1
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Yu H, Xue B, Zhang J, Liu RR, Liu Y, Meng F. Opinion cascade under perception bias in social networks. CHAOS (WOODBURY, N.Y.) 2023; 33:113107. [PMID: 37909902 DOI: 10.1063/5.0172121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2023] [Accepted: 10/09/2023] [Indexed: 11/03/2023]
Abstract
Opinion cascades, initiated by active opinions, offer a valuable avenue for exploring the dynamics of consensus and disagreement formation. Nevertheless, the impact of biased perceptions on opinion cascade, arising from the balance between global information and locally accessible information within network neighborhoods, whether intentionally or unintentionally, has received limited attention. In this study, we introduce a threshold model to simulate the opinion cascade process within social networks. Our findings reveal that consensus emerges only when the collective stubbornness of the population falls below a critical threshold. Additionally, as stubbornness decreases, we observe a higher prevalence of first-order and second-order phase transitions between consensus and disagreement. The emergence of disagreement can be attributed to the formation of echo chambers, which are tightly knit communities where agents' biased perceptions of active opinions are lower than their stubbornness, thus hindering the erosion of active opinions. This research establishes a valuable framework for investigating the relationship between perception bias and opinion formation, providing insights into addressing disagreement in the presence of biased information.
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Affiliation(s)
- Hao Yu
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Bin Xue
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Jianlin Zhang
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Run-Ran Liu
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Yu Liu
- International Academic Center of Complex Systems, Beijing Normal University, Zhuhai 519087, China
| | - Fanyuan Meng
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
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2
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Panahi S, Amaya N, Klickstein I, Novello G, Sorrentino F. Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks. Phys Rev E 2022; 105:014313. [PMID: 35193285 DOI: 10.1103/physreve.105.014313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 01/04/2022] [Indexed: 06/14/2023]
Abstract
We discuss here the application of the simultaneous block diagonalization (SBD) of matrices to the study of the stability of both complete and cluster synchronization in random (generic) networks. For both problems, we define indices that measure success (or failure) of application of the SBD technique in decoupling the stability problem into problems of lower dimensionality. We then see that in the case of random networks the extent of the dimensionality reduction achievable is the same as that produced by application of a trivial transformation.
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Affiliation(s)
- Shirin Panahi
- University of New Mexico, Albuquerque, New Mexico 80131, USA
| | - Nelson Amaya
- University of New Mexico, Albuquerque, New Mexico 80131, USA
| | | | - Galen Novello
- University of New Mexico, Albuquerque, New Mexico 80131, USA
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3
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Cui D, Shen AZ, Zhang Y. MLCOR Model for Suppressing the Cascade of Edge Failures in Complex Network. INT J PATTERN RECOGN 2021. [DOI: 10.1142/s0218001421510162] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
As a decisive parameter of network robustness and network economy, the capacity of network edges can directly affect the operation stability and the construction cost of the network. This paper proposes a multilevel load–capacity optimal relationship (MLCOR) model that can substantially improve the network economy on the premise of network safety. The model is verified in artificially created networks including free-scale networks, small-world networks, and in the real network structure of the Shanghai Metro network as well. By numerical simulation, it is revealed that under the premise of ensuring the stability of the network from the destruction caused by initial internal or external damage on edge, the MLCOR model can effectively reduce the cost of the entire network compared to the other two linear load–capacity models regardless of what extent of the destruction that the network edges suffer initially. It is also proved that there exists an optimal tunable parameter and the corresponding optimal network cost for any BA and NW network topology, which can provide the reference for setting reasonable capacities for network edges in a real network at the stage of network planning and construction, promoting security and stability of network operation.
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Affiliation(s)
- Dan Cui
- School of Management, Shanghai University of Engineering Science, Shanghai 201620, P. R. China
| | - Ai Zhong Shen
- Faculty of Professional Finance and Accountancy, Shanghai Business School, Shanghai 200235, P. R. China
| | - Yingli Zhang
- College of Economics & Management, Shanghai Ocean University, Shanghai 201306, P. R. China
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4
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Zanin M, Aitya NA, Basilio J, Baumbach J, Benis A, Behera CK, Bucholc M, Castiglione F, Chouvarda I, Comte B, Dao TT, Ding X, Pujos-Guillot E, Filipovic N, Finn DP, Glass DH, Harel N, Iesmantas T, Ivanoska I, Joshi A, Boudjeltia KZ, Kaoui B, Kaur D, Maguire LP, McClean PL, McCombe N, de Miranda JL, Moisescu MA, Pappalardo F, Polster A, Prasad G, Rozman D, Sacala I, Sanchez-Bornot JM, Schmid JA, Sharp T, Solé-Casals J, Spiwok V, Spyrou GM, Stalidzans E, Stres B, Sustersic T, Symeonidis I, Tieri P, Todd S, Van Steen K, Veneva M, Wang DH, Wang H, Wang H, Watterson S, Wong-Lin K, Yang S, Zou X, Schmidt HH. An Early Stage Researcher's Primer on Systems Medicine Terminology. NETWORK AND SYSTEMS MEDICINE 2021; 4:2-50. [PMID: 33659919 PMCID: PMC7919422 DOI: 10.1089/nsm.2020.0003] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/27/2020] [Indexed: 12/19/2022] Open
Abstract
Background: Systems Medicine is a novel approach to medicine, that is, an interdisciplinary field that considers the human body as a system, composed of multiple parts and of complex relationships at multiple levels, and further integrated into an environment. Exploring Systems Medicine implies understanding and combining concepts coming from diametral different fields, including medicine, biology, statistics, modeling and simulation, and data science. Such heterogeneity leads to semantic issues, which may slow down implementation and fruitful interaction between these highly diverse fields. Methods: In this review, we collect and explain more than100 terms related to Systems Medicine. These include both modeling and data science terms and basic systems medicine terms, along with some synthetic definitions, examples of applications, and lists of relevant references. Results: This glossary aims at being a first aid kit for the Systems Medicine researcher facing an unfamiliar term, where he/she can get a first understanding of them, and, more importantly, examples and references for digging into the topic.
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Affiliation(s)
- Massimiliano Zanin
- Centro de Tecnología Biomédica, Universidad Politécnica de Madrid, Madrid, Spain
| | - Nadim A.A. Aitya
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - José Basilio
- Center for Physiology and Pharmacology, Institute of Vascular Biology and Thrombosis Research, Medical University of Vienna, Vienna, Austria
| | - Jan Baumbach
- TUM School of Life Sciences Weihenstephan, Technical University of Munich, Freising, Germany
| | - Arriel Benis
- Faculty of Technology Management, Holon Institute of Technology (HIT), Holon, Israel
| | - Chandan K. Behera
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - Magda Bucholc
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - Filippo Castiglione
- CNR National Research Council, IAC Institute for Applied Computing, Rome, Italy
| | - Ioanna Chouvarda
- Lab of Computing, Medical Informatics, and Biomedical Imaging Technologies, School of Medicine, Aristotle University of Thessaloniki, Thessaloniki, Greece
| | - Blandine Comte
- Université Clermont Auvergne, INRAE, UNH, Plateforme d'Exploration du Métabolisme, MetaboHUB Clermont, Clermont-Ferrand, France
| | - Tien-Tuan Dao
- Biomechanics and Bioengineering Laboratory (UMR CNRS 7338), Université de Technologie de Compiègne, Compiègne, France
- Labex MS2T “Control of Technological Systems-of-Systems,” CNRS and Université de Technologie de Compiègne, Compiègne, France
| | - Xuemei Ding
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - Estelle Pujos-Guillot
- Université Clermont Auvergne, INRAE, UNH, Plateforme d'Exploration du Métabolisme, MetaboHUB Clermont, Clermont-Ferrand, France
| | - Nenad Filipovic
- Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia
- Bioengineering Research and Development Center (BioIRC), Kragujevac, Serbia
- Steinbeis Advanced Risk Technologies Institute doo Kragujevac, Kragujevac, Serbia
| | - David P. Finn
- Pharmacology and Therapeutics, School of Medicine, Galway Neuroscience Centre, National University of Ireland, Galway, Republic of Ireland
| | - David H. Glass
- School of Computing, Ulster University, Ulster, United Kingdom
| | - Nissim Harel
- Faculty of Sciences, Holon Institute of Technology (HIT), Holon, Israel
| | - Tomas Iesmantas
- Department of Mathematics and Natural Sciences, Kaunas University of Technology, Kaunas, Lithuania
| | - Ilinka Ivanoska
- Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University, Skopje, Macedonia
| | - Alok Joshi
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - Karim Zouaoui Boudjeltia
- Laboratory of Experimental Medicine (ULB 222), Medicine Faculty, Université libre de Bruxelles, CHU de Charleroi, Charleroi, Belgium
| | - Badr Kaoui
- Biomechanics and Bioengineering Laboratory (UMR CNRS 7338), Université de Technologie de Compiègne, Compiègne, France
- Labex MS2T “Control of Technological Systems-of-Systems,” CNRS and Université de Technologie de Compiègne, Compiègne, France
| | - Daman Kaur
- Northern Ireland Centre for Stratified Medicine, Biomedical Sciences Research Institute, Ulster University, Ulster, United Kingdom
| | - Liam P. Maguire
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - Paula L. McClean
- Northern Ireland Centre for Stratified Medicine, Biomedical Sciences Research Institute, Ulster University, Ulster, United Kingdom
| | - Niamh McCombe
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - João Luís de Miranda
- Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Portalegre, Portalegre, Portugal
- Centro de Recursos Naturais e Ambiente (CERENA), Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
| | | | | | - Annikka Polster
- Centre for Molecular Medicine Norway (NCMM), Forskningparken, Oslo, Norway
| | - Girijesh Prasad
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - Damjana Rozman
- Centre for Functional Genomics and Bio-Chips, Institute of Biochemistry, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia
| | - Ioan Sacala
- Faculty of Automatic Control and Computers, University Politehnica of Bucharest, Bucharest, Romania
| | - Jose M. Sanchez-Bornot
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - Johannes A. Schmid
- Center for Physiology and Pharmacology, Institute of Vascular Biology and Thrombosis Research, Medical University of Vienna, Vienna, Austria
| | - Trevor Sharp
- Department of Pharmacology, University of Oxford, Oxford, United Kingdom
| | - Jordi Solé-Casals
- Data and Signal Processing Research Group, University of Vic–Central University of Catalonia, Vic, Spain
- Department of Psychiatry, University of Cambridge, Cambridge, United Kingdom
- College of Artificial Intelligence, Nankai University, Tianjin, China
| | - Vojtěch Spiwok
- Department of Biochemistry and Microbiology, University of Chemistry and Technology, Prague, Czech Republic
| | - George M. Spyrou
- The Cyprus School of Molecular Medicine, The Cyprus Institute of Neurology and Genetics, Nicosia, Cyprus
| | - Egils Stalidzans
- Computational Systems Biology Group, Institute of Microbiology and Biotechnology, University of Latvia, Riga, Latvia
| | - Blaž Stres
- Department of Animal Science, Biotechnical Faculty, University of Ljubljana, Ljubljana, Slovenia
- Faculty of Civil and Geodetic Engineering, University of Ljubljana, Ljubljana, Slovenia
- Department of Automation, Biocybernetics and Robotics, Jozef Stefan Institute, Ljubljana, Slovenia
| | - Tijana Sustersic
- Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia
- Bioengineering Research and Development Center (BioIRC), Kragujevac, Serbia
- Steinbeis Advanced Risk Technologies Institute doo Kragujevac, Kragujevac, Serbia
| | - Ioannis Symeonidis
- Center for Research and Technology Hellas, Hellenic Institute of Transport, Thessaloniki, Greece
| | - Paolo Tieri
- CNR National Research Council, IAC Institute for Applied Computing, Rome, Italy
| | - Stephen Todd
- Altnagelvin Area Hospital, Western Health and Social Care Trust, Altnagelvin, United Kingdom
| | - Kristel Van Steen
- BIO3-Systems Genetics, GIGA-R, University of Liege, Liege, Belgium
- BIO3-Systems Medicine, Department of Human Genetics, KU Leuven, Leuven, Belgium
| | | | - Da-Hui Wang
- State Key Laboratory of Cognitive Neuroscience and Learning, and School of Systems Science, Beijing Normal University, Beijing, China
| | - Haiying Wang
- School of Computing, Ulster University, Ulster, United Kingdom
| | - Hui Wang
- School of Computing, Ulster University, Ulster, United Kingdom
| | - Steven Watterson
- Northern Ireland Centre for Stratified Medicine, Ulster University, Londonderry, United Kingdom
| | - KongFatt Wong-Lin
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - Su Yang
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Ulster, United Kingdom
| | - Xin Zou
- Shanghai Centre for Systems Biomedicine, Key Laboratory of Systems Biomedicine (Ministry of Education), Shanghai Jiao Tong University, Shanghai, China
| | - Harald H.H.W. Schmidt
- Faculty of Health, Medicine & Life Science, Maastricht University, Maastricht, The Netherlands
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5
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Lin ZH, Feng M, Tang M, Liu Z, Xu C, Hui PM, Lai YC. Non-Markovian recovery makes complex networks more resilient against large-scale failures. Nat Commun 2020; 11:2490. [PMID: 32427821 PMCID: PMC7237476 DOI: 10.1038/s41467-020-15860-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2019] [Accepted: 03/26/2020] [Indexed: 11/10/2022] Open
Abstract
Non-Markovian spontaneous recovery processes with a time delay (memory) are ubiquitous in the real world. How does the non-Markovian characteristic affect failure propagation in complex networks? We consider failures due to internal causes at the nodal level and external failures due to an adverse environment, and develop a pair approximation analysis taking into account the two-node correlation. In general, a high failure stationary state can arise, corresponding to large-scale failures that can significantly compromise the functioning of the network. We uncover a striking phenomenon: memory associated with nodal recovery can counter-intuitively make the network more resilient against large-scale failures. In natural systems, the intrinsic non-Markovian characteristic of nodal recovery may thus be one reason for their resilience. In engineering design, incorporating certain non-Markovian features into the network may be beneficial to equipping it with a strong resilient capability to resist catastrophic failures.
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Affiliation(s)
- Zhao-Hua Lin
- State Key Laboratory of Precision Spectroscopy and School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, China
| | - Mi Feng
- Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai, 200241, China
| | - Ming Tang
- State Key Laboratory of Precision Spectroscopy and School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, China. .,Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai, 200241, China.
| | - Zonghua Liu
- State Key Laboratory of Precision Spectroscopy and School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, China.
| | - Chen Xu
- School of Physical Science and Technology, Soochow University, Suzhou, 215006, China
| | - Pak Ming Hui
- Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, 85287, USA
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6
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Liu RR, Jia CX, Lai YC. Asymmetry in interdependence makes a multilayer system more robust against cascading failures. Phys Rev E 2019; 100:052306. [PMID: 31870033 DOI: 10.1103/physreve.100.052306] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2019] [Indexed: 11/07/2022]
Abstract
Multilayer networked systems are ubiquitous in nature and engineering, and the robustness of these systems against failures is of great interest. A main line of theoretical pursuit has been percolation-induced cascading failures, where interdependence between network layers is conveniently and tacitly assumed to be symmetric. In the real world, interdependent interactions are generally asymmetric. To uncover and quantify the impact of asymmetry in interdependence on network robustness, we focus on percolation dynamics in double-layer systems and implement the following failure mechanism: Once a node in a network layer fails, the damage it can cause depends not only on its position in the layer but also on the position of its counterpart neighbor in the other layer. We find that the characteristics of the percolation transition depend on the degree of asymmetry, where the striking phenomenon of a switch in the nature of the phase transition from first to second order arises. We derive a theory to calculate the percolation transition points in both network layers, as well as the transition switching point, with strong numerical support from synthetic and empirical networks. Not only does our work shed light on the factors that determine the robustness of multilayer networks against cascading failures, but it also provides a scenario by which the system can be designed or controlled to reach a desirable level of resilience.
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Affiliation(s)
- Run-Ran Liu
- Alibaba Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou, Zhejiang 311121, China
| | - Chun-Xiao Jia
- Alibaba Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou, Zhejiang 311121, China
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.,Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
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7
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Liu RR, Eisenberg DA, Seager TP, Lai YC. The "weak" interdependence of infrastructure systems produces mixed percolation transitions in multilayer networks. Sci Rep 2018; 8:2111. [PMID: 29391411 PMCID: PMC5794991 DOI: 10.1038/s41598-018-20019-7] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2017] [Accepted: 01/09/2018] [Indexed: 11/25/2022] Open
Abstract
Previous studies of multilayer network robustness model cascading failures via a node-to-node percolation process that assumes "strong" interdependence across layers-once a node in any layer fails, its neighbors in other layers fail immediately and completely with all links removed. This assumption is not true of real interdependent infrastructures that have emergency procedures to buffer against cascades. In this work, we consider a node-to-link failure propagation mechanism and establish "weak" interdependence across layers via a tolerance parameter α which quantifies the likelihood that a node survives when one of its interdependent neighbors fails. Analytical and numerical results show that weak interdependence produces a striking phenomenon: layers at different positions within the multilayer system experience distinct percolation transitions. Especially, layers with high super degree values percolate in an abrupt manner, while those with low super degree values exhibit both continuous and discontinuous transitions. This novel phenomenon we call mixed percolation transitions has significant implications for network robustness. Previous results that do not consider cascade tolerance and layer super degree may be under- or over-estimating the vulnerability of real systems. Moreover, our model reveals how nodal protection activities influence failure dynamics in interdependent, multilayer systems.
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Affiliation(s)
- Run-Ran Liu
- Alibaba Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou, Zhejiang, 311121, China.
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ, 85287, USA.
| | - Daniel A Eisenberg
- School of Sustainable Engineering and Built Environment, Arizona State University, Tempe, AZ, 85287, USA
| | - Thomas P Seager
- School of Sustainable Engineering and Built Environment, Arizona State University, Tempe, AZ, 85287, USA
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ, 85287, USA
- Department of Physics, Arizona State University, Tempe, AZ, 85287, USA
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8
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Shu P, Gao L, Zhao P, Wang W, Stanley HE. Social contagions on interdependent lattice networks. Sci Rep 2017; 7:44669. [PMID: 28300198 PMCID: PMC5353708 DOI: 10.1038/srep44669] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2016] [Accepted: 02/13/2017] [Indexed: 11/15/2022] Open
Abstract
Although an increasing amount of research is being done on the dynamical processes on interdependent spatial networks, knowledge of how interdependent spatial networks influence the dynamics of social contagion in them is sparse. Here we present a novel non-Markovian social contagion model on interdependent spatial networks composed of two identical two-dimensional lattices. We compare the dynamics of social contagion on networks with different fractions of dependency links and find that the density of final recovered nodes increases as the number of dependency links is increased. We use a finite-size analysis method to identify the type of phase transition in the giant connected components (GCC) of the final adopted nodes and find that as we increase the fraction of dependency links, the phase transition switches from second-order to first-order. In strong interdependent spatial networks with abundant dependency links, increasing the fraction of initial adopted nodes can induce the switch from a first-order to second-order phase transition associated with social contagion dynamics. In networks with a small number of dependency links, the phase transition remains second-order. In addition, both the second-order and first-order phase transition points can be decreased by increasing the fraction of dependency links or the number of initially-adopted nodes.
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Affiliation(s)
- Panpan Shu
- School of Sciences, Xi’an University of Technology, Xi’an, 710054, China
| | - Lei Gao
- Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - Pengcheng Zhao
- School of Physics and Optoelectronic Engineering, Xidian University, Xi’an, 710071, China
| | - Wei Wang
- Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, 610054, China
- Big data research center, University of Electronic Science and Technology of China, Chengdu 610054, China
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts, 02215, USA
| | - H. Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts, 02215, USA
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9
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Growth, collapse, and self-organized criticality in complex networks. Sci Rep 2016; 6:24445. [PMID: 27079515 PMCID: PMC4832202 DOI: 10.1038/srep24445] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2016] [Accepted: 03/30/2016] [Indexed: 11/26/2022] Open
Abstract
Network growth is ubiquitous in nature (e.g., biological networks) and technological systems (e.g., modern infrastructures). To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the question of whether a complex network of nonlinear oscillators can maintain its synchronization stability as it expands. We find that a large scale avalanche over the entire network can be triggered in the sense that the individual nodal dynamics diverges from the synchronous state in a cascading manner within a relatively short time period. In particular, after an initial stage of linear growth, the network typically evolves into a critical state where the addition of a single new node can cause a group of nodes to lose synchronization, leading to synchronization collapse for the entire network. A statistical analysis reveals that the collapse size is approximately algebraically distributed, indicating the emergence of self-organized criticality. We demonstrate the generality of the phenomenon of synchronization collapse using a variety of complex network models, and uncover the underlying dynamical mechanism through an eigenvector analysis.
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10
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Kobayashi T. Trend-driven information cascades on random networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062823. [PMID: 26764760 DOI: 10.1103/physreve.92.062823] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2015] [Indexed: 06/05/2023]
Abstract
Threshold models of global cascades have been extensively used to model real-world collective behavior, such as the contagious spread of fads and the adoption of new technologies. A common property of those cascade models is that a vanishingly small seed fraction can spread to a finite fraction of an infinitely large network through local infections. In social and economic networks, however, individuals' behavior is often influenced not only by what their direct neighbors are doing, but also by what the majority of people are doing as a trend. A trend affects individuals' behavior while individuals' behavior creates a trend. To analyze such a complex interplay between local- and global-scale phenomena, I generalize the standard threshold model by introducing a type of node called global nodes (or trend followers), whose activation probability depends on a global-scale trend, specifically the percentage of activated nodes in the population. The model shows that global nodes play a role as accelerating cascades once a trend emerges while reducing the probability of a trend emerging. Global nodes thus either facilitate or inhibit cascades, suggesting that a moderate share of trend followers may maximize the average size of cascades.
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Affiliation(s)
- Teruyoshi Kobayashi
- Graduate School of Economics, Kobe University, 2-1 Rokkodai, Nada, Kobe 657-8501, Japan
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11
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Gao J, Zhou T, Hu Y. Bootstrap percolation on spatial networks. Sci Rep 2015; 5:14662. [PMID: 26423347 PMCID: PMC4589777 DOI: 10.1038/srep14662] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2015] [Accepted: 09/03/2015] [Indexed: 11/11/2022] Open
Abstract
Bootstrap percolation is a general representation of some networked activation process, which has found applications in explaining many important social phenomena, such as the propagation of information. Inspired by some recent findings on spatial structure of online social networks, here we study bootstrap percolation on undirected spatial networks, with the probability density function of long-range links' lengths being a power law with tunable exponent. Setting the size of the giant active component as the order parameter, we find a parameter-dependent critical value for the power-law exponent, above which there is a double phase transition, mixed of a second-order phase transition and a hybrid phase transition with two varying critical points, otherwise there is only a second-order phase transition. We further find a parameter-independent critical value around -1, about which the two critical points for the double phase transition are almost constant. To our surprise, this critical value -1 is just equal or very close to the values of many real online social networks, including LiveJournal, HP Labs email network, Belgian mobile phone network, etc. This work helps us in better understanding the self-organization of spatial structure of online social networks, in terms of the effective function for information spreading.
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Affiliation(s)
- Jian Gao
- CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Tao Zhou
- CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Yanqing Hu
- School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
- School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China
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12
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Feng L, Hu Y, Li B, Stanley HE, Havlin S, Braunstein LA. Competing for Attention in Social Media under Information Overload Conditions. PLoS One 2015; 10:e0126090. [PMID: 26161956 PMCID: PMC4498816 DOI: 10.1371/journal.pone.0126090] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2015] [Accepted: 03/23/2015] [Indexed: 11/21/2022] Open
Abstract
Modern social media are becoming overloaded with information because of the rapidly-expanding number of information feeds. We analyze the user-generated content in Sina Weibo, and find evidence that the spread of popular messages often follow a mechanism that differs from the spread of disease, in contrast to common belief. In this mechanism, an individual with more friends needs more repeated exposures to spread further the information. Moreover, our data suggest that for certain messages the chance of an individual to share the message is proportional to the fraction of its neighbours who shared it with him/her, which is a result of competition for attention. We model this process using a fractional susceptible infected recovered (FSIR) model, where the infection probability of a node is proportional to its fraction of infected neighbors. Our findings have dramatic implications for information contagion. For example, using the FSIR model we find that real-world social networks have a finite epidemic threshold in contrast to the zero threshold in disease epidemic models. This means that when individuals are overloaded with excess information feeds, the information either reaches out the population if it is above the critical epidemic threshold, or it would never be well received.
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Affiliation(s)
- Ling Feng
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117542, Singapore
- Complex Systems Programme, Institute of High Performance Computing, Agency for Science Technology and Research, 138632, Singapore
| | - Yanqing Hu
- School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China
- School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
| | - Baowen Li
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117542, Singapore
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092, Shanghai, China
| | - H. Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, United States of America
| | - Shlomo Havlin
- Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
| | - Lidia A. Braunstein
- Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), Universidad Nacional de Mar del Plata-CONICET, Funes 3350, (7600) Mar del Plata, Argentina
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13
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Wang W, Tang M, Zhang HF, Lai YC. Dynamics of social contagions with memory of nonredundant information. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012820. [PMID: 26274238 DOI: 10.1103/physreve.92.012820] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2015] [Indexed: 05/20/2023]
Abstract
A key ingredient in social contagion dynamics is reinforcement, as adopting a certain social behavior requires verification of its credibility and legitimacy. Memory of nonredundant information plays an important role in reinforcement, which so far has eluded theoretical analysis. We first propose a general social contagion model with reinforcement derived from nonredundant information memory. Then, we develop a unified edge-based compartmental theory to analyze this model, and a remarkable agreement with numerics is obtained on some specific models. We use a spreading threshold model as a specific example to understand the memory effect, in which each individual adopts a social behavior only when the cumulative pieces of information that the individual received from his or her neighbors exceeds an adoption threshold. Through analysis and numerical simulations, we find that the memory characteristic markedly affects the dynamics as quantified by the final adoption size. Strikingly, we uncover a transition phenomenon in which the dependence of the final adoption size on some key parameters, such as the transmission probability, can change from being discontinuous to being continuous. The transition can be triggered by proper parameters and structural perturbations to the system, such as decreasing individuals' adoption threshold, increasing initial seed size, or enhancing the network heterogeneity.
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Affiliation(s)
- Wei Wang
- Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Ming Tang
- Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China
- State key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Hai-Feng Zhang
- School of Mathematical Science, Anhui University, Hefei 230039, China
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
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14
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Brummitt CD, Kobayashi T. Cascades in multiplex financial networks with debts of different seniority. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062813. [PMID: 26172760 DOI: 10.1103/physreve.91.062813] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2015] [Indexed: 06/04/2023]
Abstract
The seniority of debt, which determines the order in which a bankrupt institution repays its debts, is an important and sometimes contentious feature of financial crises, yet its impact on systemwide stability is not well understood. We capture seniority of debt in a multiplex network, a graph of nodes connected by multiple types of edges. Here an edge between banks denotes a debt contract of a certain level of seniority. Next we study cascading default. There exist multiple kinds of bankruptcy, indexed by the highest level of seniority at which a bank cannot repay all its debts. Self-interested banks would prefer that all their loans be made at the most senior level. However, mixing debts of different seniority levels makes the system more stable in that it shrinks the set of network densities for which bankruptcies spread widely. We compute the optimal ratio of senior to junior debts, which we call the optimal seniority ratio, for two uncorrelated Erdős-Rényi networks. If institutions erode their buffer against insolvency, then this optimal seniority ratio rises; in other words, if default thresholds fall, then more loans should be senior. We generalize the analytical results to arbitrarily many levels of seniority and to heavy-tailed degree distributions.
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Affiliation(s)
- Charles D Brummitt
- Center for the Management of Systemic Risk, Columbia University, New York, New York 10027, USA
| | - Teruyoshi Kobayashi
- Graduate School of Economics, Kobe University, 2-1 Rokkodai, Nada, Kobe 657-8501, Japan
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Watanabe S, Kabashima Y. Cavity-based robustness analysis of interdependent networks: influences of intranetwork and internetwork degree-degree correlations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012808. [PMID: 24580282 DOI: 10.1103/physreve.89.012808] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2013] [Indexed: 06/03/2023]
Abstract
We develop a methodology for analyzing the percolation phenomena of two mutually coupled (interdependent) networks based on the cavity method of statistical mechanics. In particular, we take into account the influence of degree-degree correlations inside and between the networks on the network robustness against targeted (random degree-dependent) attacks and random failures. We show that the developed methodology is reduced to the well-known generating function formalism in the absence of degree-degree correlations. The validity of the developed methodology is confirmed by a comparison with the results of numerical experiments. Our analytical results indicate that the robustness of the interdependent networks depends on both the intranetwork and internetwork degree-degree correlations in a nontrivial way for both cases of random failures and targeted attacks.
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Affiliation(s)
- Shunsuke Watanabe
- Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 2268502, Japan
| | - Yoshiyuki Kabashima
- Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 2268502, Japan
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