Pub Date : 2024-12-27DOI: 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.
{"title":"Extremal function of two independent chorded cycles in a bipartite graph","authors":"Panpan Cheng, Yunshu Gao","doi":"10.1016/j.amc.2024.129253","DOIUrl":"10.1016/j.amc.2024.129253","url":null,"abstract":"<div><div>Let <em>G</em> be a bipartite graph. In this paper, by constructing two extremal graphs, we completely determine the minimum number of edges of <em>G</em> that guaranteeing the existence of two independent chorded cycles. As a byproduct, our result also implies that <em>G</em> contains two independent cycles of different lengths.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129253"},"PeriodicalIF":3.5,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889268","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 : 2024-12-24DOI: 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.
{"title":"A study on multi-information diffusion model considering dual social reinforcement effect from the perspective of evolutionary game","authors":"Yuanyuan Ma , Qiannan Zhang , Leilei Xie","doi":"10.1016/j.amc.2024.129255","DOIUrl":"10.1016/j.amc.2024.129255","url":null,"abstract":"<div><div>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-SF<sub>D</sub>F<sub>R</sub>R 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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129255"},"PeriodicalIF":3.5,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889317","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 : 2024-12-24DOI: 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.
{"title":"A mathematical model for the bullying dynamics in schools","authors":"Nuno Crokidakis","doi":"10.1016/j.amc.2024.129254","DOIUrl":"10.1016/j.amc.2024.129254","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129254"},"PeriodicalIF":3.5,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889258","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 : 2024-12-19DOI: 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.
{"title":"Supervised cooperation on interdependent public goods games","authors":"Ting Ling , Zhang Li , Minyu Feng , Attila Szolnoki","doi":"10.1016/j.amc.2024.129249","DOIUrl":"10.1016/j.amc.2024.129249","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129249"},"PeriodicalIF":3.5,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874014","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}
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.
{"title":"A novel localized least-squares collocation method for coupled bulk-surface problems","authors":"Zhuochao Tang , Zhuojia Fu , Meng Chen , Leevan Ling","doi":"10.1016/j.amc.2024.129250","DOIUrl":"10.1016/j.amc.2024.129250","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129250"},"PeriodicalIF":3.5,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874015","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 : 2024-12-18DOI: 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].
{"title":"Erratum on “Synchronization and chimeras in asymmetrically coupled memristive Tabu learning neuron network” [Appl. Math. Compt. 489 (2025) 129163]","authors":"A. Prasina , V. Samuthira Pandi , W. Nancy , K. Thilagam , K. Veena , A. Muniyappan","doi":"10.1016/j.amc.2024.129248","DOIUrl":"10.1016/j.amc.2024.129248","url":null,"abstract":"<div><div>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].</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129248"},"PeriodicalIF":3.5,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874016","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 : 2024-12-18DOI: 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.
{"title":"WENO based adaptive image zooming algorithm","authors":"Bojan Crnković , Jerko Škifić , Tina Bosner","doi":"10.1016/j.amc.2024.129228","DOIUrl":"10.1016/j.amc.2024.129228","url":null,"abstract":"<div><div>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.</div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129228"},"PeriodicalIF":3.5,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874070","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 : 2024-12-17DOI: 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 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.
{"title":"Protocol-based H∞ estimation for Markovian jumping delayed systems with partially unknown transition probability","authors":"Guixiu Liu, Bing Li","doi":"10.1016/j.amc.2024.129247","DOIUrl":"10.1016/j.amc.2024.129247","url":null,"abstract":"<div><div>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 <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> 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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129247"},"PeriodicalIF":3.5,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874071","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 : 2024-12-16DOI: 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.
{"title":"On the numerical verification of a counterexample on parameter-dependent Lyapunov functions","authors":"Birgül Aksoy, Taner Büyükköroğlu, Vakif Dzhafarov","doi":"10.1016/j.amc.2024.129246","DOIUrl":"10.1016/j.amc.2024.129246","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129246"},"PeriodicalIF":3.5,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874072","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 : 2024-12-13DOI: 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.
{"title":"Inverse spectral problems for Sturm-Liouville operators with many frozen arguments","authors":"Chung-Tsun Shieh , Tzong-Mo Tsai","doi":"10.1016/j.amc.2024.129235","DOIUrl":"10.1016/j.amc.2024.129235","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129235"},"PeriodicalIF":3.5,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142823229","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}