Mathematics and Computers in Simulation最新文献

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IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-22 DOI: 10.1016/S0378-4754(25)00540-3

引用次数: 0

A unified one-step joint optimization framework for sparse subspace clustering and self-constrained spectral clustering 稀疏子空间聚类与自约束谱聚类的统一一步联合优化框架

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-18 DOI: 10.1016/j.matcom.2025.12.011

Chengmao Wu, Yilong Zhu

Subspace clustering aims to explore multiple low-dimensional subspaces within data to more effectively represent the essential structure of high-dimensional datasets. Traditional subspace clustering methods typically employ a two-step strategy: first, constructing a similarity matrix based on the relevance between samples, and then performing spectral clustering on this matrix. Although these approaches achieve local optimality at each stage, they do not guarantee the global optimality of the clustering results. To address these issues, this study introduces an algorithm that integrates subspace clustering and spectral clustering, enabling the simultaneous optimization of the similarity matrix and the clustering indicator matrix in a low-dimensional space. In the subspace clustering module, an -

ℓ_{0, 2}

norm constraint is applied to the self-representation coefficient matrix to enhance the sparsity of the similarity matrix. For the spectral clustering component, we employ self-constrained spectral clustering to improve the graph-cut performance, resulting in higher-quality clustering indicator matrices. To integrate the two components, we develop a unified one-step joint optimization framework that addresses the clustering problem through a proximal alternating minimization approach with proven convergence. Its innovation lies in constructing a simultaneous optimization model for the similarity and cluster indicator matrices, effectively solved using the proximal alternating minimization (PAM) method to tackle the problem's inherent nonlinearity. The proposed algorithm has demonstrated strong performance across various datasets, outperforming eight representative comparison algorithms.

子空间聚类旨在探索数据内部的多个低维子空间，以更有效地表示高维数据集的本质结构。传统的子空间聚类方法通常采用两步策略：首先根据样本之间的相关性构造相似矩阵，然后对该矩阵进行谱聚类。虽然这些方法在每个阶段都实现了局部最优性，但它们不能保证聚类结果的全局最优性。针对这些问题，本研究引入了一种融合子空间聚类和谱聚类的算法，实现了在低维空间内相似性矩阵和聚类指标矩阵的同时优化。在子空间聚类模块中，对自表示系数矩阵施加- l0,2范数约束，增强相似性矩阵的稀疏性。对于谱聚类组件，我们采用自约束谱聚类来提高图切性能，从而获得更高质量的聚类指标矩阵。为了整合这两个组件，我们开发了一个统一的一步联合优化框架，该框架通过具有证明收敛性的近端交替最小化方法来解决聚类问题。该方法的创新之处在于构建了相似度和聚类指标矩阵的同时优化模型，利用最近邻交替极小化（PAM）方法有效地解决了该问题固有的非线性。该算法在各种数据集上表现出强大的性能，优于8种代表性的比较算法。

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引用次数: 0

Dynamic analysis and optimal control of a stochastic tumor-immune model 随机肿瘤免疫模型的动态分析与最优控制

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-18 DOI: 10.1016/j.matcom.2025.12.010

Xi Wang, Zijian Liu, Yuanshun Tan, Yu Mu

Competition between tumor cells and normal tissue cells due to limited resources is considered as a key dynamic in tumor development. Therefore, in this paper, we develop a stochastic model of the interaction between tumor cells, helper T cells, effector cells, and host cells. The existence and uniqueness of the global positive solutions, stochastic eventual boundedness, and stochastic persistence of the model are proved by establishing appropriate Lyapunov functions. Additionally, we derive the threshold condition for tumor cell extinction and investigate the system’s steady-state distribution. Furthermore, we obtain the optimal control strategy through stochastic control theory. The results and numerical simulations demonstrate that stochastic perturbations can inhibit tumor cell growth, the control strategy can accelerate tumor extinction while reducing damage to effector cells, and increasing the competition coefficient of normal tissue cells against tumor cells can accelerate tumor extinction.

由于资源有限，肿瘤细胞与正常组织细胞之间的竞争被认为是肿瘤发展的关键动力。因此，在本文中，我们建立了肿瘤细胞、辅助T细胞、效应细胞和宿主细胞之间相互作用的随机模型。通过建立适当的Lyapunov函数，证明了该模型整体正解的存在唯一性、最终有界性和随机持久性。此外，我们还推导了肿瘤细胞消失的阈值条件，并研究了系统的稳态分布。在此基础上，利用随机控制理论得到了最优控制策略。结果和数值模拟表明，随机扰动可以抑制肿瘤细胞的生长，控制策略可以在减少效应细胞损伤的同时加速肿瘤的消失，增加正常组织细胞对肿瘤细胞的竞争系数可以加速肿瘤的消失。

引用次数: 0

Optimal power flow in distribution networks: Reconfiguration and self-healing via Benders’ decomposition 配电网的最优潮流：通过Benders分解的重新配置和自愈

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-13 DOI: 10.1016/j.matcom.2025.12.008

Fábio Castro , Bruno Canizes , João Soares , Sérgio Ramos , Zita Vale

Electric power systems are undergoing rapid evolution driven by increasing loads, widespread renewable energy integration, distributed generation, sector liberalization, and the rise of emerging technologies like electric vehicles. These transformations necessitate intelligent and efficient management of distribution networks, marking the transition to Smart Grids. This study introduces a novel optimization framework utilizing Benders’ Decomposition to tackle network reconfiguration and self-healing challenges in medium-voltage distribution networks during contingency scenarios. The proposed methodology supports decision-making by optimizing network topology and balancing supply-demand dynamics, minimizing operational costs while ensuring system resilience and reliability. Key contributions include the development of a robust tool capable of delivering optimal reconfiguration solutions with low computational latency, adaptable to networks of various sizes and topologies. Simulations on both 13-bus and 180-bus networks demonstrated the model’s scalability and effectiveness, ensuring operational continuity even under severe contingencies. Additionally, this approach accommodates modern network elements such as energy storage systems, electric vehicle charging infrastructure, and distributed renewable generation, enabling a comprehensive Smart Grid framework. The study highlights the potential for integrating this tool into real-time operational systems, ensuring proactive network management and enhanced resilience.

在负荷增加、可再生能源广泛整合、分布式发电、行业自由化以及电动汽车等新兴技术兴起的推动下，电力系统正在经历快速演变。这些转变需要对配电网络进行智能和高效的管理，标志着向智能电网的过渡。本研究引入了一种新的优化框架，利用Benders分解来解决中压配电网在突发情况下的网络重构和自愈挑战。所提出的方法通过优化网络拓扑和平衡供需动态来支持决策，在确保系统弹性和可靠性的同时最大限度地降低运营成本。主要贡献包括开发了一种强大的工具，能够提供具有低计算延迟的最佳重新配置解决方案，可适应各种大小和拓扑的网络。在13总线和180总线网络上的仿真证明了该模型的可扩展性和有效性，即使在严重的突发事件下也能确保运行的连续性。此外，这种方法适应现代网络元素，如能源存储系统、电动汽车充电基础设施和分布式可再生能源发电，从而实现全面的智能电网框架。该研究强调了将该工具集成到实时操作系统中的潜力，确保了主动的网络管理和增强的弹性。

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引用次数: 0

Computational time efficiency analysis for resonance studies in transmission grids and microgrid clusters 输电网和微电网集群共振研究的计算时间效率分析

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-13 DOI: 10.1016/j.matcom.2025.12.009

Oriol Cartiel , Juan-José Mesas , Lluís Monjo , Luis Sainz

The limitations of traditional methods for identifying resonance frequencies have driven the development of Resonance Mode Analysis (RMA) as a more effective alternative. Despite its potential, RMA faces challenges in computational efficiency, particularly in multi-terminal transmission grids. To address this, Rapid RMA, a power iteration (PI)-based approach for determining the dominant eigenvalue of the nodal impedance matrix, was introduced. However, the PI-based approach can exhibit slow convergence or fail under certain conditions. To overcome these limitations, recent advancements have proposed two new methodologies: Faster RMA, a modified shifted-inverse PI-based method, and Lanczos-based RMA, a non-Hermitian Lanczos method. This paper evaluates the computational performance of RMA-based methods using various software tools (including normal computation, parallel computation and sparse techniques) across three distinct hardware-computing systems. The study highlights practical differences in computational speed and efficiency for RMA applications under diverse scenarios. By emphasising the critical role of optimising computational tools, the paper examines how hardware and software configurations influence RMA performance, particularly in transmission grids and microgrid clusters, using MATLAB/Simulink simulations. Finally, the paper proposes an efficient RMA-based methodology that is adaptable to a wide range of grid configurations and computational environments. This approach is applied to stability studies using the positive-mode-damping stability criterion, thereby offering a robust framework for advancing harmonic resonance analysis in power systems.

传统识别共振频率方法的局限性促使共振模态分析（RMA）作为一种更有效的替代方法的发展。尽管具有潜力，但RMA在计算效率方面面临挑战，特别是在多终端输电网中。为了解决这个问题，引入了基于功率迭代（PI）的快速RMA方法来确定节点阻抗矩阵的主导特征值。然而，基于pi的方法在某些条件下可能表现出缓慢的收敛或失败。为了克服这些限制，最近的进展提出了两种新方法：更快的RMA，一种改进的基于移位逆pi的方法，以及基于Lanczos的RMA，一种非厄米Lanczos方法。本文在三种不同的硬件计算系统中使用各种软件工具（包括正常计算、并行计算和稀疏技术）评估基于rma的方法的计算性能。该研究强调了不同场景下军事革命应用在计算速度和效率方面的实际差异。通过强调优化计算工具的关键作用，本文研究了硬件和软件配置如何影响RMA性能，特别是在输电网和微电网集群中，使用MATLAB/Simulink模拟。最后，本文提出了一种有效的基于rma的方法，该方法适用于各种网格配置和计算环境。该方法应用于使用正模阻尼稳定性判据的稳定性研究，从而为推进电力系统的谐波共振分析提供了一个强大的框架。

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引用次数: 0

Optimal control of chaos in a novel SITR epidemic model with generalized incidence and adaptive treatment dynamics: A deep neural network analysis 具有广义发病率和自适应治疗动力学的新型SITR流行病模型混沌的最优控制：深度神经网络分析

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-11 DOI: 10.1016/j.matcom.2025.12.005

A. El-Mesady , M.A. Abdelkawy , Muhammad Farhan , Mohammad Izadi

This paper introduces a novel SITR (Susceptible-Infected-Treated-Recovered) epidemic model that incorporates a Holling Type III incidence rate and a saturated treatment function to capture superspreading dynamics and finite healthcare capacity. We establish the model’s well-posedness by proving the positivity and boundedness of solutions. A comprehensive bifurcation analysis reveals that the system exhibits rich dynamical behaviors, including Transcritical, Saddle–node, and Hopf bifurcations, which delineate thresholds between disease extinction, persistence, and oscillatory states. An optimal control framework is subsequently formulated to derive effective intervention strategies. The core methodological contribution is the development of a hybrid deep neural network (DNN) architecture, utilizing Tanh and ReLU activations, to serve as a high-fidelity surrogate for the model’s complex dynamics. This approach is validated within a stochastic numerical scheme, employing a 70%–15%–15% data split for robust training and testing. The DNN achieves exceptional predictive accuracy, with a mean squared error of

1 0^{- 10}

and a minimum absolute error of

1 0^{- 8}

, demonstrating precise alignment with benchmark solutions. This work establishes a novel paradigm that integrates sophisticated dynamical systems theory with advanced deep learning, resulting in a computationally efficient and highly accurate framework for analyzing and controlling complex epidemic systems.

本文介绍了一种新的SITR（易感-感染-治疗-恢复）流行病模型，该模型结合了Holling III型发病率和饱和治疗函数，以捕捉超传播动力学和有限的医疗保健能力。通过证明解的正性和有界性，建立了模型的适定性。综合分岔分析表明，该系统表现出丰富的动力学行为，包括跨临界分岔、鞍节点分岔和Hopf分岔，它们描绘了疾病灭绝、持续和振荡状态之间的阈值。随后制定了最优控制框架，以获得有效的干预策略。核心方法贡献是开发混合深度神经网络（DNN）架构，利用Tanh和ReLU激活，作为模型复杂动态的高保真代理。该方法在随机数值方案中得到验证，采用70%-15%-15%的数据分割进行鲁棒性训练和测试。DNN实现了卓越的预测精度，均方误差为10−10，最小绝对误差为10−8，证明了与基准解决方案的精确一致性。这项工作建立了一个新的范例，将复杂的动力系统理论与先进的深度学习相结合，形成了一个计算效率高、精度高的框架，用于分析和控制复杂的流行病系统。

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引用次数: 0

Mathematical models, numerical methods and scientific computing technologies for new arising problems (MATHSCICOMP2023) 新出现问题的数学模型、数值方法和科学计算技术（MATHSCICOMP2023）

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-10 DOI: 10.1016/j.matcom.2025.12.006

Sandra Carillo, Costanza Conti, Daniela Mansutti, Francesca Pitolli, Rosa Maria Spitaleri

引用次数: 0

A highly efficient decoupled algorithm for two-phase ferrohydrodynamics model based on Gauge-Uzawa method 基于Gauge-Uzawa法的两相铁流体力学模型高效解耦算法

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-10 DOI: 10.1016/j.matcom.2025.12.007

Kaiwen Shi , Haohao Li , Haiyan Su , Xiaodi Zhang

In this paper, we design a decoupled, linear and unconditionally energy stable algorithm for the two-phase ferrohydrodynamics (CHFHD) model. The proposed algorithm employs a semi-implicit stabilization approach to solve the phase-field equations, while the ferrohydrodynamics (FHD) part is discretized using the Gauge-Uzawa method. Furthermore, the nonlinear terms of the model are handled by stabilization method with some implicit-explicit treatments. Compared to the standard projection method, our approach resolves the issues related to the initial value selection for pressure

p

and the handling of artificial boundary conditions on

p

, which often lead to the formation of boundary layers and reduced numerical accuracy. Finally, several numerical examples are provided to demonstrate the effectiveness and validity of the proposed algorithm.

本文设计了一种解耦的、线性的、无条件能量稳定的两相铁流体动力学（CHFHD）模型算法。该算法采用半隐式稳定化方法求解相场方程，并采用Gauge-Uzawa方法对铁流体力学部分进行离散化。在此基础上，对模型的非线性项进行了稳定化处理，并进行了隐式显式处理。与标准投影法相比，我们的方法解决了与压力p的初始值选择和p上的人工边界条件处理有关的问题，这些问题通常会导致边界层的形成和数值精度的降低。最后通过数值算例验证了该算法的有效性和有效性。

引用次数: 0

Equilibrium reinsurance and investment strategies for insurers with random risk aversion under Heston’s SV model Heston的SV模型下随机风险规避保险人的均衡再保险与投资策略

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-08 DOI: 10.1016/j.matcom.2025.12.004

Jian-hao Kang , Zhun Gou , Nan-jing Huang

This study employs expected certainty equivalents to explore the reinsurance and investment issue pertaining to an insurer that aims to maximize the expected utility while being subject to random risk aversion. The insurer’s surplus process is modeled approximately by a drifted Brownian motion, and the financial market is comprised of a risk-free asset and a risky asset with its price depicted by Heston’s stochastic volatility (SV) model. Within a game theory framework, a strict verification theorem is formulated to delineate the equilibrium reinsurance and investment strategies as well as the corresponding value function. Furthermore, through solving the pseudo Hamilton–Jacobi–Bellman (HJB) system, semi-analytical formulations for the equilibrium reinsurance and investment strategies and the associated value function are obtained under the exponential utility. Additionally, several numerical experiments are carried out to demonstrate the characteristics of the equilibrium reinsurance and investment strategies.

本研究运用预期确定性等价物，探讨以预期效用最大化为目标的保险公司在随机风险规避下的再保险与投资问题。保险公司的盈余过程用漂移布朗运动近似建模，金融市场由无风险资产和风险资产组成，其价格由赫斯顿随机波动率（SV）模型描述。在博弈论的框架下，提出了一个严格的验证定理来描述均衡再保险和投资策略以及相应的价值函数。进一步，通过求解伪Hamilton-Jacobi-Bellman （HJB）系统，得到了指数效用下均衡再保险和投资策略及其相关价值函数的半解析表达式。此外，通过数值实验验证了均衡再保险和均衡投资策略的特点。

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IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-04 DOI: 10.1016/S0378-4754(25)00509-9

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