发布求助
文献互助 智能选刊 最新文献

arXiv - MATH - Dynamical Systems最新文献

筛选
英文 中文
Spectral clustering of time-evolving networks using the inflated dynamic Laplacian for graphs 利用图的膨胀动态拉普拉奇对随时间变化的网络进行频谱聚类
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-18 DOI: arxiv-2409.11984
Gary Froyland, Manu Kalia, Peter Koltai
{"title":"Spectral clustering of time-evolving networks using the inflated dynamic Laplacian for graphs","authors":"Gary Froyland, Manu Kalia, Peter Koltai","doi":"arxiv-2409.11984","DOIUrl":"https://doi.org/arxiv-2409.11984","url":null,"abstract":"Complex time-varying networks are prominent models for a wide variety of\u0000spatiotemporal phenomena. The functioning of networks depends crucially on\u0000their connectivity, yet reliable techniques for determining communities in\u0000spacetime networks remain elusive. We adapt successful spectral techniques from\u0000continuous-time dynamics on manifolds to the graph setting to fill this gap. We\u0000formulate an {it inflated dynamic Laplacian} for graphs and develop a spectral\u0000theory to underpin the corresponding algorithmic realisations. We develop\u0000spectral clustering approaches for both multiplex and non-multiplex networks,\u0000based on the eigenvectors of the inflated dynamic Laplacian and specialised\u0000Sparse EigenBasis Approximation (SEBA) post-processing of these eigenvectors.\u0000We demonstrate that our approach can outperform the Leiden algorithm applied\u0000both in spacetime and layer-by-layer, and we analyse voting data from the US\u0000senate (where senators come and go as congresses evolve) to quantify increasing\u0000polarisation in time.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and explicit formula for a semigroup related to some network problems with unbounded edges 与某些无边网络问题有关的半群的存在性和显公式
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-18 DOI: arxiv-2409.11903
Adam Błoch
{"title":"Existence and explicit formula for a semigroup related to some network problems with unbounded edges","authors":"Adam Błoch","doi":"arxiv-2409.11903","DOIUrl":"https://doi.org/arxiv-2409.11903","url":null,"abstract":"In this paper we consider an initial-boundary value problem related to some\u0000network dynamics where the underlying graph has unbounded edges. We show that\u0000there exists a C0-semigroup for this problem using a general result from the\u0000literature. We also find an explicit formula for this semigroup. This is\u0000achieved using the method of characteristics and then showing that the Laplace\u0000transform of the solution is equal to the resolvent operator of the generator.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"191 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Meromorphic functions whose action on their Julia sets is Non-Ergodic 对其朱利亚集的作用为非极性的单态函数
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-18 DOI: arxiv-2409.12127
Tao Chen, Yunping Jiang, Linda Keen
{"title":"Meromorphic functions whose action on their Julia sets is Non-Ergodic","authors":"Tao Chen, Yunping Jiang, Linda Keen","doi":"arxiv-2409.12127","DOIUrl":"https://doi.org/arxiv-2409.12127","url":null,"abstract":"the action of the function on its Julia set is still ergodic if some, but not\u0000all of the asymptotic values land on infinity, and the remaining ones land on a\u0000compact repeller. In this paper, we complete the characterization of ergodicity\u0000for Nevanlinna functions but proving that if all the asymptotic values land on\u0000infinity, then the Julia set is the whole sphere and the action of the map\u0000there is non-ergodic.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ergodic properties of infinite extension of symmetric interval exchange transformations 对称区间交换变换无限扩展的遍历特性
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-18 DOI: arxiv-2409.12168
Przemysław Berk, Frank Trujillo, Hao Wu
{"title":"Ergodic properties of infinite extension of symmetric interval exchange transformations","authors":"Przemysław Berk, Frank Trujillo, Hao Wu","doi":"arxiv-2409.12168","DOIUrl":"https://doi.org/arxiv-2409.12168","url":null,"abstract":"We prove that skew products with the cocycle given by the function\u0000$f(x)=a(x-1/2)$ with $aneq 0$ are ergodic for every ergodic symmetric IET in\u0000the base, thus giving the full characterization of ergodic extensions in this\u0000family. Moreover, we prove that under an additional natural assumption of\u0000unique ergodicity on the IET, we can replace $f$ with any differentiable\u0000function with a non-zero sum of jumps. Finally, by considering weakly mixing\u0000IETs instead of just ergodic, we show that the skew products with cocycle given\u0000by $f$ have infinite ergodic index.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computational Dynamical Systems 计算动力系统
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-18 DOI: arxiv-2409.12179
Jordan Cotler, Semon Rezchikov
{"title":"Computational Dynamical Systems","authors":"Jordan Cotler, Semon Rezchikov","doi":"arxiv-2409.12179","DOIUrl":"https://doi.org/arxiv-2409.12179","url":null,"abstract":"We study the computational complexity theory of smooth, finite-dimensional\u0000dynamical systems. Building off of previous work, we give definitions for what\u0000it means for a smooth dynamical system to simulate a Turing machine. We then\u0000show that 'chaotic' dynamical systems (more precisely, Axiom A systems) and\u0000'integrable' dynamical systems (more generally, measure-preserving systems)\u0000cannot robustly simulate universal Turing machines, although such machines can\u0000be robustly simulated by other kinds of dynamical systems. Subsequently, we\u0000show that any Turing machine that can be encoded into a structurally stable\u0000one-dimensional dynamical system must have a decidable halting problem, and\u0000moreover an explicit time complexity bound in instances where it does halt.\u0000More broadly, our work elucidates what it means for one 'machine' to simulate\u0000another, and emphasizes the necessity of defining low-complexity 'encoders' and\u0000'decoders' to translate between the dynamics of the simulation and the system\u0000being simulated. We highlight how the notion of a computational dynamical\u0000system leads to questions at the intersection of computational complexity\u0000theory, dynamical systems theory, and real algebraic geometry.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Consensus in Models for Opinion Dynamics with Generalized-Bias 带有普遍偏见的舆论动态模型中的共识
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-17 DOI: arxiv-2409.10809
Juan Paz, Camilo Rocha, Luis Tobòn, Frank Valencia
{"title":"Consensus in Models for Opinion Dynamics with Generalized-Bias","authors":"Juan Paz, Camilo Rocha, Luis Tobòn, Frank Valencia","doi":"arxiv-2409.10809","DOIUrl":"https://doi.org/arxiv-2409.10809","url":null,"abstract":"Interest is growing in social learning models where users share opinions and\u0000adjust their beliefs in response to others. This paper introduces\u0000generalized-bias opinion models, an extension of the DeGroot model, that\u0000captures a broader range of cognitive biases. These models can capture, among\u0000others, dynamic (changing) influences as well as ingroup favoritism and\u0000out-group hostility, a bias where agents may react differently to opinions from\u0000members of their own group compared to those from outside. The reactions are\u0000formalized as arbitrary functions that depend, not only on opinion difference,\u0000but also on the particular opinions of the individuals interacting. Under\u0000certain reasonable conditions, all agents (despite their biases) will converge\u0000to a consensus if the influence graph is strongly connected, as in the original\u0000DeGroot model. The proposed approach combines different biases, providing\u0000deeper insights into the mechanics of opinion dynamics and influence within\u0000social networks.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A first engineering principles model for dynamical simulation of cement pyro-process cyclones 用于水泥热法旋流器动态模拟的第一工程原理模型
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-17 DOI: arxiv-2409.10916
Jan Lorenz Svensen, Nicola Cantisani, Wilson Ricardo Leal da Silva, Javier Pigazo Merino, Dinesh Sampath, John Bagterp Jørgensen
{"title":"A first engineering principles model for dynamical simulation of cement pyro-process cyclones","authors":"Jan Lorenz Svensen, Nicola Cantisani, Wilson Ricardo Leal da Silva, Javier Pigazo Merino, Dinesh Sampath, John Bagterp Jørgensen","doi":"arxiv-2409.10916","DOIUrl":"https://doi.org/arxiv-2409.10916","url":null,"abstract":"We provide a cyclone model for dynamical simulations in the pyro-process of\u0000cement production. The model is given as an index-1 differential-algebraic\u0000equation (DAE) model based on first engineering principle. Using a systematic\u0000approach, the model integrates cyclone geometry, thermo-physical aspects,\u0000stoichiometry and kinetics, mass and energy balances, and algebraic equations\u0000for volume and internal energy. The paper provides simulation results that fit expected dynamics. The cyclone model is part of an overall model for dynamical simulations of\u0000the pyro-process in a cement plant. This model can be used in the design of\u0000control and optimization systems to improve energy efficiency and reduce CO2\u0000emission.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Ruelle operator for holomorphic correspondences 全态对应的鲁埃尔算子
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-17 DOI: arxiv-2409.11085
Shrihari Sridharan, Subith G
{"title":"A Ruelle operator for holomorphic correspondences","authors":"Shrihari Sridharan, Subith G","doi":"arxiv-2409.11085","DOIUrl":"https://doi.org/arxiv-2409.11085","url":null,"abstract":"In this paper, we extend the ideas of certain notions that one studies in\u0000thermodynamic formalism of maps to the context when the dynamics in the phase\u0000space evolves by complex holomorphic correspondences. Towards that end, we\u0000define the topological entropy of holomorphic correspondences using spanning\u0000sets. We then, define the pressure of a real-valued continuous function defined\u0000on the Riemann sphere and investigate the Ruelle operator with respect to the\u0000H\"{o}lder continuous function, however restricted on the support of the\u0000Dinh-Sibony measure.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Entropy for compact operators and results on entropy and specification 紧凑算子的熵以及关于熵和规范的结果
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-17 DOI: arxiv-2409.10844
Paulo Lupatini, Felipe Silva, Régis Varão
{"title":"Entropy for compact operators and results on entropy and specification","authors":"Paulo Lupatini, Felipe Silva, Régis Varão","doi":"arxiv-2409.10844","DOIUrl":"https://doi.org/arxiv-2409.10844","url":null,"abstract":"We prove that the specification property implies infinite topological entropy\u0000for operators acting on infinite dimensional $F$-spaces. Furthermore, we\u0000establish compact operators acting on Banach spaces exhibit finite entropy and\u0000the entropy depends exclusively on the operator's point spectrum. Additionally,\u0000we prove that the variational principle does not hold for compact operators\u0000acting on Banach spaces.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Averaging theory and catastrophes: The persistence of bifurcations under time-varying perturbations 平均理论与灾难：时变扰动下分岔的持续性
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-17 DOI: arxiv-2409.11054
Pedro C. C. R. Pereira, Mike R. Jeffrey, Douglas D. Novaes
{"title":"Averaging theory and catastrophes: The persistence of bifurcations under time-varying perturbations","authors":"Pedro C. C. R. Pereira, Mike R. Jeffrey, Douglas D. Novaes","doi":"arxiv-2409.11054","DOIUrl":"https://doi.org/arxiv-2409.11054","url":null,"abstract":"When a dynamical system is subject to a periodic perturbation, the averaging\u0000method can be applied to obtain an autonomous leading order `guiding system',\u0000placing the time dependence at higher orders. Recent research focused on\u0000investigating invariant structures in non-autonomous differential systems\u0000arising from hyperbolic structures in the guiding system, such as periodic\u0000orbits and invariant tori. The effect that bifurcations in the guiding system\u0000have on the original non-autonomous one has also been recently explored. This\u0000paper extends the study by providing a broader description of the dynamics that\u0000can emerge from non-hyperbolic structures of the guiding system. Specifically,\u0000we prove here that $K$-universal bifurcations in the guiding system persist in\u0000the original non-autonomous one, while non-versal bifurcations, such as the\u0000transcritical and pitchfork, do not, being instead perturbed into stable\u0000bifurcation families. We illustrate the results on examples of a fold, a\u0000transcritical, a pitchfork, and a saddle-focus. By applying these results to\u0000the physical scenario of systems with time-varying parameters, we show that the\u0000average parameter value becomes a bifurcation parameter of the averaged system.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信