组中,低风险组患者总生存期明显高于高风险组患者(P<0.05)。与高风险组相比,低风险组G1~2,G3~4,Ⅰ~Ⅱ期、Ⅲ~Ⅳ期、年龄≤65岁、>65岁患者总生存期较高(P<0.05)。对高、低风险组获取差异基因富集分析:主要富集含有肌收缩、横纹肌细胞分化、肌原纤维、受体激活活性、血管平滑肌收缩等。高风险组和低风险组最高的驱动基因进行展示变异频率及变异信息,其风险评分与T细胞、浆细胞的浸润程度呈正相关(r=0.638,P=0.001)。结论基于生物信息学分析N6-甲基腺苷相关LncRNA配对模型有助于预测肾癌患者的预后。为肾癌预后评估和最佳治疗策略提供了新思路,有助于未来进一步分析胃癌发生及发展的分子机制。展开更多
Condensation of D-glucose, o-phenylenediamine and N,N-benzylphenylhydrazine hydrochloride (NNBPHH) in a one-pot reaction, or condensation of 2-(D-arabino-tetritol-1-yl) quinoxaline and NNBPHH, gave 3-(D-erythro-glycer...Condensation of D-glucose, o-phenylenediamine and N,N-benzylphenylhydrazine hydrochloride (NNBPHH) in a one-pot reaction, or condensation of 2-(D-arabino-tetritol-1-yl) quinoxaline and NNBPHH, gave 3-(D-erythro-glycerol-1- yl)-1-phenyl-1H-pyrazolo[3,4-b]quinoxaline. The structure of the latter was determined by 1H NMR spectroscopy and by synthesis using phenylhydrazine hydrochloride instead of NNBPHH. Condensation of D-glucose and 4,5-dichloro-o-phenylenediamine gave 6,7-dichloro-2-(D-arabino-tetritol-1-yl)quinoxaline, which upon condensation with NNBPHH gave the corresponding 6,7-dichloro-3-(D-erythro-glycerol-1-yl)-1-phenyl-1H-pyrazolo[3,4-b]quinoxaline. The structure and mechanism of formation of these compounds are discussed.展开更多
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
文摘目的探究基于癌症基因组图谱(the cancer genome atlas,TCGA)数据库生物信息学分析构建肾癌N6-甲基腺苷相关长链非编码RNA(long non-coding RNA,LncRNA)配对模型及其预后预测价值。方法从TCGA数据库中下载肾癌的RNA-sep转录组数据及相关临床信息,后通过Perl软件对转录组数据进行数据整理、分离LncRNA和信使RNA(messenger RNA,mRNA)。总共得到564例肾癌患者的肾癌组织和72例正常组织,最终纳入540例肾癌患者。使用caret将540例肾癌患者采用随机数据表法分为训练集组(n=275)和验证集组(n=265)。根据单因素和多因素COX回归分析建立N6-甲基腺苷相关LncRNA配对模型。以LASSO回归算法获取风险评估方程。根据该方程分别计算出风险评分,并以中位风险值最佳临界点将所有患者分为高风险组及低风险组。采用Kaplan-Meier生存分析对总体样本中高、低风险组患者的生存差异作出生存曲线图。利用Cluster Profiler软件包中对基因本体论(gene ontology,GO)和京都基因与基因组百库全书(Kyoto encyclopedia of genes and genomes,KEGG)进行通路富集分析。运用R软件分析N6-甲基腺苷相关LncRNA配对模型与免疫细胞浸润的关系。结果根据Kaplan-Meier生存分析显示,在训练组中,低风险组患者总生存期明显高于高风险组患者(P<0.05)。与高风险组相比,低风险组G1~2,G3~4,Ⅰ~Ⅱ期、Ⅲ~Ⅳ期、年龄≤65岁、>65岁患者总生存期较高(P<0.05)。对高、低风险组获取差异基因富集分析:主要富集含有肌收缩、横纹肌细胞分化、肌原纤维、受体激活活性、血管平滑肌收缩等。高风险组和低风险组最高的驱动基因进行展示变异频率及变异信息,其风险评分与T细胞、浆细胞的浸润程度呈正相关(r=0.638,P=0.001)。结论基于生物信息学分析N6-甲基腺苷相关LncRNA配对模型有助于预测肾癌患者的预后。为肾癌预后评估和最佳治疗策略提供了新思路,有助于未来进一步分析胃癌发生及发展的分子机制。
文摘Condensation of D-glucose, o-phenylenediamine and N,N-benzylphenylhydrazine hydrochloride (NNBPHH) in a one-pot reaction, or condensation of 2-(D-arabino-tetritol-1-yl) quinoxaline and NNBPHH, gave 3-(D-erythro-glycerol-1- yl)-1-phenyl-1H-pyrazolo[3,4-b]quinoxaline. The structure of the latter was determined by 1H NMR spectroscopy and by synthesis using phenylhydrazine hydrochloride instead of NNBPHH. Condensation of D-glucose and 4,5-dichloro-o-phenylenediamine gave 6,7-dichloro-2-(D-arabino-tetritol-1-yl)quinoxaline, which upon condensation with NNBPHH gave the corresponding 6,7-dichloro-3-(D-erythro-glycerol-1-yl)-1-phenyl-1H-pyrazolo[3,4-b]quinoxaline. The structure and mechanism of formation of these compounds are discussed.
