Pub Date : 2025-04-26DOI: 10.1016/j.dam.2025.04.048
Jiawen Bo , Zhipeng Gao , Xiaopan Lian , Jianing Liu
Let denote the order of a longest path in a digraph . For disjoint , if , we say that is a partition of . The Directed Path Partition Conjecture (DPPC) states that for every digraph and every integer with , there is a partition of such that and .
Arroyo and Galeana-Sánchez (2013) proved that every strong 3-quasi-transitive digraph satisfies the DPPC. They also showed that the DPPC holds for compositions over an acyclic digraph with digraphs that meet the DPPC. In the paper, we show that non-strong 3-quasi-transitive digraphs and strong 4-transitive digraphs also satisfy the DPPC. Additionally, we show that the DPPC holds for the compositions over a unicyclic digraph with digraphs that satisfy the DPPC and certain other conditions. Furthermore, by applying different arguments, we show that the compositions over a cycle with arbitrary digraphs meets the DPPC.
{"title":"Some digraph classes that meet the directed path partition conjecture","authors":"Jiawen Bo , Zhipeng Gao , Xiaopan Lian , Jianing Liu","doi":"10.1016/j.dam.2025.04.048","DOIUrl":"10.1016/j.dam.2025.04.048","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span> denote the order of a longest path in a digraph <span><math><mi>D</mi></math></span>. For disjoint <span><math><mrow><mi>A</mi><mo>,</mo><mi>B</mi><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span>, if <span><math><mrow><mi>A</mi><mo>∪</mo><mi>B</mi><mo>=</mo><mi>V</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span>, we say that <span><math><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></math></span> is a partition of <span><math><mi>D</mi></math></span>. The Directed Path Partition Conjecture (DPPC) states that for every digraph <span><math><mi>D</mi></math></span> and every integer <span><math><mi>q</mi></math></span> with <span><math><mrow><mi>q</mi><mo><</mo><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span>, there is a partition <span><math><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></math></span> of <span><math><mi>D</mi></math></span> such that <span><math><mrow><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mrow><mo>[</mo><mi>A</mi><mo>]</mo></mrow><mo>)</mo></mrow><mo>≤</mo><mi>q</mi></mrow></math></span> and <span><math><mrow><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mrow><mo>[</mo><mi>B</mi><mo>]</mo></mrow><mo>)</mo></mrow><mo>≤</mo><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>−</mo><mi>q</mi></mrow></math></span>.</div><div>Arroyo and Galeana-Sánchez (2013) proved that every strong 3-quasi-transitive digraph satisfies the DPPC. They also showed that the DPPC holds for compositions over an acyclic digraph with digraphs that meet the DPPC. In the paper, we show that non-strong 3-quasi-transitive digraphs and strong 4-transitive digraphs also satisfy the DPPC. Additionally, we show that the DPPC holds for the compositions over a unicyclic digraph with digraphs that satisfy the DPPC and certain other conditions. Furthermore, by applying different arguments, we show that the compositions over a cycle with arbitrary digraphs meets the DPPC.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 260-267"},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.na.2025.113817
L. Desvillettes , L. Fiorentino , T. Mautone
We consider a system of three reaction–diffusion equations modeling the interaction between a prey species and two predators species including functional responses of Holly type-II and Leslie–Gower type. We propose a reaction–diffusion model with five equations with simpler functional responses which, in the fast reaction limit, allows to recover the zero-th order terms of the initially considered system. The diffusive part of the initial equations is however modified and cross diffusion terms pop up. We first study the equilibria of this new system and show that no Turing instability appears. We then rigorously prove a partial result of convergence for the fast reaction limit (in 1D and 2D).
{"title":"Fast reaction limit for a Leslie–Gower model including preys, meso-predators and top-predators","authors":"L. Desvillettes , L. Fiorentino , T. Mautone","doi":"10.1016/j.na.2025.113817","DOIUrl":"10.1016/j.na.2025.113817","url":null,"abstract":"<div><div>We consider a system of three reaction–diffusion equations modeling the interaction between a prey species and two predators species including functional responses of Holly type-II and Leslie–Gower type. We propose a reaction–diffusion model with five equations with simpler functional responses which, in the fast reaction limit, allows to recover the zero-th order terms of the initially considered system. The diffusive part of the initial equations is however modified and cross diffusion terms pop up. We first study the equilibria of this new system and show that no Turing instability appears. We then rigorously prove a partial result of convergence for the fast reaction limit (in 1D and 2D).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113817"},"PeriodicalIF":1.3,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874392","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 : 2025-04-26DOI: 10.1007/s10878-025-01281-8
Anis Naanaa
Chaos optimization algorithm (COA) is an interesting alternative in a global optimization problem. Due to the non-repetition and ergodicity of chaos, it can explore the global search space at higher speeds than stochastic searches that depend on probabilities. To adjust the solution obtained by COA, guided local search algorithm (GLS) is integrated with COA to form a hybrid algorithm. GLS is a metaheuristic optimization algorithm that combines elements of local search with strategic guidance to efficiently explore the solution space. This study proposes a chaotic guided local search algorithm to search for global solutions. The proposed algorithm, namely COA-GLS, contributes to optimization problems by providing a balance between quick convergence and good solution quality. Its combination of local refinement, strategic guidance, diversification strategies, and adaptability makes it a powerful metaheuristic capable of efficiently navigating complex solution spaces and finding high-quality solutions in a relatively short amount of time. Simulation results show that the present algorithms significantly outperform the existing methods in terms of convergence speed, numerical stability, and a better optimal solution than other algorithms.
{"title":"Chaotic guided local search algorithm for solving global optimization and engineering problems","authors":"Anis Naanaa","doi":"10.1007/s10878-025-01281-8","DOIUrl":"https://doi.org/10.1007/s10878-025-01281-8","url":null,"abstract":"<p>Chaos optimization algorithm (COA) is an interesting alternative in a global optimization problem. Due to the non-repetition and ergodicity of chaos, it can explore the global search space at higher speeds than stochastic searches that depend on probabilities. To adjust the solution obtained by COA, guided local search algorithm (GLS) is integrated with COA to form a hybrid algorithm. GLS is a metaheuristic optimization algorithm that combines elements of local search with strategic guidance to efficiently explore the solution space. This study proposes a chaotic guided local search algorithm to search for global solutions. The proposed algorithm, namely COA-GLS, contributes to optimization problems by providing a balance between quick convergence and good solution quality. Its combination of local refinement, strategic guidance, diversification strategies, and adaptability makes it a powerful metaheuristic capable of efficiently navigating complex solution spaces and finding high-quality solutions in a relatively short amount of time. Simulation results show that the present algorithms significantly outperform the existing methods in terms of convergence speed, numerical stability, and a better optimal solution than other algorithms.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"53 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a structure preserving spatio-temporal discretization for incompressible magnetohydrodynamics (MHD) on the sphere. Discretization in space is based on the theory of geometric quantization, which yields a spatially discretized analogue of the MHD equations as a finite-dimensional Lie–Poisson system on the dual of the magnetic extension Lie algebra $mathfrak{f}=mathfrak{su}(N)ltimes mathfrak{su}(N)^{*}$. We also give accompanying structure preserving time discretizations for Lie–Poisson systems on the dual of semidirect product Lie algebras of the form $mathfrak{f}=mathfrak{g}ltimes mathfrak{g^{*}}$, where $mathfrak{g}$ is a $J$-quadratic Lie algebra. The time integration method is free of computationally costly matrix exponentials. We prove that the full method preserves a modified Lie–Poisson structure and corresponding Casimir functions, and that the modified structure and Casimirs converge to the continuous ones. The method is demonstrated for two models of magnetic fluids: incompressible MHD and Hazeltine’s model.
{"title":"Spatio-temporal Lie–Poisson discretization for incompressible magnetohydrodynamics on the sphere","authors":"Klas Modin, Michael Roop","doi":"10.1093/imanum/draf024","DOIUrl":"https://doi.org/10.1093/imanum/draf024","url":null,"abstract":"We give a structure preserving spatio-temporal discretization for incompressible magnetohydrodynamics (MHD) on the sphere. Discretization in space is based on the theory of geometric quantization, which yields a spatially discretized analogue of the MHD equations as a finite-dimensional Lie–Poisson system on the dual of the magnetic extension Lie algebra $mathfrak{f}=mathfrak{su}(N)ltimes mathfrak{su}(N)^{*}$. We also give accompanying structure preserving time discretizations for Lie–Poisson systems on the dual of semidirect product Lie algebras of the form $mathfrak{f}=mathfrak{g}ltimes mathfrak{g^{*}}$, where $mathfrak{g}$ is a $J$-quadratic Lie algebra. The time integration method is free of computationally costly matrix exponentials. We prove that the full method preserves a modified Lie–Poisson structure and corresponding Casimir functions, and that the modified structure and Casimirs converge to the continuous ones. The method is demonstrated for two models of magnetic fluids: incompressible MHD and Hazeltine’s model.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"26 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878131","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 : 2025-04-26DOI: 10.1007/s10878-025-01289-0
Lara Löhken, Michael Stiglmayr
The cable-trench problem is defined as a linear combination of the shortest path and the minimum spanning tree problem. In particular, the goal is to find a spanning tree that simultaneously minimizes its total length and the total path length from a pre-defined root to all other vertices. Both, the minimum spanning tree and the shortest path problem are known to be efficiently solvable. However, a linear combination of these two objectives results in a highly complex problem. In this article, we introduce the bi-objective cable-trench problem which separates the two cost functions. We show that in general, the bi-objective formulation has additional compromise solutions compared to the cable-trench problem in its original formulation. To determine the set of non-dominated points and efficient solutions, we use (varepsilon )-constraint scalarizations in combination with a problem-specific cutting plane. Moreover, we present numerical results on different types of graphs analyzing the impact of density and cost structure on the cardinality of the non-dominated set and the solution time.
{"title":"A multi-objective perspective on the cable-trench problem","authors":"Lara Löhken, Michael Stiglmayr","doi":"10.1007/s10878-025-01289-0","DOIUrl":"https://doi.org/10.1007/s10878-025-01289-0","url":null,"abstract":"<p>The cable-trench problem is defined as a linear combination of the shortest path and the minimum spanning tree problem. In particular, the goal is to find a spanning tree that simultaneously minimizes its total length and the total path length from a pre-defined root to all other vertices. Both, the minimum spanning tree and the shortest path problem are known to be efficiently solvable. However, a linear combination of these two objectives results in a highly complex problem. In this article, we introduce the bi-objective cable-trench problem which separates the two cost functions. We show that in general, the bi-objective formulation has additional compromise solutions compared to the cable-trench problem in its original formulation. To determine the set of non-dominated points and efficient solutions, we use <span>(varepsilon )</span>-constraint scalarizations in combination with a problem-specific cutting plane. Moreover, we present numerical results on different types of graphs analyzing the impact of density and cost structure on the cardinality of the non-dominated set and the solution time.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.nonrwa.2025.104385
Yongjian Liu , Stanisław Migórski , Sylwia Dudek
In this paper a class of time-dependent multivalued quasi-variational inequalities of elliptic type with a solution dependent constraint set, is studied. Its solvability and the closedness of the solution set are proved. Then, the results are applied to constrained quasi-variational–hemivariational inequalities for which the relaxed monotonicity condition is not required. Finally, the abstract results are illustrated by two applications. The first one is a time-dependent frictional contact problem with locking materials, and the second one is the stationary incompressible Navier–Stokes equation which models a generalized Newtonian fluid of Bingham type. Results on existence and the closedness of the solution sets are established for both applications.
{"title":"A class of time-dependent quasi-variational–hemivariational inequalities with applications","authors":"Yongjian Liu , Stanisław Migórski , Sylwia Dudek","doi":"10.1016/j.nonrwa.2025.104385","DOIUrl":"10.1016/j.nonrwa.2025.104385","url":null,"abstract":"<div><div>In this paper a class of time-dependent multivalued quasi-variational inequalities of elliptic type with a solution dependent constraint set, is studied. Its solvability and the closedness of the solution set are proved. Then, the results are applied to constrained quasi-variational–hemivariational inequalities for which the relaxed monotonicity condition is not required. Finally, the abstract results are illustrated by two applications. The first one is a time-dependent frictional contact problem with locking materials, and the second one is the stationary incompressible Navier–Stokes equation which models a generalized Newtonian fluid of Bingham type. Results on existence and the closedness of the solution sets are established for both applications.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104385"},"PeriodicalIF":1.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.chaos.2025.116506
Xinlin Dai , Yaoyao Qi , Qixing Yu , Chaojian He , Song Yang , Zhiwei Lu
This study investigates the robustness of the quadratic and pure-quartic solitons within mode-locked fiber lasers subjected to white Gaussian noise disturbances. We assess the dynamic responses of both solitons under standardized noise conditions using a numerical simulation model. The results reveal that pure-quartic solitons exhibit enhanced robustness, stabilizing more rapidly after disturbances compared to quadratic solitons under the same condition. The superior robustness performance of pure-quartic soliton is mainly attributed to its higher emission energy, which mitigates the effects of noise-induced fluctuations. Notably, the differences in robustness between the two solitons diminish when their energies are equal, indicating energy as a crucial determinant of soliton stability. This research enhances our understanding of soliton behavior in noisy environments and offers insights into improving the design and performance of fiber lasers in optical communications and signal processing applications.
{"title":"Comparative robustness analysis of quadratic solitons and pure-quartic solitons","authors":"Xinlin Dai , Yaoyao Qi , Qixing Yu , Chaojian He , Song Yang , Zhiwei Lu","doi":"10.1016/j.chaos.2025.116506","DOIUrl":"10.1016/j.chaos.2025.116506","url":null,"abstract":"<div><div>This study investigates the robustness of the quadratic and pure-quartic solitons within mode-locked fiber lasers subjected to white Gaussian noise disturbances. We assess the dynamic responses of both solitons under standardized noise conditions using a numerical simulation model. The results reveal that pure-quartic solitons exhibit enhanced robustness, stabilizing more rapidly after disturbances compared to quadratic solitons under the same condition. The superior robustness performance of pure-quartic soliton is mainly attributed to its higher emission energy, which mitigates the effects of noise-induced fluctuations. Notably, the differences in robustness between the two solitons diminish when their energies are equal, indicating energy as a crucial determinant of soliton stability. This research enhances our understanding of soliton behavior in noisy environments and offers insights into improving the design and performance of fiber lasers in optical communications and signal processing applications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116506"},"PeriodicalIF":5.3,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.dam.2025.04.045
Shu-Guang Guo, Rong Zhang
The spectral extremal problem is a classic problem in spectral graph theory. For a simple graph , let denote the -spectral radius. We first characterize the graphs with maximal -spectral radius among all graphs of size with maximum degree . For two graphs and of size , employing this result, we prove that if and , which improves the main result of [Bull. Malays. Math. Sci. Soc. 45(2022)2165-2174]. Let be an integer. Employing the above results, we completely characterize the graphs with maximal -spectral radius among all connected graphs of size with maximum degree at most , with covering number and with independence number , respectively.
{"title":"An ordering theorem on the Q-spectral radius of graphs with given size and its applications","authors":"Shu-Guang Guo, Rong Zhang","doi":"10.1016/j.dam.2025.04.045","DOIUrl":"10.1016/j.dam.2025.04.045","url":null,"abstract":"<div><div>The spectral extremal problem is a classic problem in spectral graph theory. For a simple graph <span><math><mi>G</mi></math></span>, let <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> denote the <span><math><mi>Q</mi></math></span>-spectral radius. We first characterize the graphs with maximal <span><math><mi>Q</mi></math></span>-spectral radius among all graphs of size <span><math><mi>m</mi></math></span> with maximum degree <span><math><mrow><mi>Δ</mi><mo>≥</mo><mfrac><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>. For two graphs <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> of size <span><math><mrow><mi>m</mi><mo>≥</mo><mn>11</mn></mrow></math></span>, employing this result, we prove that <span><math><mrow><mi>q</mi><mrow><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>></mo><mi>q</mi><mrow><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span> if <span><math><mrow><mi>Δ</mi><mrow><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>></mo><mi>Δ</mi><mrow><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>Δ</mi><mrow><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>≥</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>3</mn></mrow></math></span>, which improves the main result of [Bull. Malays. Math. Sci. Soc. 45(2022)2165-2174]. Let <span><math><mrow><mi>r</mi><mo>≥</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>3</mn></mrow></math></span> be an integer. Employing the above results, we completely characterize the graphs with maximal <span><math><mi>Q</mi></math></span>-spectral radius among all connected graphs of size <span><math><mi>m</mi></math></span> with maximum degree at most <span><math><mi>r</mi></math></span>, with covering number <span><math><mi>β</mi></math></span> and with independence number <span><math><mrow><mi>α</mi><mo>≥</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></math></span>, respectively.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 91-98"},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.dam.2025.04.049
Ligang Jin , Eckhard Steffen
We introduce a model of information dissemination in signed networks. It is a discrete-time process in which uninformed actors incrementally receive information from their informed neighbors or from the outside. Our goal is to minimize the number of confused actors — that is, the number of actors who receive contradictory information. We prove upper bounds for the number of confused actors in signed networks and in equivalence classes of signed networks. In particular, we show that there are signed networks where, for any information placement strategy, almost 60% of the actors are confused. Furthermore, this is also the case when considering the minimum number of confused actors within an equivalence class of signed graphs.
{"title":"Information dissemination and confusion in signed networks","authors":"Ligang Jin , Eckhard Steffen","doi":"10.1016/j.dam.2025.04.049","DOIUrl":"10.1016/j.dam.2025.04.049","url":null,"abstract":"<div><div>We introduce a model of information dissemination in signed networks. It is a discrete-time process in which uninformed actors incrementally receive information from their informed neighbors or from the outside. Our goal is to minimize the number of confused actors — that is, the number of actors who receive contradictory information. We prove upper bounds for the number of confused actors in signed networks and in equivalence classes of signed networks. In particular, we show that there are signed networks where, for any information placement strategy, almost 60% of the actors are confused. Furthermore, this is also the case when considering the minimum number of confused actors within an equivalence class of signed graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 99-106"},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.chaos.2025.116465
Suhyeon Kim, Junpyo Park
Basin entropy is a useful tool for predicting uncertainty in nonlinear dynamical systems, and it is proposed as a way to present biodiversity in the rock–paper–scissors game in a classic manner. As new interaction can be allowed in the system, such biodiversity can be changed, and the system can present different features. In this paper, we investigate the role of basin entropy in the spatial rock–paper–scissors (RPS) game, where the system allows competition within the same species, which can lead to various biodiversity. From extensive numerical simulations, we found that calculating basin entropy may be ambiguous in identifying biodiversity in the spatial RPS game, even if it plays an important role in the system in a classic manner. As intraspecific competition is induced, it disturbs the collective behaviors of species associated with the coexistence state and leads to the change in the level of basin entropy having various values. Similar phenomena are found by considering the symmetry-breaking of intraspecific competition that leads to diverse survival states. Our findings address that basin entropy can be a candidate to predict biodiversity but not always, and they may provide new insight into basin entropy in a different framework- a double-edged effect.
{"title":"A double-edged aspect of basin entropy for predicting biodiversity in spatial rock–paper–scissors games","authors":"Suhyeon Kim, Junpyo Park","doi":"10.1016/j.chaos.2025.116465","DOIUrl":"10.1016/j.chaos.2025.116465","url":null,"abstract":"<div><div>Basin entropy is a useful tool for predicting uncertainty in nonlinear dynamical systems, and it is proposed as a way to present biodiversity in the rock–paper–scissors game in a classic manner. As new interaction can be allowed in the system, such biodiversity can be changed, and the system can present different features. In this paper, we investigate the role of basin entropy in the spatial rock–paper–scissors (RPS) game, where the system allows competition within the same species, which can lead to various biodiversity. From extensive numerical simulations, we found that calculating basin entropy may be ambiguous in identifying biodiversity in the spatial RPS game, even if it plays an important role in the system in a classic manner. As intraspecific competition is induced, it disturbs the collective behaviors of species associated with the coexistence state and leads to the change in the level of basin entropy having various values. Similar phenomena are found by considering the symmetry-breaking of intraspecific competition that leads to diverse survival states. Our findings address that basin entropy can be a candidate to predict biodiversity but not always, and they may provide new insight into basin entropy in a different framework- a double-edged effect.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116465"},"PeriodicalIF":5.3,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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