Applied Mathematics and Computation最新文献

{"title":"Learning a robust shape parameter for RBF approximation","authors":"Maria Han Veiga ,&nbsp;Faezeh Nassajian Mojarrad ,&nbsp;Fatemeh Nassajian Mojarrad","doi":"10.1016/j.amc.2025.129706","DOIUrl":"10.1016/j.amc.2025.129706","url":null,"abstract":"<div><div>Radial basis functions (RBFs) play an important role in function interpolation, in particular, when considering an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a parameter called the <em>shape parameter</em>. There are many approaches in the literature on how to appropriately choose it to increase the accuracy of interpolation while avoiding stability issues. However, finding the optimal shape parameter remains a challenge in general. We introduce a new method for determining the shape parameter in RBFs. First, we construct an optimization problem to obtain a shape parameter that leads to a bounded condition number for the interpolation matrix, then, we introduce a data-driven method that controls the condition number of the interpolation matrix to avoid numerically unstable interpolations, while keeping good accuracy. In addition, a fallback procedure is proposed to enforce a strict upper bound on the condition number, as well as a learning strategy to improve the performance of the data-driven method by learning from previously run simulations. Several numerical results are presented to demonstrate the robustness of our strategy in both 1- and 2-dimensional spaces.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129706"},"PeriodicalIF":3.4,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018684","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}

{"title":"Visualization of Escher-like hyperbolic tessellations","authors":"Peichang Ouyang ,&nbsp;Kwok Wai Chung ,&nbsp;Alain Nicolas ,&nbsp;Robert W. Fathauer ,&nbsp;David Bailey ,&nbsp;Krzysztof Gdawiec","doi":"10.1016/j.amc.2025.129710","DOIUrl":"10.1016/j.amc.2025.129710","url":null,"abstract":"<div><div>By combining mathematical principles, modern computer graphics techniques, and the efforts of mathematically inclined artists, we present a visualization method for generating aesthetic patterns in hyperbolic space. To this end, we first establish fast algorithms to construct hyperbolic tilings in the Poincaré disk model. Then, using templates designed by graphic artists, we specify computer techniques to render hyperbolic tilings, which results in Escher-like patterns. Moreover, we present a simple method to realize novel hyperbolic kaleidoscopic effect. To obtain more diverse patterns, we introduce several conformal mappings to create visually appealing tessellations on the other spaces. The proposed methods can be easily implemented using shaders to obtain high-quality tessellations, which have good potential for application in the field of artistic decoration.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129710"},"PeriodicalIF":3.4,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018683","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}

{"title":"Prescribed-time reinforcement learning formation control of nonlinear MASs with an unknown dynamic leader","authors":"Benxin Zhao ,&nbsp;Yuan-Xin Li ,&nbsp;Zhongsheng Hou","doi":"10.1016/j.amc.2025.129711","DOIUrl":"10.1016/j.amc.2025.129711","url":null,"abstract":"<div><div>This paper investigates the prescribed-time optimal formation control problem for nonlinear multi-agent systems (MASs) with an unknown dynamic leader. The agents need to not only form a predefined formation pattern but also track the leader’s trajectory in a prescribed time. A hierarchical control framework, which includes the communication layer and the tracking control layer, is established to address the formulated issue. In the communication layer, a distributed prescribed-time observer is established to accurately estimate the leader’s information, which can make observation error convergences to zero in a prescribed time. In particular, the leaders’ uncertainties are solved by constructing a novel adaptive law. With the estimated results, a novel transformation relationship and the prescribed-time adjustment function are constructed to guarantee that formation tracking error converges to the predefined accuracy in a prescribed time. Subsequently, the reinforcement learning (RL) algorithm with the fuzzy logic systems (FLSs) is devised to optimize system performance. Based on the Lyapunov stability theory, it is shown that the formation errors <span><math><mrow><msub><mi>ξ</mi><mrow><mi>i</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>x</mi><mrow><mi>i</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>−</mo><msub><mover><mi>y</mi><mo>^</mo></mover><mrow><mn>0</mn><mo>,</mo><mi>i</mi></mrow></msub><mo>−</mo><msub><mi>η</mi><mrow><mi>i</mi><mo>,</mo><mi>d</mi></mrow></msub></mrow></math></span> are consistently confined within an interval <span><math><mrow><mo>(</mo><mi>tan</mi><mrow><mo>(</mo><mo>−</mo><mfrac><mi>π</mi><mrow><mn>2</mn><msub><mi>μ</mi><mn>2</mn></msub></mrow></mfrac><mo>)</mo></mrow><mo>,</mo><mi>tan</mi><mrow><mo>(</mo><mfrac><mi>π</mi><mrow><mn>2</mn><msub><mi>μ</mi><mn>2</mn></msub></mrow></mfrac><mo>)</mo></mrow><mo>)</mo></mrow></math></span>, while all signals of the closed-loop system are bounded. Ultimately, the superiority of the devised algorithm is demonstrated by a representative example.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129711"},"PeriodicalIF":3.4,"publicationDate":"2025-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145009089","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}

{"title":"Trapezoid and trapezoidal prism for the maximum relative drawdown: Probability, crash options pricing, and risk","authors":"Jia-Hao Syu,&nbsp;Yuh-Dauh Lyuu","doi":"10.1016/j.amc.2025.129708","DOIUrl":"10.1016/j.amc.2025.129708","url":null,"abstract":"<div><div>Maximum drawdown (MDD) and maximum relative drawdown (MrDD) are well-known in portfolio management and performance evaluations. They can also form the basis of a stop-loss strategy. But there is no closed-form formula for the probability that the MrDD (MDD) ever reaches some positive threshold over a period of time. This paper focuses on MrDD and employs a random walk to approximate the underlying geometric Brownian motion (GBM) for the price, taking care to match the threshold for faster convergence. Let <span><math><mi>n</mi></math></span> be the number of time steps. This paper proposes an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mi>n</mi><mrow><mn>1.5</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-sized trapezoid to calculate the above-mentioned probability. The trapezoid can price the crash option with a digital payoff accurately. This paper further proposes an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mi>n</mi><mrow><mn>2.5</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-sized trapezoidal prism to price the crash option with a resetting payoff accurately and calculate the expected return rate and common risk measures of an MrDD-based stop-loss strategy.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129708"},"PeriodicalIF":3.4,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996175","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}

{"title":"Gravitational least squares twin support vector machine based on optimal angle for class imbalance learning","authors":"Abdullah Mohammadi ,&nbsp;Jalal A. Nasiri ,&nbsp;Sohrab Effati","doi":"10.1016/j.amc.2025.129705","DOIUrl":"10.1016/j.amc.2025.129705","url":null,"abstract":"<div><div>This paper introduces the Gravitational Least Squares Twin Support Vector Machine for Class Imbalance Learning (GLSTSVM-CIL), a novel binary classification method designed to address critical limitations in existing approaches for imbalanced large-scale datasets. Traditional methods like Fuzzy TSVM and KNN-based weighting fail to simultaneously capture both global positional relationships and local density characteristics of data points. Our proposed gravitational weighting function innovatively models data samples as masses influenced by their distance from class centroids and neighborhood density, effectively prioritizing representative points while suppressing outliers. The optimization framework uniquely incorporates angular constraints between hyperplanes to enhance structural risk control and generalization capability. For scalability, we reformulate the solution into a linear system solvable via conjugate gradient methods, avoiding computationally expensive matrix inversions. Comprehensive evaluations on 92 datasets (including synthetic, noisy, medical, text, and large-scale NDC benchmarks) demonstrate GLSTSVM-CIL’s superior performance, particularly in minority-class recognition where it achieves average F1-Score improvements over baseline methods. The model maintains robust Accuracy under high noise (20 %) and extreme class imbalance (ratio 20:1) while ables to process datasets up to 50,000 samples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129705"},"PeriodicalIF":3.4,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996174","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}

{"title":"Incentive-based control of networked evolutionary coordination games under asynchronous best-response dynamics","authors":"Aixin Liu ,&nbsp;Haitao Li ,&nbsp;Lin Wang ,&nbsp;Guanrong Chen","doi":"10.1016/j.amc.2025.129684","DOIUrl":"10.1016/j.amc.2025.129684","url":null,"abstract":"<div><div>Incentive-based control mechanisms in game-theoretic models aim to steer players toward socially desirable strategies through appropriately designed utility rewards or penalties. In this paper, we propose an algebraic framework for incentive-based control in networked evolutionary coordination games (NECGs) under asynchronous myopic best-response dynamics. We establish a fundamental connection between the reward policy and the attainability of a desired equilibrium, demonstrating that a fully cooperative equilibrium is implementable if and only if there exists a reward vector that makes it reachable from the initial fully non-cooperative strategies in the incentivized NECG. Moreover, leveraging the strategy profile reachability sets, we demonstrate that the incentive control problem reduces to verifying the reachability of the set associated with the desired equilibrium. We prove that the reachable set of the desired equilibrium in the original NECG is contained within that of its incentivized counterpart. This, to some extent, simplifies the verification for computing the reachable set of the desired equilibrium in the incentivized NECG. Finally, we show an example to illustrate the proposed result.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"509 ","pages":"Article 129684"},"PeriodicalIF":3.4,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931948","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}

{"title":"On reduced Hamilton walks","authors":"Aleksander Malnič ,&nbsp;Rok Požar","doi":"10.1016/j.amc.2025.129695","DOIUrl":"10.1016/j.amc.2025.129695","url":null,"abstract":"<div><div>A Hamilton walk in a finite graph is a walk, either open or closed, that traverses every vertex at least once. Here, we introduce Hamilton walks that are reduced in the sense that they avoid immediate backtracking: a reduced Hamilton walk never traverses the same edge forth and back consecutively.</div><div>While every connected graph admits a Hamilton walk, existence of a reduced Hamilton walk is not guaranteed for all graphs. However, we prove that a reduced Hamilton walk does exist in a connected graph with minimal valency at least 2.</div><div>Furthermore, given such a graph on <span><math><mi>n</mi></math></span> vertices, we present an <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mn>2</mn></msup><mo>)</mo></mrow></math></span>-time algorithm that constructs a reduced Hamilton walk of length at most <span><math><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo><mo>/</mo><mn>2</mn></mrow></math></span>. Specifically, for a graph belonging to a family of regular expander graphs, we can find a reduced Hamilton walk of length at most <span><math><mrow><mi>c</mi><mo>(</mo><mn>6</mn><mi>n</mi><mo>−</mo><mn>2</mn><mo>)</mo><mi>log</mi><mi>n</mi><mo>+</mo><mn>2</mn><mi>n</mi></mrow></math></span>, where <span><math><mi>c</mi></math></span> is a constant independent of <span><math><mi>n</mi></math></span>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129695"},"PeriodicalIF":3.4,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932974","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}

{"title":"Components of flip graphs of domino tilings in quadriculated cylinder and torus","authors":"Qianqian Liu ,&nbsp;Jingfeng Wang ,&nbsp;Chunmei Li ,&nbsp;Heping Zhang","doi":"10.1016/j.amc.2025.129697","DOIUrl":"10.1016/j.amc.2025.129697","url":null,"abstract":"<div><div>Let <span><math><mi>R</mi></math></span> be a quadriculated surface, possibly with boundary, consisting of unit squares, and each interior vertex being surrounded by 4 squares. A tiling of <span><math><mi>R</mi></math></span> is a placement of dominoes (a pair of adjacent squares) so that there are no gaps or overlaps. The flip graph of <span><math><mi>R</mi></math></span> is a graph whose vertices are all tilings of <span><math><mi>R</mi></math></span> and two tilings are adjacent if we can obtain one from another by a flip (<span><math><msup><mn>90</mn><mo>∘</mo></msup></math></span> rotation of a pair of side-by-side dominoes). By using graph-theoretical approach, we prove that the flip graph of <span><math><mrow><mn>2</mn><mi>m</mi><mo>×</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span> quadriculated cylinder is still connected, but that of <span><math><mrow><mn>2</mn><mi>m</mi><mo>×</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span> quadriculated torus consists of two isomorphic components. For a tiling <span><math><mi>t</mi></math></span>, we associate an integer, called forcing number, as the minimum number of dominoes in <span><math><mi>t</mi></math></span> that is contained in no other tilings. As a consequence, we obtain that the forcing numbers of all tilings in <span><math><mrow><mn>2</mn><mi>m</mi><mo>×</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span> quadriculated cylinder and torus form respectively an integer interval whose maximum value is <span><math><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mi>m</mi></mrow></math></span>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129697"},"PeriodicalIF":3.4,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925588","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}

{"title":"Community detection methods for GBF-PUM signal approximation on graphs","authors":"Roberto Cavoretto ,&nbsp;Chiara Comoglio ,&nbsp;Alessandra De Rossi","doi":"10.1016/j.amc.2025.129702","DOIUrl":"10.1016/j.amc.2025.129702","url":null,"abstract":"<div><div>Graph signal approximation plays a key role in processing irregularly distributed data on graphs, where achieving smooth and computationally efficient interpolation is essential. In this work, we introduce a new approach that combines a spectral community detection technique with the partition of unity method (PUM) applied to signal approximation on graphs. The PUM provides an effective technique for handling irregularly distributed data by dividing the graph into smaller subgraphs, constructing local interpolants and combining them to produce a global approximation. Since the first step in the PUM consists in dividing the graph into disjoint communities, we focus in particular on exploring and testing some community detection algorithms based on the maximization of the modularity. Then, we integrate the PUM with a local graph basis function approximation scheme, resulting in an accurate and computationally efficient approach for graph signal approximation.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129702"},"PeriodicalIF":3.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925587","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}

{"title":"Induced cycles vertex number and (1,2)-domination in cubic graphs","authors":"Rija Erveš ,&nbsp;Aleksandra Tepeh","doi":"10.1016/j.amc.2025.129700","DOIUrl":"10.1016/j.amc.2025.129700","url":null,"abstract":"<div><div>A (1,2)-dominating set in a graph <span><math><mi>G</mi></math></span> is a set <span><math><mi>S</mi></math></span> such that every vertex outside <span><math><mi>S</mi></math></span> has at least one neighbor in <span><math><mi>S</mi></math></span>, and each vertex in <span><math><mi>S</mi></math></span> has at least two neighbors in <span><math><mi>S</mi></math></span>. The (1,2)-domination number, <span><math><mrow><msub><mi>γ</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, is the minimum size of such a set, while <span><math><mrow><msub><mi>c</mi><mrow><mrow><mi>i</mi></mrow><mi>n</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> is the cardinality of the largest vertex set in <span><math><mi>G</mi></math></span> that induces one or more cycles. In this paper, we initiate the study of a relationship between these two concepts and discuss how establishing such a connection can contribute to solving a conjecture on the lower bound of <span><math><mrow><msub><mi>c</mi><mrow><mrow><mi>i</mi></mrow><mi>n</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> for cubic graphs. We also establish an upper bound on <span><math><mrow><msub><mi>c</mi><mrow><mrow><mi>i</mi></mrow><mi>n</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> for cubic graphs and characterize graphs that achieve this bound.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129700"},"PeriodicalIF":3.4,"publicationDate":"2025-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920267","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}