Evolutionary dynamics of cancer:From epigenetic regulation to cell population dynamics——mathematical model framework, applications,and open problems

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.

Some Open Problems in Parameterized Complexity Related to the Work of Jianer Chen

This short paper highlights some open problems related to the work of Jianer Chen in the area of parameterized/multivariate algorithmics.

Solving open vehicle problem with time window by hybrid column generation algorithm

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.

A Coordination-Based Algorithm for Dedicated Destination Vehicle Routing in B2B E-Commerce

This paper proposes a solution to the open vehicle routing problem with time windows(OVRPTW)considering third-party logistics(3PL).For the typical OVRPTW problem,most researchers consider time windows,capacity,routing limitations,vehicle destination,etc.Most researchers who previously investigated this problem assumed the vehicle would not return to the depot,but did not consider its final destination.However,by considering 3PL in the B2B e-commerce,the vehicle is required back to the nearest 3PL location with available space.This paper formulates the problem as a mixed integer linear programming(MILP)model with the objective of minimizing the total travel distance.A coordinate representation particle swarm optimization(CRPSO)algorithm is developed to obtain the best delivery sequencing and the capacity of each vehicle.Results of the computational study show that the proposed method provides solution within a reasonable amount of time.Finally,the result compared to PSO also indicates that the CRPSO is effective.

PERIODICITY AND STRICT OSCILLATION FOR GENERALIZED LYNESS EQUATIONS

A generalized Lyness equation is investigated as follows x(n+1) = x(n)/(a + bx(n)) x(n-1), n = 0,1,2,..., (*) where a,b is an element of [0, infinity) with a + b > 0 and where the initial values x(-1),x(0) are arbitrary positive numbers. Same new results, mainly a necessary and sufficient condition for the periodicity of the solutions of Eq.(*) and a sufficient condition for the strict oscillation of all solutions of Eq (*), are obtained. As an application, the results solve an open problem presented by G. Ladas.

BOUNDEDNESS AND PERSISTENCE AND GLOBAL ASYMPTOTIC STABILITY FOR A CLASS OF DELAY DIFFERENCE EQUATIONS WITH HIGHER ORDER

Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open problems and extend some known results.

Global asymptotical stability in a rational difference equation

In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results completely solve an open problem and some conjectures proposed in[1,2,3,4].