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Extremal function of two independent chorded cycles in a bipartite graph 二部图中两个独立弦环的极值函数
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-27 DOI: 10.1016/j.amc.2024.129253
Panpan Cheng, Yunshu Gao
Let G be a bipartite graph. In this paper, by constructing two extremal graphs, we completely determine the minimum number of edges of G that guaranteeing the existence of two independent chorded cycles. As a byproduct, our result also implies that G contains two independent cycles of different lengths.
设G是一个二部图。本文通过构造两个极值图,完整地确定了保证两个独立弦环存在的G的最小边数。作为副产品,我们的结果还表明G包含两个不同长度的独立循环。
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引用次数: 0
A study on multi-information diffusion model considering dual social reinforcement effect from the perspective of evolutionary game 进化博弈视角下考虑双重社会强化效应的多信息扩散模型研究
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-24 DOI: 10.1016/j.amc.2024.129255
Yuanyuan Ma , Qiannan Zhang , Leilei Xie
The dynamic interactions of multi-information in online social networks present new challenges for understanding and forecasting information dissemination trends, especially the bounded rational decision-making of users when faced with various information. This article introduces evolutionary game theory to analyze user strategies amidst varying information. By using the Fermi function to calculate the imitation probability of netizens and considering the attractiveness of information and the dual social reinforcement effect, a class of G-SFDFRR multi-information delay propagation models has been established. The propagation threshold is calculated using the next-generation matrix method, and the global asymptotic stability of the system is analyzed using the time-delay Lyapunov function. Empirical analysis based on a Twitter dataset validated the model's effectiveness, showing an improvement in the fitting degree of 38.91 and 19.21 % over the SCIR and SICMR models, respectively. Further quantitative analysis through numerical calculations revealed that evolutionary games can delay the peak of information dissemination and accelerate the decline of rumors, highlighting the key role of strategic interaction in curbing rumor spread. Additionally, regulating the positive and negative social reinforcement effects and propagation probabilities can optimize the effect of rumor refutation, with short-term forced silence measures being more effective than long-term ones.
在线社交网络中多种信息的动态交互对信息传播趋势的理解和预测提出了新的挑战,特别是用户面对多种信息时的有限理性决策。本文引入进化博弈论来分析用户在不同信息下的策略。利用费米函数计算网民的模仿概率,考虑信息的吸引力和双重社会强化效应,建立了一类G-SFDFRR多信息延迟传播模型。采用新一代矩阵法计算了传播阈值,并利用时滞Lyapunov函数分析了系统的全局渐近稳定性。基于Twitter数据集的实证分析验证了该模型的有效性,与SCIR和SICMR模型相比,拟合程度分别提高了38.91%和19.21%。进一步通过数值计算进行定量分析,发现进化博弈可以延缓信息传播的高峰,加速谣言的衰落,凸显了战略互动在遏制谣言传播中的关键作用。此外,调节正、负社会强化效应和传播概率可以优化辟谣效果,短期强制沉默措施比长期强制沉默措施更有效。
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引用次数: 0
A mathematical model for the bullying dynamics in schools 校园欺凌动态的数学模型
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-24 DOI: 10.1016/j.amc.2024.129254
Nuno Crokidakis
We analyze a mathematical model to understand the dynamics of bullying in schools. The model considers a population divided into four groups: susceptible individuals, bullies, individuals exposed to bullying, and violent individuals. Transitions between these states occur at rates designed to capture the complex interactions among students, influenced by factors such as romantic rejection, conflicts with peers and teachers, and other school-related challenges. These interactions can escalate into bullying and violent behavior. The model also incorporates the role of parents and school administrators in mitigating bullying through intervention strategies. The results suggest that bullying can be effectively controlled if anti-bullying programs implemented by schools are sufficiently robust. Additionally, the conditions under which bullying persists are explored.
我们分析了一个数学模型来理解校园欺凌的动态。该模型将人口分为四组:易受影响的个体、欺凌者、暴露于欺凌的个体和暴力个体。这些状态之间的转换速度被设计为捕捉学生之间复杂的互动,受到诸如浪漫拒绝、与同伴和老师的冲突以及其他与学校有关的挑战等因素的影响。这些互动可能会升级为欺凌和暴力行为。该模型还纳入了家长和学校管理人员通过干预策略减轻欺凌的作用。结果表明,如果学校实施的反欺凌计划足够健全,欺凌可以得到有效控制。此外,还探讨了欺凌持续存在的条件。
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引用次数: 0
Supervised cooperation on interdependent public goods games 相互依存的公共产品博弈的监督合作
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-19 DOI: 10.1016/j.amc.2024.129249
Ting Ling , Zhang Li , Minyu Feng , Attila Szolnoki
It is a challenging task to reach global cooperation among self-interested agents, which often requires sophisticated design or usage of incentives. For example, we may apply supervisors or referees who are able to detect and punish selfishness. As a response, defectors may offer bribes for corrupt referees to remain hidden, hence generating a new conflict among supervisors. By using the interdependent network approach, we model the key element of the coevolution between strategy and judgment. In a game layer, agents play public goods game by using one of the two major strategies of a social dilemma. In a monitoring layer, supervisors follow the strategy change and may alter the income of competitors. Fair referees punish defectors while corrupt referees remain silent for a bribe. Importantly, there is a learning process not only among players but also among referees. Our results suggest that large fines and bribes boost the emergence of cooperation by significantly reducing the phase transition threshold between the pure defection state and the mixed solution where competing strategies coexist. Interestingly, the presence of bribes could be as harmful for defectors as the usage of harsh fines. The explanation of this system behavior is based on a strong correlation between cooperators and fair referees, which is cemented via overlapping clusters in both layers.
实现自利主体之间的全球合作是一项具有挑战性的任务,这通常需要复杂的激励设计或使用。例如,我们可以聘请能够发现和惩罚自私的主管或裁判。作为回应,叛逃者可能会向腐败裁判行贿,以使其保持隐匿,从而在监管者之间产生新的冲突。通过使用相互依赖的网络方法,我们对战略和判断之间共同进化的关键要素进行了建模。在博弈层中,代理人通过使用社会困境的两种主要策略中的一种来进行公共物品博弈。在监控层,管理者跟踪战略变化,可能会改变竞争对手的收入。公正的裁判惩罚叛逃者,而腐败的裁判则对贿赂保持沉默。重要的是,不仅球员之间,裁判之间也有一个学习的过程。我们的研究结果表明,大额罚款和贿赂通过显著降低纯背叛状态和竞争策略共存的混合解决方案之间的相变阈值来促进合作的出现。有趣的是,对脱北者来说,贿赂的存在可能和使用严厉的罚款一样有害。这种系统行为的解释是基于合作者和公平裁判之间的强相关性,这种相关性通过两层的重叠集群得到巩固。
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引用次数: 0
A novel localized least-squares collocation method for coupled bulk-surface problems 耦合体面问题的一种新的局部最小二乘配置方法
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-18 DOI: 10.1016/j.amc.2024.129250
Zhuochao Tang , Zhuojia Fu , Meng Chen , Leevan Ling
In this paper, we present a novel least-squares formulation of the Generalized Finite Difference Method (GFDM) and utilize its high-order schemes to solve the coupled bulk-surface reaction-diffusion equations. The coupled bulk-surface problems are composed of bulk equations and surface equations and coupled via some Robin-type boundary conditions. For differential operators on curved surfaces, we focus on the extrinsic definition that defines the surface operators using projection operator to tangent spaces of the surface. By utilizing localization and FD data points, the coupled model is discretized as a large sparse system using the LS-GFDM with two sets of arbitrarily distributed points. Compared with the original GFDM, the LS-GFDM brings about the advantage that it gains flexibility to use FD data points at locations different from the unknown nodal solution values. Finally, numerical demonstrations and applications of Turing pattern formations verify the effectiveness and robustness of the proposed method.
本文提出了一种新的广义有限差分法(GFDM)的最小二乘形式,并利用它的高阶格式来求解耦合体-表面反应-扩散方程。耦合体-面问题由体方程和面方程组成,并通过一些robbin型边界条件进行耦合。对于曲面上的微分算子,我们着重于用曲面上切空间的投影算子来定义曲面算子的外在定义。利用定位和FD数据点,利用LS-GFDM将耦合模型离散为具有两组任意分布点的大型稀疏系统。与原始GFDM相比,LS-GFDM的优点是可以灵活地在不同于未知节点解值的位置使用FD数据点。最后,图灵模式形成的数值演示和应用验证了该方法的有效性和鲁棒性。
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引用次数: 0
Erratum on “Synchronization and chimeras in asymmetrically coupled memristive Tabu learning neuron network” [Appl. Math. Compt. 489 (2025) 129163] “非对称耦合记忆禁忌学习神经元网络的同步和嵌合体”的校误[j]。数学。Compt. 489 (2025) 129163]
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-18 DOI: 10.1016/j.amc.2024.129248
A. Prasina , V. Samuthira Pandi , W. Nancy , K. Thilagam , K. Veena , A. Muniyappan
The errors in the recent paper [Appl. Math. Compt. 489 (2025) 129163] have been corrected in this article. We have confirmed that the modification does not impact the primary results or conclusions of Ref. Prasina et al. [1].
最近的论文[苹果]中的错误。数学。Compt. 489(2025) 129163]已在本文中更正。我们已经确认该修改不影响Ref. Prasina等人的初步结果和结论。
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引用次数: 0
WENO based adaptive image zooming algorithm 基于WENO的自适应图像缩放算法
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-18 DOI: 10.1016/j.amc.2024.129228
Bojan Crnković , Jerko Škifić , Tina Bosner
Zooming or upsampling images is a common technique and an essential step in many image processing algorithms. This process introduces new information that can lead to numerical effects such as ringing artifacts, aliasing effects and blurring of the image. In this paper, we propose a polynomial interpolation algorithm based on the WENO algorithm for upsampling images, which provides high accuracy in smooth regions, preserves edges and reduces aliasing effects. Although this is not the first application of WENO interpolation for image resampling, it is designed to have comparable complexity and memory load with better image quality than the separable WENO algorithm.
We show that the algorithm performs equally well on smooth functions, artificial pixel art and real digital images. The comparison with similar methods on test images shows good results on standard metrics and also provides visually satisfying results. Furthermore, the low complexity of the algorithm is ensured by a small local approximation stencil and the appropriate choice of smoothness indicators.
放大或上采样图像是一种常见的技术,也是许多图像处理算法的重要步骤。这个过程引入了新的信息,这些信息可能导致诸如环形伪影、混叠效应和图像模糊等数值效应。在本文中,我们提出了一种基于WENO算法的上采样图像多项式插值算法,该算法在光滑区域提供了较高的精度,保留了边缘并减少了混叠效应。虽然这不是WENO插值在图像重采样中的首次应用,但其设计具有与可分离WENO算法相当的复杂性和内存负载,并且具有更好的图像质量。
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引用次数: 0
Protocol-based H∞ estimation for Markovian jumping delayed systems with partially unknown transition probability 转移概率部分未知的马尔可夫跳跃延迟系统基于协议的H∞估计
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-17 DOI: 10.1016/j.amc.2024.129247
Guixiu Liu, Bing Li
This article pays attention to estimation issue for the state of a particular kind of Markovian jumping delayed systems (MJDSs) with exogenous disturbances. The transition probability of Markovian process is assumed to be partially unknown for accurately reflecting the real complexity of mode switching. To avoid data collision while retaining the necessary requirement of information updating, a scheduling named MEF-TOD protocol is adopted to dynamically allocate access authorization of sensor nodes to estimator. By virtue of binary delta operator, a mode-dependent estimator is built to asymptotically approximate the real state of original system. Through taking a suitable energy functional and exploiting stochastic analysis method, several novel approaches are given to sufficiently make the error asymptotically stable under constraint of H performance. The gain matrices for estimator are ultimately formed through settling a series of inequalities of matrix. At last, a numerical instance exhibits the validity of proposed results.
研究一类具有外源扰动的马尔可夫跳变时滞系统的状态估计问题。为了准确反映模式切换的真实复杂性,假设马尔可夫过程的转移概率部分未知。为了避免数据冲突,同时保留信息更新的必要要求,采用MEF-TOD调度协议将传感器节点的访问授权动态分配给估计器。利用二元算子,构造了一个模相关的估计量来渐近逼近原系统的真实状态。通过选取合适的能量泛函和利用随机分析方法,给出了在H∞性能约束下使误差渐近稳定的几种新方法。通过求解矩阵的一系列不等式,最终得到了估计器的增益矩阵。最后,通过数值算例验证了所提结果的有效性。
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引用次数: 0
On the numerical verification of a counterexample on parameter-dependent Lyapunov functions 参数相关李雅普诺夫函数反例的数值验证
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-16 DOI: 10.1016/j.amc.2024.129246
Birgül Aksoy, Taner Büyükköroğlu, Vakif Dzhafarov
We consider the existence problem of an affine parameter-dependent quadratic Lyapunov function for a robust Hurwitz stable matrix segment. Numerical verification of the known counterexample to the known Barmish's conjecture is provided. Second order parameter-dependent quadratic Lyapunov function for this counterexample is constructed. Sufficient conditions for the existence of an affine parameter-dependent Lyapunov function are given.
研究一类鲁棒Hurwitz稳定矩阵段仿射参数相关二次Lyapunov函数的存在性问题。给出了已知Barmish猜想的已知反例的数值验证。构造了该反例的二阶参数相关二次Lyapunov函数。给出仿射参数相关Lyapunov函数存在的充分条件。
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引用次数: 0
Inverse spectral problems for Sturm-Liouville operators with many frozen arguments 具有许多固定参数的Sturm-Liouville算子的逆谱问题
IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-12-13 DOI: 10.1016/j.amc.2024.129235
Chung-Tsun Shieh , Tzong-Mo Tsai
This study is devoted to the inverse spectral problems of the Sturm-Liouville operator with many frozen arguments. Under certain assumptions, the authors obtained the uniqueness theorems for recovering the operator from one spectrum. Finally, a numerical simulation of the inverse problem is given.
本文研究了Sturm-Liouville算子具有许多固定参数的逆谱问题。在一定的假设条件下,得到了从一个谱中恢复算子的唯一性定理。最后,给出了反问题的数值模拟。
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引用次数: 0
期刊
Applied Mathematics and Computation
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