Applied Mathematics and Computation最新文献

Explaining the emergence of cooperation is a challenging issue. Recently, research on ecological evolutionary games has combined human behavior with environmental feedback, demonstrating that the co-evolution of cooperation and the environment exhibits rich dynamics, thereby attracting widespread attention. In this work, we aim to extend the theory of environmental feedback by exploring environmental evolution that incorporates spatial factors. Our model considers the context of a local environment, where an individual's environment is influenced only by herself and her neighbors, and the environment affects only the outcome of the game interactions in which she participates. By means of Monte Carlo simulations, our results suggest that cooperation can emerge in the co-evolution of local environments and can be facilitated more effectively with a higher degree of maximum possible environmental degradation. In particular, we discovered that environmental degradation of peripheral individuals in cooperative clusters reduces the profits of defectors, acting as a shield to protect clusters from defectors. However, in a more easily recoverable environment, this protective effect weakens, allowing free-riders to take advantage. Our research elucidates the co-evolutionary process within local environments and emphasizes the crucial role of environmental feedback in the evolution of cooperation.

This paper presents new criteria for the oscillation of all solutions of the third-order nonlinear delay differential equations with noncanonical operators. Our approach to establishing new criteria essentially simplifies and refines the main results obtained in Džurina and Jadlovská (2018) and Grace et al. (2019). Examples illustrating the importance of our results are presented.

In this paper, we propose a novel adaptive technique, named adaptive trajectories sampling (ATS), to select training points for learning the solution of partial differential equations (PDEs). By the ATS, the training points are selected adaptively according to an empirical-value-type instead of residual-type error indicator from trajectories which are generated by a PDE-related stochastic process. We incorporate the ATS into three known deep learning solvers for PDEs, namely, the adaptive physics-informed neural network method (ATS-PINN), the adaptive derivative-free-loss method (ATS-DFLM), and the adaptive temporal-difference method for forward-backward stochastic differential equations (ATS-FBSTD). Our numerical experiments show that the ATS remarkably improves the computational accuracy and efficiency of the original deep solvers. In particular, for a high-dimensional peak problem, the relative errors by the ATS-PINN can achieve the order of $O\left({10}^{-3}\right)$, even when the vanilla PINN fails.

This paper addresses the reachable set problem on nonlinear switched singular systems with impulsive performance and time-delay under bounded disturbance. The goal is to provide a real-time bounding set containing all reachable states. Originally, a real-time bounding criterion is developed by analyzing the variation of subinterval piecewise function and combining the definition of the average impulsive interval. Additionally, a lower bound on the Lyapunov function is provided by introducing an inequality scaling technique to avoid acquiring state bounds based on system decomposition techniques. Subsequently, the real-time bounding closed set, including all reachable states of the system, is estimated by calculating the Dini derivative of the Lyapunov function and using the real-time bounding criterion and the integral inequality technique. Finally, several numerical examples are given to illustrate the validity of the results obtained in this study.

This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of n points in $R^2$, where some octagon and hexadecagon are used for discarding most of the given points interior to these polygons. In this way, the scope of the given problem can be reduced significantly. In particular, the convex hull of n points distributed $b_{\mathrm{least}}$-$b_{\mathrm{most}}$-boundedly in some rectangle can be determined with the complexity $O\left(n\right)$. Computational experiments demonstrate that our algorithms outperform the Quickhull algorithm by a significant factor of up to 47 times when applied to the tested data sets. The speedup compared to the CGAL library is even more pronounced.

Weak degeneracy of a graph is a variation of degeneracy that has a close relationship to many graph coloring parameters. In this article, we prove that planar graphs with distance of 3-cycles at least 2 and no cycles of lengths $5,6,7$ are weakly 2-degenerate. Furthermore, such graphs can be vertex-partitioned into two subgraphs, one of which has no edges, and the other is a forest.

In this paper, the new type of Gradient Neural Network (GNN) model is proposed for the following linear system of matrix equations: $AX=C,XB=D$. The convergence analysis of given models is shown. The model is applied for the computation of the regular matrix inverse, as well as Moore-Penrose and Drazin generalized inverses. Some illustrative examples and simulations are given to verify theoretical results.

In this paper, a prescribed-time unknown input observer (PTUIO) is developed for the simultaneous state and fault estimation. Firstly, for the uncertain system containing both the actuator fault and the sensor fault, a series of reformulations are proposed, which provides a more straightforward way to estimate the state and the faults. Subsequently, based on the reformulations, a PTUIO is developed such that the state, the actuator fault and the sensor fault can all be estimated within an arbitrarily prescribed time regardless of what the initial conditions are. In addition, the necessary and sufficient conditions for the existence of the PTUIO are given in terms of the original system matrices. Finally, a numerical example is given to verify the effectiveness of the proposed method.

This paper introduces Deep Policy Iteration (DPI), a novel approach that integrates the strengths of Neural Networks with the stability and convergence advantages of Policy Iteration (PI) to address high-dimensional stochastic Mean Field Games (MFG). DPI overcomes the limitations of PI, which is constrained by the curse of dimensionality to low-dimensional problems, by iteratively training three neural networks to solve PI equations and satisfy forward-backwards conditions. Our findings indicate that DPI achieves comparable convergence levels to the Mean Field Deep Galerkin Method (MFDGM), with additional advantages. Furthermore, deep learning techniques show promise in handling separable Hamiltonian cases where PI alone is less effective. DPI effectively manages high-dimensional problems, extending the applicability of PI to both separable and non-separable Hamiltonians.

Road traffic conditions exhibit spatial and temporal variations influenced by factors such as construction, speed limits, and accidents. Accurate and efficient modeling of vehicular flow on changing road conditions is crucial for understanding intricate traffic phenomena and analyzing dynamic characteristics in real-world scenarios. In this paper, we develop a rapid numerical approach that computes traffic flow solutions for roads divided into multiple sections with varying traffic conditions, utilizing the Lighthill-Whitham-Richards model as the mathematical framework. The key aspect of our approach lies in solving the flow at the dividing point between consecutive road sections with different traffic conditions. For the two-section road scenario, we integrate the Hamilton-Jacobi formulation of the traffic model with the triangular fundamental diagram, capturing the explicit relationship between flow and density. This integration allows us to derive the spatiotemporal solution for a single dividing point. By accounting for the dynamic interaction between adjacent dividing points, we extend the applicability of our approach to an arbitrary number of road sections based on a semi-analytic Lax-Hopf formula. Our semi-analytical method is distinguished by grid-free computing, reducing computational demands and ensuring exceptional simulation speed. Particularly noteworthy is the formulation's remarkable efficacy in handling the complexities of heterogeneous road traffic conditions, marked by dynamic variations in both time and space, surpassing traditional macroscopic traffic flow simulations. To demonstrate its effectiveness, we apply the proposed approach to an optimization example involving traffic signal timing in a complex road environment. Additionally, we showcase its predictive capabilities by efficiently evaluating the impact of traffic accidents on the surrounding traffic flow. This research provides valuable insights for traffic management, optimization, and decision-making, enabling the analysis of complex scenarios and facilitating the development of strategies to enhance traffic efficiency and safety.