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Deng S, Ódor G. Chimera-like states in neural networks and power systems. CHAOS (WOODBURY, N.Y.) 2024; 34:033135. [PMID: 38526980 DOI: 10.1063/5.0154581] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Accepted: 02/27/2024] [Indexed: 03/27/2024]
Abstract
Partial, frustrated synchronization, and chimera-like states are expected to occur in Kuramoto-like models if the spectral dimension of the underlying graph is low: ds<4. We provide numerical evidence that this really happens in the case of the high-voltage power grid of Europe (ds<2), a large human connectome (KKI113) and in the case of the largest, exactly known brain network corresponding to the fruit-fly (FF) connectome (ds<4), even though their graph dimensions are much higher, i.e., dgEU≃2.6(1) and dgFF≃5.4(1), dgKKI113≃3.4(1). We provide local synchronization results of the first- and second-order (Shinomoto) Kuramoto models by numerical solutions on the FF and the European power-grid graphs, respectively, and show the emergence of chimera-like patterns on the graph community level as well as by the local order parameters.
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Affiliation(s)
- Shengfeng Deng
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Géza Ódor
- Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, P.O. Box 49, Budapest H-1525, Hungary
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Papo D, Buldú JM. Does the brain behave like a (complex) network? I. Dynamics. Phys Life Rev 2024; 48:47-98. [PMID: 38145591 DOI: 10.1016/j.plrev.2023.12.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 12/10/2023] [Indexed: 12/27/2023]
Abstract
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.
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Affiliation(s)
- D Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, Ferrara, Italy; Center for Translational Neurophysiology, Fondazione Istituto Italiano di Tecnologia, Ferrara, Italy.
| | - J M Buldú
- Complex Systems Group & G.I.S.C., Universidad Rey Juan Carlos, Madrid, Spain
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Guo Z, Zhao X, Yao L, Long Z. Improved brain community structure detection by two-step weighted modularity maximization. PLoS One 2023; 18:e0295428. [PMID: 38064462 PMCID: PMC10707683 DOI: 10.1371/journal.pone.0295428] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 11/21/2023] [Indexed: 12/18/2023] Open
Abstract
The human brain can be regarded as a complex network with interacting connections between brain regions. Complex brain network analyses have been widely applied to functional magnetic resonance imaging (fMRI) data and have revealed the existence of community structures in brain networks. The identification of communities may provide insight into understanding the topological functions of brain networks. Among various community detection methods, the modularity maximization (MM) method has the advantages of model conciseness, fast convergence and strong adaptability to large-scale networks and has been extended from single-layer networks to multilayer networks to investigate the community structure changes of brain networks. However, the problems of MM, suffering from instability and failing to detect hierarchical community structure in networks, largely limit the application of MM in the community detection of brain networks. In this study, we proposed the weighted modularity maximization (WMM) method by using the weight matrix to weight the adjacency matrix and improve the performance of MM. Moreover, we further proposed the two-step WMM method to detect the hierarchical community structures of networks by utilizing node attributes. The results of the synthetic networks without node attributes demonstrated that WMM showed better partition accuracy than both MM and robust MM and better stability than MM. The two-step WMM method showed better accuracy of community partitioning than WMM for synthetic networks with node attributes. Moreover, the results of resting state fMRI (rs-fMRI) data showed that two-step WMM had the advantage of detecting the hierarchical communities over WMM and was more insensitive to the density of the rs-fMRI networks than WMM.
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Affiliation(s)
- Zhitao Guo
- School of Artificial Intelligence, Beijing Normal University, Beijing, China
| | - Xiaojie Zhao
- School of Artificial Intelligence, Beijing Normal University, Beijing, China
| | - Li Yao
- School of Artificial Intelligence, Beijing Normal University, Beijing, China
| | - Zhiying Long
- School of Artificial Intelligence, Beijing Normal University, Beijing, China
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Wang SH, Siebenhühner F, Arnulfo G, Myrov V, Nobili L, Breakspear M, Palva S, Palva JM. Critical-like Brain Dynamics in a Continuum from Second- to First-Order Phase Transition. J Neurosci 2023; 43:7642-7656. [PMID: 37816599 PMCID: PMC10634584 DOI: 10.1523/jneurosci.1889-22.2023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Revised: 06/07/2023] [Accepted: 09/25/2023] [Indexed: 10/12/2023] Open
Abstract
The classic brain criticality hypothesis postulates that the brain benefits from operating near a continuous second-order phase transition. Slow feedback regulation of neuronal activity could, however, lead to a discontinuous first-order transition and thereby bistable activity. Observations of bistability in awake brain activity have nonetheless remained scarce and its functional significance unclear. Moreover, there is no empirical evidence to support the hypothesis that the human brain could flexibly operate near either a first- or second-order phase transition despite such a continuum being common in models. Here, using computational modeling, we found bistable synchronization dynamics to emerge through elevated positive feedback and occur exclusively in a regimen of critical-like dynamics. We then assessed bistability in vivo with resting-state MEG in healthy adults (7 females, 11 males) and stereo-electroencephalography in epilepsy patients (28 females, 36 males). This analysis revealed that a large fraction of the neocortices exhibited varying degrees of bistability in neuronal oscillations from 3 to 200 Hz. In line with our modeling results, the neuronal bistability was positively correlated with classic assessment of brain criticality across narrow-band frequencies. Excessive bistability was predictive of epileptic pathophysiology in the patients, whereas moderate bistability was positively correlated with task performance in the healthy subjects. These empirical findings thus reveal the human brain as a one-of-a-kind complex system that exhibits critical-like dynamics in a continuum between continuous and discontinuous phase transitions.SIGNIFICANCE STATEMENT In the model, while synchrony per se was controlled by connectivity, increasing positive local feedback led to gradually emerging bistable synchrony with scale-free dynamics, suggesting a continuum between second- and first-order phase transitions in synchrony dynamics inside a critical-like regimen. In resting-state MEG and SEEG, bistability of ongoing neuronal oscillations was pervasive across brain areas and frequency bands and was observed only with concurring critical-like dynamics as the modeling predicted. As evidence for functional relevance, moderate bistability was positively correlated with executive functioning in the healthy subjects, and excessive bistability was associated with epileptic pathophysiology. These findings show that critical-like neuronal dynamics in vivo involves both continuous and discontinuous phase transitions in a frequency-, neuroanatomy-, and state-dependent manner.
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Affiliation(s)
- Sheng H Wang
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Doctoral Programme Brain & Mind, University of Helsinki, 00014 Helsinki, Finland
- BioMag Laboratory, HUS Medical Imaging Center, 00290 Helsinki, Finland
- Department of Neuroscience and Biomedical Engineering, Aalto University, 00076 Espoo, Finland
| | - Felix Siebenhühner
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- BioMag Laboratory, HUS Medical Imaging Center, 00290 Helsinki, Finland
| | - Gabriele Arnulfo
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Department of Informatics, Bioengineering, Robotics and System Engineering, University of Genoa, 16136 Genoa, Italy
| | - Vladislav Myrov
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Department of Neuroscience and Biomedical Engineering, Aalto University, 00076 Espoo, Finland
| | - Lino Nobili
- Department of Neurosciences, Rehabilitation, Ophthalmology, Genetics and Maternal and Children's Sciences, University of Genoa, 16136 Genoa, Italy
- Child Neuropsychiatry Unit, Istituto Di Ricovero e Cura a Carattere Scientifico Istituto Giannina Gaslini, 16147 Genoa, Italy
- Centre of Epilepsy Surgery "C. Munari," Department of Neuroscience, Niguarda Hospital, 20162 Milan, Italy
| | - Michael Breakspear
- College of Engineering, Science and Environment, College of Health and Medicine, University of Newcastle, Callaghan, 2308 Australia
| | - Satu Palva
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Centre for Cognitive Neuroimaging, Institute of Neuroscience & Psychology, University of Glasgow, Glasgow G12 8QB, United Kingdom
| | - J Matias Palva
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Department of Neuroscience and Biomedical Engineering, Aalto University, 00076 Espoo, Finland
- Centre for Cognitive Neuroimaging, Institute of Neuroscience & Psychology, University of Glasgow, Glasgow G12 8QB, United Kingdom
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Rabuffo G, Sorrentino P, Bernard C, Jirsa V. Spontaneous neuronal avalanches as a correlate of access consciousness. Front Psychol 2022; 13:1008407. [PMID: 36337573 PMCID: PMC9634647 DOI: 10.3389/fpsyg.2022.1008407] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2022] [Accepted: 10/04/2022] [Indexed: 09/03/2023] Open
Abstract
Decades of research have advanced our understanding of the biophysical mechanisms underlying consciousness. However, an overarching framework bridging between models of consciousness and the large-scale organization of spontaneous brain activity is still missing. Based on the observation that spontaneous brain activity dynamically switches between epochs of segregation and large-scale integration of information, we hypothesize a brain-state dependence of conscious access, whereby the presence of either segregated or integrated states marks distinct modes of information processing. We first review influential works on the neuronal correlates of consciousness, spontaneous resting-state brain activity and dynamical system theory. Then, we propose a test experiment to validate our hypothesis that conscious access occurs in aperiodic cycles, alternating windows where new incoming information is collected but not experienced, to punctuated short-lived integration events, where conscious access to previously collected content occurs. In particular, we suggest that the integration events correspond to neuronal avalanches, which are collective bursts of neuronal activity ubiquitously observed in electrophysiological recordings. If confirmed, the proposed framework would link the physics of spontaneous cortical dynamics, to the concept of ignition within the global neuronal workspace theory, whereby conscious access manifest itself as a burst of neuronal activity.
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Affiliation(s)
- Giovanni Rabuffo
- Institut de Neurosciences des Systemes, Aix-Marseille University, Marseille, France
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Artime O, De Domenico M. From the origin of life to pandemics: emergent phenomena in complex systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200410. [PMID: 35599559 PMCID: PMC9125231 DOI: 10.1098/rsta.2020.0410] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Accepted: 02/08/2022] [Indexed: 05/31/2023]
Abstract
When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This non-trivial phenomenon, known as emergence, characterizes a broad range of distinct complex systems-from physical to biological and social-and is often related to collective behaviour. It is ubiquitous, from non-living entities such as oscillators that under specific conditions synchronize, to living ones, such as birds flocking or fish schooling. Despite the ample phenomenological evidence of the existence of systems' emergent properties, central theoretical questions to the study of emergence remain unanswered, such as the lack of a widely accepted, rigorous definition of the phenomenon or the identification of the essential physical conditions that favour emergence. We offer here a general overview of the phenomenon of emergence and sketch current and future challenges on the topic. Our short review also serves as an introduction to the theme issue Emergent phenomena in complex physical and socio-technical systems: from cells to societies, where we provide a synthesis of the contents tackled in the issue and outline how they relate to these challenges, spanning from current advances in our understanding on the origin of life to the large-scale propagation of infectious diseases. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- Oriol Artime
- Fondazione Bruno Kessler, Via Sommarive 18, Povo, TN 38123, Italy
| | - Manlio De Domenico
- Department of Physics and Astronomy ‘Galileo Galilei’, University of Padua, Padova, Veneto, Italy
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