For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system (A, G, α), G<sub>α</sub><sup>×</sup> A =...For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system (A, G, α), G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.展开更多
We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an actio...We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.展开更多
The tumor suppressor p53 plays a key role in protecting genetic integrity. Its dynamics have important physiological significance, which may be related to the cell fate. Previous experiments have shown that the wild-t...The tumor suppressor p53 plays a key role in protecting genetic integrity. Its dynamics have important physiological significance, which may be related to the cell fate. Previous experiments have shown that the wild-type p53-induced phosphatase 1(Wip1) protein could maintain p53 oscillation. Therefore, we add Wip1 to remodel the p53 network. Firstly,we use the binomial τ-leap algorithm to prove our model stable under internal noise. Then, we make a series of bifurcation diagrams, that is, p53 levels as a function of p53 degradation rate at different Wip1 generation rates. The results illustrate that Wip1 is essential for p53 oscillation. Finally, a two-dimensional bifurcation diagram is made and the stability of some p53 dynamics under external noise is analyzed by potential landscape. Our results may have some implications for artificially interfering with p53 dynamics to achieve tumor suppression.展开更多
文摘For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system (A, G, α), G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.
文摘We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.
基金National Natural Science Foundation of China(Grant No.11762011).
文摘The tumor suppressor p53 plays a key role in protecting genetic integrity. Its dynamics have important physiological significance, which may be related to the cell fate. Previous experiments have shown that the wild-type p53-induced phosphatase 1(Wip1) protein could maintain p53 oscillation. Therefore, we add Wip1 to remodel the p53 network. Firstly,we use the binomial τ-leap algorithm to prove our model stable under internal noise. Then, we make a series of bifurcation diagrams, that is, p53 levels as a function of p53 degradation rate at different Wip1 generation rates. The results illustrate that Wip1 is essential for p53 oscillation. Finally, a two-dimensional bifurcation diagram is made and the stability of some p53 dynamics under external noise is analyzed by potential landscape. Our results may have some implications for artificially interfering with p53 dynamics to achieve tumor suppression.