Pub Date : 2024-11-12DOI: 10.1016/j.amc.2024.129160
Yayu Yang, Mingzu Zhang, Jixiang Meng
<div><div>The interconnection network between the storage system and the multi-core computing system is the bridge for communication of enormous amounts of data access and storage, which is the critical factor in affecting the performance of high-performance computing systems. By enforcing additional restrictions on the definition of <em>R</em>-structure and <em>R</em>-substructure connectivities to satisfy that each remaining vertex has not less than <em>r</em> neighbors, we can dynamically assess the cardinality of the separated component to meet the above conditions under structure faulty, thereby enhancing the evaluation of the fault tolerance and reliability of high-performance computing systems. Let <em>R</em> be a connected subgraph of a connected graph <em>G</em>. The <em>r</em>-restricted <em>R</em>-structure connectivity <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>;</mo><mi>R</mi><mo>)</mo></math></span> (resp. <em>r</em>-restricted <em>R</em>-substructure connectivity <span><math><msubsup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>(</mo><mi>G</mi><mo>;</mo><mi>R</mi><mo>)</mo></math></span>) of <em>G</em> is the minimum cardinality of a set of subgraphs <span><math><mi>F</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>}</mo></math></span> such that <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is isomorphic to <em>R</em> (resp. <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is a connected subgraph of <em>R</em>) for <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>m</mi></math></span>, and <span><math><mi>G</mi><mo>−</mo><mi>F</mi></math></span> is disconnected with the minimum degree of each component being at least <em>r</em>. Note that <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>;</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span> reduces to <em>r</em>-restricted connectivity <span><math><msup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math></span> (also called <em>r</em>-good neighbor connectivity). In this paper, we focus on <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msubsup><mo>;</mo><mi>R</mi><mo>)</mo></math></span> and <span><math><msubsup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msubsup><mo>;</mo><mi>R</mi><mo>)</mo></math></span> for the <em>L</em>-ary <em>n</em>-dimensional hamming graph
存储系统和多核计算系统之间的互连网络是海量数据访问和存储的通信桥梁，是影响高性能计算系统性能的关键因素。通过对 R-结构和 R-子结构连通性的定义进行额外限制，满足每个剩余顶点的邻居不少于 r 个，我们就可以动态评估分离组件的明细度，以满足结构故障下的上述条件，从而提高对高性能计算系统容错性和可靠性的评估。设 R 是连通图 G 的一个连通子图。G 的 r 限制 R 结构连通性 κr(G;R)（或 r 限制 R 子结构连通性 κrs(G;R)）是 Fi 与 R 同构（或 Fi 是连通子图 F={F1,F2,...,Fm}）的子图集合的最小卡片度。请注意，κr(G;K1) 简化为 r 限制连通性 κr(G)（也称为 r 好邻居连通性）。在本文中，我们主要研究 Lary n 维汉明图 KLn 的 κr(KLn;R) 和 κrs(KLn;R) ，其中 R∈{K1,K1,1,KL1} 。对于 0≤r≤n-3、n≥3 和 L≥3，我们确定了 KLn 的（L-1）r-好邻居连通性，即 κ(L-1)r(KLn)=(L-1)(n-r)Lr，以及 KLn 在 PMC 模型和 MM* 模型下的（L-1）r-好邻居可诊断性，即 t(L-1)r(KLn)=[(L-1)(n-r)-1]Lr-1。同时，我们还推导出 1≤r≤n-3, n≥4 时，κ(L-1)r(KLn;K1,1)=κ(L-1)rs(KLn;K1,1)=12(L-1)Lr(n-r)。此外，我们还给出了 n≥3 时的 κ2(KLn;KL1) (resp. κ2s(KLn;KL1))上限，并证明它对于三元 n 立方体 K3n 是尖锐的。具体地说，当 n≥3 时，κ2(K3n;K31)=κ2s(K3n;K31)=2(n-1)。
{"title":"Fault tolerance assessment for hamming graphs based on r-restricted R-structure(substructure) fault pattern","authors":"Yayu Yang, Mingzu Zhang, Jixiang Meng","doi":"10.1016/j.amc.2024.129160","DOIUrl":"10.1016/j.amc.2024.129160","url":null,"abstract":"<div><div>The interconnection network between the storage system and the multi-core computing system is the bridge for communication of enormous amounts of data access and storage, which is the critical factor in affecting the performance of high-performance computing systems. By enforcing additional restrictions on the definition of <em>R</em>-structure and <em>R</em>-substructure connectivities to satisfy that each remaining vertex has not less than <em>r</em> neighbors, we can dynamically assess the cardinality of the separated component to meet the above conditions under structure faulty, thereby enhancing the evaluation of the fault tolerance and reliability of high-performance computing systems. Let <em>R</em> be a connected subgraph of a connected graph <em>G</em>. The <em>r</em>-restricted <em>R</em>-structure connectivity <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>;</mo><mi>R</mi><mo>)</mo></math></span> (resp. <em>r</em>-restricted <em>R</em>-substructure connectivity <span><math><msubsup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>(</mo><mi>G</mi><mo>;</mo><mi>R</mi><mo>)</mo></math></span>) of <em>G</em> is the minimum cardinality of a set of subgraphs <span><math><mi>F</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>}</mo></math></span> such that <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is isomorphic to <em>R</em> (resp. <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is a connected subgraph of <em>R</em>) for <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>m</mi></math></span>, and <span><math><mi>G</mi><mo>−</mo><mi>F</mi></math></span> is disconnected with the minimum degree of each component being at least <em>r</em>. Note that <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>;</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span> reduces to <em>r</em>-restricted connectivity <span><math><msup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math></span> (also called <em>r</em>-good neighbor connectivity). In this paper, we focus on <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msubsup><mo>;</mo><mi>R</mi><mo>)</mo></math></span> and <span><math><msubsup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msubsup><mo>;</mo><mi>R</mi><mo>)</mo></math></span> for the <em>L</em>-ary <em>n</em>-dimensional hamming graph ","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129160"},"PeriodicalIF":3.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-12DOI: 10.1016/j.amc.2024.129149
Yang Yang , Shuocong Geng , Dong Yue , Sergey Gorbachev , Iakov Korovin
An event-triggered formation control strategy is proposed for a multi-agent system (MAS) suffered from unknown disturbances. In identifier-critic-actor neural networks (NNs), the strategy only needs to calculate the negative gradient of an approximated Hamilton-Jacobi-Bellman (HJB) equation, instead of the gradient descent method associated with Bellman residual errors. This simplified method removes the requirement for a complicated gradient calculation process of residual square of HJB equation. The weights in critic-actor NNs only update as the triggered condition is violated, and the computational burdens caused by frequent updates are thus reduced. Without dynamics information in prior, a disturbance observer is also constructed to approximate disturbances in an MAS. From stability analysis, it is proven that all signals are bounded. Two numerical examples are illustrated to verify that the proposed control strategy is effective.
本文针对遭受未知干扰的多代理系统（MAS）提出了一种事件触发的编队控制策略。在识别器-批判者-行动者神经网络（NNs）中，该策略只需计算近似汉密尔顿-雅各比-贝尔曼（HJB）方程的负梯度，而无需采用与贝尔曼残差相关的梯度下降法。这种简化方法消除了对 HJB 方程残差平方的复杂梯度计算过程的要求。批判-行为网络中的权重只在触发条件被违反时更新，因此减少了频繁更新带来的计算负担。在没有先验动态信息的情况下，还构建了一个扰动观测器来近似 MAS 中的扰动。稳定性分析证明，所有信号都是有界的。两个数值示例验证了所提出的控制策略是有效的。
{"title":"Event-triggered approximately optimized formation control of multi-agent systems with unknown disturbances via simplified reinforcement learning","authors":"Yang Yang , Shuocong Geng , Dong Yue , Sergey Gorbachev , Iakov Korovin","doi":"10.1016/j.amc.2024.129149","DOIUrl":"10.1016/j.amc.2024.129149","url":null,"abstract":"<div><div>An event-triggered formation control strategy is proposed for a multi-agent system (MAS) suffered from unknown disturbances. In identifier-critic-actor neural networks (NNs), the strategy only needs to calculate the negative gradient of an approximated Hamilton-Jacobi-Bellman (HJB) equation, instead of the gradient descent method associated with Bellman residual errors. This simplified method removes the requirement for a complicated gradient calculation process of residual square of HJB equation. The weights in critic-actor NNs only update as the triggered condition is violated, and the computational burdens caused by frequent updates are thus reduced. Without dynamics information in prior, a disturbance observer is also constructed to approximate disturbances in an MAS. From stability analysis, it is proven that all signals are bounded. Two numerical examples are illustrated to verify that the proposed control strategy is effective.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129149"},"PeriodicalIF":3.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-12DOI: 10.1016/j.amc.2024.129176
Xuelong Liu, Guoju Ye, Wei Liu, Fangfang Shi
This work aims to solve a fuzzy initial value problem for fractional difference equations and to study a class of discrete fractional cobweb models with fuzzy data under the Caputo granular difference operator. Based on relative-distance-measure fuzzy interval arithmetic, we first present several new concepts for fuzzy functions in the field of fuzzy discrete fractional calculus, such as the forward granular difference operator, Riemann-Liouville fractional granular sum, Riemann-Liouville and Caputo granular differences. The composition rules and Leibniz laws used to solve a fuzzy initial value problem for fractional difference equations are also presented. As applications, we obtain the solutions of fuzzy discrete Caputo fractional cobweb models, provide conditions for the convergence of the solution to the equilibrium value, and discuss different cases of how the trajectory of the granular solution converges to the equilibrium value. The developed results are also illustrated through several numerical examples.
{"title":"Fuzzy discrete fractional granular calculus and its application to fractional cobweb models","authors":"Xuelong Liu, Guoju Ye, Wei Liu, Fangfang Shi","doi":"10.1016/j.amc.2024.129176","DOIUrl":"10.1016/j.amc.2024.129176","url":null,"abstract":"<div><div>This work aims to solve a fuzzy initial value problem for fractional difference equations and to study a class of discrete fractional cobweb models with fuzzy data under the Caputo granular difference operator. Based on relative-distance-measure fuzzy interval arithmetic, we first present several new concepts for fuzzy functions in the field of fuzzy discrete fractional calculus, such as the forward granular difference operator, Riemann-Liouville fractional granular sum, Riemann-Liouville and Caputo granular differences. The composition rules and Leibniz laws used to solve a fuzzy initial value problem for fractional difference equations are also presented. As applications, we obtain the solutions of fuzzy discrete Caputo fractional cobweb models, provide conditions for the convergence of the solution to the equilibrium value, and discuss different cases of how the trajectory of the granular solution converges to the equilibrium value. The developed results are also illustrated through several numerical examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129176"},"PeriodicalIF":3.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-12DOI: 10.1016/j.amc.2024.129174
Jie Liu , Driss Boutat , Da-Yan Liu , Xue-Feng Zhang
This research note establishes a specific framework for transforming nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms without using differential geometry techniques. For this purpose, the nonlinear MIMO systems whose nonlinear terms do not need to be Lipschitz, are proposed. First, a change of coordinates is designed to eliminate the square items and coupled items for each nonlinear dynamical subsystem. Second, coupled auxiliary dynamics are constructed to transform the nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms such that the finite-time and robust step-by-step sliding mode observer can be applied. Then, the state variables for the considered nonlinear dynamical systems are estimated by using the inverse of the transformations. Finally, the validity of the proposed design methods is verified by two numerical examples.
本研究论文建立了一个特定框架，无需使用微分几何技术，即可将非线性多输入和多输出差分系统转化为扩展的可观测正则表达式。为此，本文提出了非线性 MIMO 系统，其非线性项无需为 Lipschitz。首先，设计了一种坐标变化，以消除每个非线性动力学子系统的平方项和耦合项。其次，构建耦合辅助动力学，将非线性多输入和多输出差分系统转化为扩展的可观测正态形式，从而应用有限时间和鲁棒逐步滑模观测器。然后，利用逆变换估计所考虑的非线性动力系统的状态变量。最后，通过两个数值示例验证了所提设计方法的有效性。
{"title":"Nonlinear MIMO observable normal forms with output injection and output diffeomorphism","authors":"Jie Liu , Driss Boutat , Da-Yan Liu , Xue-Feng Zhang","doi":"10.1016/j.amc.2024.129174","DOIUrl":"10.1016/j.amc.2024.129174","url":null,"abstract":"<div><div>This research note establishes a specific framework for transforming nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms without using differential geometry techniques. For this purpose, the nonlinear MIMO systems whose nonlinear terms do not need to be Lipschitz, are proposed. First, a change of coordinates is designed to eliminate the square items and coupled items for each nonlinear dynamical subsystem. Second, coupled auxiliary dynamics are constructed to transform the nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms such that the finite-time and robust step-by-step sliding mode observer can be applied. Then, the state variables for the considered nonlinear dynamical systems are estimated by using the inverse of the transformations. Finally, the validity of the proposed design methods is verified by two numerical examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129174"},"PeriodicalIF":3.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-12DOI: 10.1016/j.amc.2024.129161
Renjun Qiu, Ming Xu, Pengfei Zhu
In this study, a novel reproducing kernel Hilbert space (RKHS) method is introduced to show that high-order linear Fredholm integro-differential equations (IDEs) with variable coefficients can be transformed into ordinary differential equation (ODEs). The RKHS method constructs multiple types of RKHSs related to the given terms based on the H- formulation, which are utilized to determine solutions of the Fredholm IDEs. Then analytical and numerical solutions of the Fredholm IDEs with variable coefficients are obtained by an algorithm. Finally, the effectiveness and feasibility of RKHS method have been provided to confirm our theoretical findings by some numerical results and comparisons.
本研究引入了一种新颖的重现核希尔伯特空间（RKHS）方法，以证明具有可变系数的高阶线性弗雷德霍姆积分微分方程（IDE）可以转化为常微分方程（ODE）。基于 H-HK 公式，RKHS 方法构建了与给定项相关的多种类型的 RKHS，并利用这些 RKHS 确定弗雷德霍姆 IDE 的解。然后，通过算法求得具有可变系数的弗雷德霍姆 IDE 的解析解和数值解。最后，通过一些数值结果和比较，证明了 RKHS 方法的有效性和可行性，以证实我们的理论发现。
{"title":"Reproducing kernel Hilbert space method for high-order linear Fredholm integro-differential equations with variable coefficients","authors":"Renjun Qiu, Ming Xu, Pengfei Zhu","doi":"10.1016/j.amc.2024.129161","DOIUrl":"10.1016/j.amc.2024.129161","url":null,"abstract":"<div><div>In this study, a novel reproducing kernel Hilbert space (RKHS) method is introduced to show that high-order linear Fredholm integro-differential equations (IDEs) with variable coefficients can be transformed into ordinary differential equation (ODEs). The RKHS method constructs multiple types of RKHSs related to the given terms based on the <em>H</em>-<span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> formulation, which are utilized to determine solutions of the Fredholm IDEs. Then analytical and numerical solutions of the Fredholm IDEs with variable coefficients are obtained by an algorithm. Finally, the effectiveness and feasibility of RKHS method have been provided to confirm our theoretical findings by some numerical results and comparisons.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129161"},"PeriodicalIF":3.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-11DOI: 10.1016/j.amc.2024.129183
Hong Zhang
The evolution of cooperation is a pivotal area of study, essential for understanding the survival and success of complex biological and social systems. This paper investigates the dynamics of cooperation in spatial public goods games (SPGG) through a model that incorporates a fairness-driven migration mechanism. In this model, agents move towards environments perceived as fairer, influencing the spatial distribution and overall level of cooperation within the population. We examine the interplay between the time scale ratio, noise in movement, and population density. Our analysis reveals that moderate levels of movement and noise are critical for forming and maintaining cooperative clusters, while excessive movement and noise disrupt these structures, leading to reduced cooperation. Higher enhancement factors increase the resilience of cooperative behavior, extending the range of movement intensity over which high cooperation levels are maintained. Population density significantly impacts cooperative dynamics, with high-density environments promoting the coexistence of cooperators and defectors but lowering the highest achievable cooperation levels due to increased exploitation. Our findings underscore the importance of balancing movement, noise, and density to sustain cooperation and stable social structures. This research provides valuable insights for designing interventions and policies to promote cooperative behavior and social cohesion in complex populations. Future studies should further explore the adaptive mechanisms that dynamically adjust movement and strategy adaptation based on local environmental conditions.
{"title":"Evolution of cooperation among fairness-seeking agents in spatial public goods game","authors":"Hong Zhang","doi":"10.1016/j.amc.2024.129183","DOIUrl":"10.1016/j.amc.2024.129183","url":null,"abstract":"<div><div>The evolution of cooperation is a pivotal area of study, essential for understanding the survival and success of complex biological and social systems. This paper investigates the dynamics of cooperation in spatial public goods games (SPGG) through a model that incorporates a fairness-driven migration mechanism. In this model, agents move towards environments perceived as fairer, influencing the spatial distribution and overall level of cooperation within the population. We examine the interplay between the time scale ratio, noise in movement, and population density. Our analysis reveals that moderate levels of movement and noise are critical for forming and maintaining cooperative clusters, while excessive movement and noise disrupt these structures, leading to reduced cooperation. Higher enhancement factors increase the resilience of cooperative behavior, extending the range of movement intensity over which high cooperation levels are maintained. Population density significantly impacts cooperative dynamics, with high-density environments promoting the coexistence of cooperators and defectors but lowering the highest achievable cooperation levels due to increased exploitation. Our findings underscore the importance of balancing movement, noise, and density to sustain cooperation and stable social structures. This research provides valuable insights for designing interventions and policies to promote cooperative behavior and social cohesion in complex populations. Future studies should further explore the adaptive mechanisms that dynamically adjust movement and strategy adaptation based on local environmental conditions.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129183"},"PeriodicalIF":3.5,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-11DOI: 10.1016/j.amc.2024.129166
Huaijin Wang, Chuanju Xu
The Müntz polynomials are defined by contour integral associated to a complex sequence , which are large extensions of the algebraic polynomials. In this paper, we derive new recurrence formulas for Müntz polynomials, aimed at facilitating the computation of these polynomials and their related integrals. Additionally, we construct a novel class of orthogonal polynomials with respect to the logarithmic weight function on the interval . We also develop the corresponding Gauss quadrature rules, which serve as powerful techniques for accurately solving integrals involving singular terms.
{"title":"On recurrence formulae of Müntz polynomials and applications","authors":"Huaijin Wang, Chuanju Xu","doi":"10.1016/j.amc.2024.129166","DOIUrl":"10.1016/j.amc.2024.129166","url":null,"abstract":"<div><div>The Müntz polynomials are defined by contour integral associated to a complex sequence <span><math><mi>Λ</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>}</mo></math></span>, which are large extensions of the algebraic polynomials. In this paper, we derive new recurrence formulas for Müntz polynomials, aimed at facilitating the computation of these polynomials and their related integrals. Additionally, we construct a novel class of orthogonal polynomials with respect to the logarithmic weight function <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>λ</mi></mrow></msup><msup><mrow><mo>(</mo><mo>−</mo><mi>log</mi><mo></mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>μ</mi></mrow></msup></math></span> on the interval <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. We also develop the corresponding Gauss quadrature rules, which serve as powerful techniques for accurately solving integrals involving singular terms.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129166"},"PeriodicalIF":3.5,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-11DOI: 10.1016/j.amc.2024.129177
Xin Su , Ruqiang Guo , Shijia Hua , Linjie Liu , Liang Zhang
Among unrelated individuals, the emergence and maintenance of trust has always been a pressing issue to address, one that has garnered considerable attention through the framework provided by trust games. However, few studies have considered the effects of time delay in trust games. Given that decision-makers in trust games inherently exhibit lagged responses when observing the market, we explore the potential effects of time delay on the evolution of trust and develop an N-player trust game model based on investment behavior with time-delayed expected returns. We note that the system exhibits a stable interior equilibrium point, implying that investors and trustworthy trustees can coexist stably in the population, when the time delay is relatively small. Conversely, when the time delay is moderately large, the system exhibits a stable limit cycle, where the proportion in the population show oscillatory dynamics. Furthermore, we analyze the system's Hopf bifurcation points, identifying all critical thresholds responsible for inducing transitions under various conditions. The above theoretical results have been validated by numerical simulations.
在不相关的个体中，信任的产生和维持一直是一个亟待解决的问题，信任博弈提供的框架使这一问题备受关注。然而，很少有研究考虑信任博弈中时间延迟的影响。鉴于信任博弈中的决策者在观察市场时会表现出固有的滞后反应，我们探讨了时间延迟对信任演变的潜在影响，并建立了一个基于投资行为的 N 人信任博弈模型，该模型具有时间延迟的预期收益。我们注意到，当时间延迟相对较小时，系统表现出稳定的内部均衡点，这意味着投资者和值得信赖的受托人可以在人群中稳定共存。相反，当时间延迟适度增大时，系统会出现一个稳定的极限循环，即群体中的比例呈现振荡动态。此外，我们还分析了系统的霍普夫分岔点，确定了在各种条件下诱导过渡的所有临界阈值。数值模拟验证了上述理论结果。
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Pub Date : 2024-11-08DOI: 10.1016/j.amc.2024.129165
Xianbin Huang , Liming Chen , Wangyong Chen , Yao Hu
This paper addresses the challenge of change point detection in temporal networks, a critical task across various domains, including life sciences and socioeconomic activities. Continuous analysis and problem-solving within dynamic networks are essential in these fields. While much attention has been given to binary cases, this study extends the scope to include change point detection in weighted networks, an important dimension of edge analysis in dynamic networks. We introduce a novel distance metric called the Interval Sum Absolute Difference Distance (ISADD) to measure the distance between two graph snapshots. Additionally, we apply a Gaussian radial basis function to transform this distance into a similarity score between graph snapshots. This similarity score function effectively identifies individual change points. Furthermore, we employ a bisection detection algorithm to extend the method to detect multiple change points. Experimental results on both simulated and real-world data demonstrate the efficacy of the proposed framework.
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Pub Date : 2024-11-08DOI: 10.1016/j.amc.2024.129155
Donghui Wu , Ying Zhao , Mingchuan Pang , Hong Sang , Shuanghe Yu , Peng Wang
This paper studies the bumpless transfer (BT) control issue for switched systems with event-triggered (ET) control input. The aim is to reduce the jumps in control input at both switching and triggering points, while capturing the stability of the switched systems. First, a dynamic ET program is constructed with the triggering condition based on the level of suppression of input signal jumps. This not only reduces input jumps at triggering points, but also prevents Zeno behavior caused by triggering within the operation time interval of subsystems. Second, a sampled state-dependent switching signal is designed to ensure a dwell time for subsystems to prevent Zeno phenomenon induced by switching. Further, a switched ET controller with alleviated jumps is designed. Third, conditions are obtained to simultaneously reach both stabilization and BT of switched systems. Finally, the effectiveness of the theoretical results is demonstrated through a simulation of an engine model.
本文研究了具有事件触发（ET）控制输入的开关系统的无缓冲转移（BT）控制问题。目的是减少控制输入在切换点和触发点的跳变，同时保证切换系统的稳定性。首先，根据抑制输入信号跳变的程度构建动态 ET 程序的触发条件。这不仅减少了触发点上的输入跳变，还防止了在子系统运行时间间隔内触发引起的芝诺行为。其次，设计了与状态相关的采样开关信号，以确保子系统的停留时间，防止开关引起的禅诺现象。此外，还设计了一种可减轻跳跃的开关式 ET 控制器。第三，获得了开关系统同时达到稳定和 BT 的条件。最后，通过对发动机模型的仿真证明了理论结果的有效性。
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