A detailed analysis of the stability and flipping dynamics of a delayed exclusive toggle switch is performed. We use forward flux sampling method combined with delayed stochastic simulation algorithm to get the statio...A detailed analysis of the stability and flipping dynamics of a delayed exclusive toggle switch is performed. We use forward flux sampling method combined with delayed stochastic simulation algorithm to get the stationary distribution function, the switching rate, and path- ways, as well as the transition state ensemble. Interestingly, under the influence of time delay, the stationary distribution corresponding to the stable states become narrower and the population in the transition region is significantly enhanced. In addition, the flipping rate increases monotonically with delay. Such findings demonstrate that time delay could reduce the stability of the bistable genetic switch dramatically. Furthermore, the transition pathways, characterized by the difference in the protein numbers and the state of operator, show larger discrepancy between the forward and backward switching process with increas- ing delay, indicating that transcriptional and translational delay can remarkably affect the flipping dynamics. Specifically, for the transition state, the difference in the probability of finding the operator site bound by the two different protein dimers is enlarged by delay, which further illustrates the crucial role of time delay on the stability and switching dynamics of genetic toggle switches.展开更多
Earthquakes of M_S5. 6 and M_S6.1 occurred in Yingjiang,Yunnan on May 24 and May 30,2014 respectively. In this paper,we use the waveform data recorded by mobile seismic stations( KAC) which were set up in the source a...Earthquakes of M_S5. 6 and M_S6.1 occurred in Yingjiang,Yunnan on May 24 and May 30,2014 respectively. In this paper,we use the waveform data recorded by mobile seismic stations( KAC) which were set up in the source area after the Yingjiang MS5. 6earthquake on May 24,2014 to study the shear-wave splitting characteristics of Yingjiang M_S6.1 earthquake sequence with the SAM method. The result shows that predominant polarization of fast shear-waves before the M_S6.1 earthquake is consistent with the direction of regional principal compressive stress,and predominant polarization of fast shear-waves before the M_S6.1 earthquake show better consistency and smaller dispersion compared to after the M_S6.1 earthquake,and there may be a deflection for the fast shearwaves predominant polarization between the M_S6.1 earthquake sequence and foreshock sequence. We found that the time-delays generally exhibited a lower level before the M_S6.1earthquake and a relatively higher value after the M_S6.1 earthquake.展开更多
The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential...The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.展开更多
文摘A detailed analysis of the stability and flipping dynamics of a delayed exclusive toggle switch is performed. We use forward flux sampling method combined with delayed stochastic simulation algorithm to get the stationary distribution function, the switching rate, and path- ways, as well as the transition state ensemble. Interestingly, under the influence of time delay, the stationary distribution corresponding to the stable states become narrower and the population in the transition region is significantly enhanced. In addition, the flipping rate increases monotonically with delay. Such findings demonstrate that time delay could reduce the stability of the bistable genetic switch dramatically. Furthermore, the transition pathways, characterized by the difference in the protein numbers and the state of operator, show larger discrepancy between the forward and backward switching process with increas- ing delay, indicating that transcriptional and translational delay can remarkably affect the flipping dynamics. Specifically, for the transition state, the difference in the probability of finding the operator site bound by the two different protein dimers is enlarged by delay, which further illustrates the crucial role of time delay on the stability and switching dynamics of genetic toggle switches.
基金jointly supported by Task Contract for Earthquake Situation Tracking of CEA in 2015(2015010113,2015010301)fundation from Earthquake Administration of Xinjiang Uygur Autonomous Region,China(201401)
文摘Earthquakes of M_S5. 6 and M_S6.1 occurred in Yingjiang,Yunnan on May 24 and May 30,2014 respectively. In this paper,we use the waveform data recorded by mobile seismic stations( KAC) which were set up in the source area after the Yingjiang MS5. 6earthquake on May 24,2014 to study the shear-wave splitting characteristics of Yingjiang M_S6.1 earthquake sequence with the SAM method. The result shows that predominant polarization of fast shear-waves before the M_S6.1 earthquake is consistent with the direction of regional principal compressive stress,and predominant polarization of fast shear-waves before the M_S6.1 earthquake show better consistency and smaller dispersion compared to after the M_S6.1 earthquake,and there may be a deflection for the fast shearwaves predominant polarization between the M_S6.1 earthquake sequence and foreshock sequence. We found that the time-delays generally exhibited a lower level before the M_S6.1earthquake and a relatively higher value after the M_S6.1 earthquake.
基金Project supported by the 973 National Basic Research Program of China (No. 2007CB814904)the National Natural Science Foundations of China (No. 10921101)+2 种基金the Shandong Provincial Natural Science Foundation of China (No. 2008BS01024)the Science Fund for Distinguished Young Scholars of Shandong Province (No. JQ200801)the Shandong University Science Fund for Distinguished Young Scholars(No. 2009JQ004)
文摘The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.
