This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtap...This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.展开更多
A stable,rapid and effective neural differentiation method is essential for the clinical applications of human embryonic stem cells(ESCs)or induced pluripotent stem cells(iPSCs)in treating neurological disorders and d...A stable,rapid and effective neural differentiation method is essential for the clinical applications of human embryonic stem cells(ESCs)or induced pluripotent stem cells(iPSCs)in treating neurological disorders and diseases.Herein,we established a novel and robust monolayer differentiation method to produce functional neural progenitor cells(NPCs)from human ESC/iPSCs on Type I Collagen.The derived cells not only displayed the requisite markers,but also behaved similarly to classic NPCs both in vitro and in vivo.Upon transplantation into traumatic brain injury model,the derived NPCs facilitated recovery from injury.We also found that SMAD signaling stayed down throughout the differentiation process on Type I Collagen,and the pluripotent signals were rapidly downregulated along with raising up of neural early markers on the third day.Meanwhile,ATAC-seq data showed the related mediation of distinct transcriptome and global chromatin dynamics during NPC induction.Totally,our results thus provide a convenient way to generate NPCs from human ESC/iPSCs for neural diseases’treatment.展开更多
文摘This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.
基金supported by the National Key Research and Development Program of China(2017YFA0104800)the“Strategic Priority Research Program”of the Chinese Academy of Sciences(XDA16010505)+5 种基金the National Natural Science Foundation of China(81570944,31300901,and 31900547)Fountain-Valley Life Sciences Fund of University of Chinese Academy of Sciences Education FoundationScience and Technology Planning Project of Guangdong Province,China(2017B030314056)Natural Science Foundation of Guangdong Province,China(2017A030310098,2016A030313165,2015A030310026,and 2014A030313732)Science and Technology Planning Project of Guangzhou,China(201904010474)Shenzhen Peacock Plan(KQTD2016113015442590)。
文摘A stable,rapid and effective neural differentiation method is essential for the clinical applications of human embryonic stem cells(ESCs)or induced pluripotent stem cells(iPSCs)in treating neurological disorders and diseases.Herein,we established a novel and robust monolayer differentiation method to produce functional neural progenitor cells(NPCs)from human ESC/iPSCs on Type I Collagen.The derived cells not only displayed the requisite markers,but also behaved similarly to classic NPCs both in vitro and in vivo.Upon transplantation into traumatic brain injury model,the derived NPCs facilitated recovery from injury.We also found that SMAD signaling stayed down throughout the differentiation process on Type I Collagen,and the pluripotent signals were rapidly downregulated along with raising up of neural early markers on the third day.Meanwhile,ATAC-seq data showed the related mediation of distinct transcriptome and global chromatin dynamics during NPC induction.Totally,our results thus provide a convenient way to generate NPCs from human ESC/iPSCs for neural diseases’treatment.
