In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of...In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.展开更多
Grain size is an important determinant of grain yield in rice.Although dozens of grain size genes have been reported,the molecular mechanisms that control grain size remain to be fully clarified.Here,we report the clo...Grain size is an important determinant of grain yield in rice.Although dozens of grain size genes have been reported,the molecular mechanisms that control grain size remain to be fully clarified.Here,we report the cloning and characterization of GR5(GRAIN ROUND 5),which is allelic to SMOS1/SHB/RLA1/NGR5 and en-codes an AP2 transcription factor.GR5 acts as a transcriptional activator and determines grain size by influencing cell proliferation and expansion.We demonstrated that GR5 physically interacts withfive Gg subunit proteins(RGG1,RGG2,DEP1,GS3,and GGC2)and acts downstream of the G protein complex.Four downstream target genes of GR5 in grain development(DEP2,DEP3,DRW1,and CyCD5;2)were re-vealed and their core T/CGCAC motif identified by yeast one-hybrid,EMSA,and ChIP–PCR experiments.Our results revealed that GR5 interacts with Gg subunits and cooperatively determines grain size by regu-lating the expression of downstream target genes.Thesefindings provide new insight into the genetic reg-ulatory network of the G protein signaling pathway in the control of grain size and provide a potential target for high-yield rice breeding.展开更多
基金This work was supported by the Key International(Regional)Joint Research Program of the National Natural Science Foundation of China(No.12120101002).
文摘In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.
基金supported by the National Key Research and Development Program of China (2022YFF1002901)the Hainan Yazhou Bay Seed Laboratory (B21HJ0215)+4 种基金the Natural Science Foundation of China (32272109)the Nanfan special project (ZDXM2315)of CAASthe Natural Science Foundation of China (32072048,U2004204)the Qian Qian Academician Workstation,the specific research fund of the Innovation Platform for Academicians of Hainan Province (YSPTZX202303)the Key Research and Development Program of Zhejiang Province (2021C02056).
文摘Grain size is an important determinant of grain yield in rice.Although dozens of grain size genes have been reported,the molecular mechanisms that control grain size remain to be fully clarified.Here,we report the cloning and characterization of GR5(GRAIN ROUND 5),which is allelic to SMOS1/SHB/RLA1/NGR5 and en-codes an AP2 transcription factor.GR5 acts as a transcriptional activator and determines grain size by influencing cell proliferation and expansion.We demonstrated that GR5 physically interacts withfive Gg subunit proteins(RGG1,RGG2,DEP1,GS3,and GGC2)and acts downstream of the G protein complex.Four downstream target genes of GR5 in grain development(DEP2,DEP3,DRW1,and CyCD5;2)were re-vealed and their core T/CGCAC motif identified by yeast one-hybrid,EMSA,and ChIP–PCR experiments.Our results revealed that GR5 interacts with Gg subunits and cooperatively determines grain size by regu-lating the expression of downstream target genes.Thesefindings provide new insight into the genetic reg-ulatory network of the G protein signaling pathway in the control of grain size and provide a potential target for high-yield rice breeding.
