Visual assessment of tumor metastatic capacity is crucial for predicting hepatocellular carcinoma(HCC)prognosis and guiding clinical therapeutic approaches.In this study,we developed an enzyme-responsive probe based o...Visual assessment of tumor metastatic capacity is crucial for predicting hepatocellular carcinoma(HCC)prognosis and guiding clinical therapeutic approaches.In this study,we developed an enzyme-responsive probe based on the peptide GK10,which is selectively cleaved by matrix metalloproteinase-9(MMP-9),a critical marker for metastasis in HCC.The GK10 peptide was conjugated with near-infrared fiuorescent molecule IR783,fiuorescent quencher black hole quencher 3(BHQ3),and magnetic resonance(MR)contrast agent DOTA-Gd,forming the IR783-GK10-BHQ3-Gd probe.Upon MMP-9 cleavage of GK10,BHQ3 is released from the probe,thereby amplifying the previously quenched IR783 fiuorescence signal.In vitro experiments demonstrate the probe's impressive detection limit for MMP-9,as low as 1.84 ng/m L.Moreover,in vivo imaging results reveal that the probe can differentiate liver cancers with varying metastatic capacities.The fiuorescence and MR imaging signal intensity of high metastatic HCC are approximately1.2 times greater than that of low metastatic HCC.Thus,this engineered probe holds promise as a valuable tool for evaluating HCC metastatic capacity through fiuorescence-MR dual-mode imaging.展开更多
In this paper, we consider the numerical solution of decoupled mean-field forward backward stochastic differential equations with jumps (MFBSDEJs). By using finite difference approximations and the Gaussian quadrature...In this paper, we consider the numerical solution of decoupled mean-field forward backward stochastic differential equations with jumps (MFBSDEJs). By using finite difference approximations and the Gaussian quadrature rule, and the weak order 2.0 Itô-Taylor scheme to solve the forward mean-field SDEs with jumps, we propose a new second order scheme for MFBSDEJs. The proposed scheme allows an easy implementation. Some numerical experiments are carried out to demonstrate the stability, the effectiveness and the second order accuracy of the scheme.展开更多
In this paper,we consider the numerical solution of decoupled mean-field forward backward stochastic differential equations with jumps(MFBSDEJs).By using finite difference approximations and the Gaussian quadrature ru...In this paper,we consider the numerical solution of decoupled mean-field forward backward stochastic differential equations with jumps(MFBSDEJs).By using finite difference approximations and the Gaussian quadrature rule,and the weak order 2.0 Itô-Taylor scheme to solve the forward mean-field SDEs with jumps,we propose a new second order scheme for MFBSDEJs.The proposed scheme allows an easy implementation.Some numerical experiments are carried out to demonstrate the stability,the effectiveness and the second order accuracy of the scheme.展开更多
This is one of our series works on numerical methods for mean-field forward backward stochastic differential equations(MFBSDEs).In this work,we propose an explicit multistep scheme for MFBSDEs which is easy to impleme...This is one of our series works on numerical methods for mean-field forward backward stochastic differential equations(MFBSDEs).In this work,we propose an explicit multistep scheme for MFBSDEs which is easy to implement,and is of high order rate of convergence.Rigorous error estimates of the proposed multistep scheme are presented.Numerical experiments are carried out to show the efficiency and accuracy of the proposed scheme.展开更多
By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic d...By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.展开更多
基金financially supported by the National Natural Science Foundation of China(Nos.32025021,31971292,32111540257)the Zhejiang Province Financial Supporting(Nos.2020C03110 and 2023C04017)the Key Scientific and Technological Special Project of Ningbo City(No.2020Z094)。
文摘Visual assessment of tumor metastatic capacity is crucial for predicting hepatocellular carcinoma(HCC)prognosis and guiding clinical therapeutic approaches.In this study,we developed an enzyme-responsive probe based on the peptide GK10,which is selectively cleaved by matrix metalloproteinase-9(MMP-9),a critical marker for metastasis in HCC.The GK10 peptide was conjugated with near-infrared fiuorescent molecule IR783,fiuorescent quencher black hole quencher 3(BHQ3),and magnetic resonance(MR)contrast agent DOTA-Gd,forming the IR783-GK10-BHQ3-Gd probe.Upon MMP-9 cleavage of GK10,BHQ3 is released from the probe,thereby amplifying the previously quenched IR783 fiuorescence signal.In vitro experiments demonstrate the probe's impressive detection limit for MMP-9,as low as 1.84 ng/m L.Moreover,in vivo imaging results reveal that the probe can differentiate liver cancers with varying metastatic capacities.The fiuorescence and MR imaging signal intensity of high metastatic HCC are approximately1.2 times greater than that of low metastatic HCC.Thus,this engineered probe holds promise as a valuable tool for evaluating HCC metastatic capacity through fiuorescence-MR dual-mode imaging.
基金supported by the NSF of China(Grant Nos.12071261,12371398,12001539,11831010,11871068)by the China Postdoctoral Science Foundation(Grant No.2019TQ0073)by the Science Challenge Project(Grant No.TZ2018001)and by the National Key R&D Program of China(Grant No.2018YFA0703900).
文摘In this paper, we consider the numerical solution of decoupled mean-field forward backward stochastic differential equations with jumps (MFBSDEJs). By using finite difference approximations and the Gaussian quadrature rule, and the weak order 2.0 Itô-Taylor scheme to solve the forward mean-field SDEs with jumps, we propose a new second order scheme for MFBSDEJs. The proposed scheme allows an easy implementation. Some numerical experiments are carried out to demonstrate the stability, the effectiveness and the second order accuracy of the scheme.
基金supported by the NSF of China(Grant Nos.12071261,12371398,12001539,11831010,11871068)the China Postdoctoral Science Foundation(Grant No.2019TQ0073)+1 种基金the Science Challenge Project(Grant No.TZ2018001)the National Key R&D Program of China(Grant No.2018YFA0703900).
文摘In this paper,we consider the numerical solution of decoupled mean-field forward backward stochastic differential equations with jumps(MFBSDEJs).By using finite difference approximations and the Gaussian quadrature rule,and the weak order 2.0 Itô-Taylor scheme to solve the forward mean-field SDEs with jumps,we propose a new second order scheme for MFBSDEJs.The proposed scheme allows an easy implementation.Some numerical experiments are carried out to demonstrate the stability,the effectiveness and the second order accuracy of the scheme.
基金supported by the national key basic research program(Nos.2018YFB0704304,2018YFA0703900)Science Challenge Project(No.TZ2018001)+3 种基金NSF of China(Nos.11831010,11871068,11822111,11688101,11801320,12071261,12001539)Natural Science Foundation of Shandong Province(No.ZR2018BA005)NSF of Hunan Province(No.2020JJ5647)China Postdoctoral Science Foundation(No.2019TQ0073).
文摘This is one of our series works on numerical methods for mean-field forward backward stochastic differential equations(MFBSDEs).In this work,we propose an explicit multistep scheme for MFBSDEs which is easy to implement,and is of high order rate of convergence.Rigorous error estimates of the proposed multistep scheme are presented.Numerical experiments are carried out to show the efficiency and accuracy of the proposed scheme.
基金supported by the NSF of China(No.12001539)the NSF of Hunan Province(No.2020JJ5647)China Postdoctoral Science Foundation(No.2019TQ0073).
文摘By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.
