Predictive modeling of the evolutionary dynamics of cancer is a challenging issue in computational cancer biology.In this paper,we propose a general mathematical model framework for the evolutionary dynamics of cancer...Predictive modeling of the evolutionary dynamics of cancer is a challenging issue in computational cancer biology.In this paper,we propose a general mathematical model framework for the evolutionary dynamics of cancer,including plasticity and heterogeneity in cancer cells.Cancer is a group of diseases involving abnormal cell growth,during which abnormal regulation of stem cell regeneration is essential for the dynamics of cancer development.In general,the dynamics of stem cell regeneration can be simplified as a G0 phase cell cycle model,which leads to a delay differentiation equation.When cell heterogeneity and plasticity are considered,we establish a differential-integral equation based on the random transition of epigenetic states of stem cells during cell division.The proposed model highlights cell heterogeneity and plasticity;connects the heterogeneity with cell-to-cell variance in cellular behaviors(for example,proliferation,apoptosis,and differentiation/senescence);and can be extended to include gene mutation-induced tumor development.Hybrid computational models are developed based on the mathematical model framework and are applied to the processes of inflammationinduced tumorigenesis and tumor relapse after chimeric antigen receptor(CAR)-T cell therapy.Finally,we propose several mathematical problems related to the proposed differential-integral equation.Solutions to these problems are crucial for understanding the evolutionary dynamics of cancer.展开更多
Finsler geometry is just Riemannian geometry without the quadratic restriction. Recent studies on Finsler geometry have taken on a new look. In this article, we will briefly discuss recent developments and some open p...Finsler geometry is just Riemannian geometry without the quadratic restriction. Recent studies on Finsler geometry have taken on a new look. In this article, we will briefly discuss recent developments and some open problems in Finsler geometry.展开更多
This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the ...This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the total distance. This problem exists widely in real-life logistics distribution process.We propose a hybrid column generation algorithm(HCGA) for the OVRPTW, embedding both exact algorithm and metaheuristic. In HCGA, a label setting algorithm and an intelligent algorithm are designed to select columns from small and large subproblems, respectively. Moreover, a branch strategy is devised to generate the final feasible solution for the OVRPTW. The computational results show that the proposed algorithm has faster speed and can obtain the approximate optimal solution of the problem with 100 customers in a reasonable time.展开更多
By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation ...By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc.展开更多
In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an it...In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the Cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.展开更多
A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) bound...A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization;2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix;3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.91730101 and 11831015)
文摘Predictive modeling of the evolutionary dynamics of cancer is a challenging issue in computational cancer biology.In this paper,we propose a general mathematical model framework for the evolutionary dynamics of cancer,including plasticity and heterogeneity in cancer cells.Cancer is a group of diseases involving abnormal cell growth,during which abnormal regulation of stem cell regeneration is essential for the dynamics of cancer development.In general,the dynamics of stem cell regeneration can be simplified as a G0 phase cell cycle model,which leads to a delay differentiation equation.When cell heterogeneity and plasticity are considered,we establish a differential-integral equation based on the random transition of epigenetic states of stem cells during cell division.The proposed model highlights cell heterogeneity and plasticity;connects the heterogeneity with cell-to-cell variance in cellular behaviors(for example,proliferation,apoptosis,and differentiation/senescence);and can be extended to include gene mutation-induced tumor development.Hybrid computational models are developed based on the mathematical model framework and are applied to the processes of inflammationinduced tumorigenesis and tumor relapse after chimeric antigen receptor(CAR)-T cell therapy.Finally,we propose several mathematical problems related to the proposed differential-integral equation.Solutions to these problems are crucial for understanding the evolutionary dynamics of cancer.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19871001)and the Foundation of School of Mathematical Sciences, Peking University.
文摘Finsler geometry is just Riemannian geometry without the quadratic restriction. Recent studies on Finsler geometry have taken on a new look. In this article, we will briefly discuss recent developments and some open problems in Finsler geometry.
基金supported by the National Natural Science Foundation of China (61963022,51665025,61873328)。
文摘This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the total distance. This problem exists widely in real-life logistics distribution process.We propose a hybrid column generation algorithm(HCGA) for the OVRPTW, embedding both exact algorithm and metaheuristic. In HCGA, a label setting algorithm and an intelligent algorithm are designed to select columns from small and large subproblems, respectively. Moreover, a branch strategy is devised to generate the final feasible solution for the OVRPTW. The computational results show that the proposed algorithm has faster speed and can obtain the approximate optimal solution of the problem with 100 customers in a reasonable time.
基金supported by Natural Science Foundation of China (10071016)the Natural Science Foundation of Fujian Province (2008J0187)the Science and Technology Foundation of Education Department of Fujian Province (JA08255), China
文摘By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc.
基金Supported by Major State Research Development Program of China(2005CB321701)National Natural Science Foundation of China(10971083)
文摘In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the Cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.
文摘A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization;2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix;3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.
