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Di Gaetano L, Carugno G, Battiston F, Coghi F. Dynamical Fluctuations of Random Walks in Higher-Order Networks. PHYSICAL REVIEW LETTERS 2024; 133:107401. [PMID: 39303236 DOI: 10.1103/physrevlett.133.107401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Revised: 06/04/2024] [Accepted: 07/26/2024] [Indexed: 09/22/2024]
Abstract
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate how fluctuations of a dynamical quantity of a random walk exploring a higher-order network arise over time. In the quenched case, where the hypergraph structure is fixed, through large deviation theory we show that the appearance of rare events is hampered in nodes with many higher-order interactions, and promoted elsewhere. Dynamical fluctuations are further boosted in an annealed scenario, where both the diffusion process and higher-order interactions evolve in time. Here, extreme fluctuations generated by optimal higher-order configurations can be predicted in the limit of a saddle-point approximation. Our study lays the groundwork for a wide and general theory of fluctuations and rare events in higher-order networks.
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Affiliation(s)
| | | | | | - Francesco Coghi
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SEa-106 91 Stockholm, Sweden
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Han Z, Liu L, Wang X, Hao Y, Zheng H, Tang S, Zheng Z. Probabilistic activity driven model of temporal simplicial networks and its application on higher-order dynamics. CHAOS (WOODBURY, N.Y.) 2024; 34:023137. [PMID: 38407398 DOI: 10.1063/5.0167123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 01/27/2024] [Indexed: 02/27/2024]
Abstract
Network modeling characterizes the underlying principles of structural properties and is of vital significance for simulating dynamical processes in real world. However, bridging structure and dynamics is always challenging due to the multiple complexities in real systems. Here, through introducing the individual's activity rate and the possibility of group interaction, we propose a probabilistic activity-driven (PAD) model that could generate temporal higher-order networks with both power-law and high-clustering characteristics, which successfully links the two most critical structural features and a basic dynamical pattern in extensive complex systems. Surprisingly, the power-law exponents and the clustering coefficients of the aggregated PAD network could be tuned in a wide range by altering a set of model parameters. We further provide an approximation algorithm to select the proper parameters that can generate networks with given structural properties, the effectiveness of which is verified by fitting various real-world networks. Finally, we construct the co-evolution framework of the PAD model and higher-order contagion dynamics and derive the critical conditions for phase transition and bistable phenomenon using theoretical and numerical methods. Results show that tendency of participating in higher-order interactions can promote the emergence of bistability but delay the outbreak under heterogeneous activity rates. Our model provides a basic tool to reproduce complex structural properties and to study the widespread higher-order dynamics, which has great potential for applications across fields.
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Affiliation(s)
- Zhihao Han
- Institute of Artificial Intelligence, Beihang University, Beijing 100191, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing 100191, China
| | - Longzhao Liu
- Institute of Artificial Intelligence, Beihang University, Beijing 100191, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing 100191, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing 100191, China
- Zhongguancun Laboratory, Beijing 100094, People's Republic of China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing 100191, China
- PengCheng Laboratory, Shenzhen 518055, China
| | - Xin Wang
- Institute of Artificial Intelligence, Beihang University, Beijing 100191, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing 100191, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing 100191, China
- Zhongguancun Laboratory, Beijing 100094, People's Republic of China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing 100191, China
- PengCheng Laboratory, Shenzhen 518055, China
| | - Yajing Hao
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing 100191, China
- School of Mathematical Sciences, Beihang University, Beijing 100191, China
| | - Hongwei Zheng
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing 100191, China
- Beijing Academy of Blockchain and Edge Computing (BABEC), Beijing 100085, China
| | - Shaoting Tang
- Institute of Artificial Intelligence, Beihang University, Beijing 100191, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing 100191, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing 100191, China
- Zhongguancun Laboratory, Beijing 100094, People's Republic of China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing 100191, China
- PengCheng Laboratory, Shenzhen 518055, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai 264003, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
| | - Zhiming Zheng
- Institute of Artificial Intelligence, Beihang University, Beijing 100191, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing 100191, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing 100191, China
- Zhongguancun Laboratory, Beijing 100094, People's Republic of China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing 100191, China
- PengCheng Laboratory, Shenzhen 518055, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai 264003, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
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