1
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Rybalova E, Semenova N. Impact of pulse exposure on chimera state in ensemble of FitzHugh-Nagumo systems. CHAOS (WOODBURY, N.Y.) 2024; 34:071101. [PMID: 38953753 DOI: 10.1063/5.0214787] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2024] [Accepted: 06/17/2024] [Indexed: 07/04/2024]
Abstract
In this article, we consider the influence of a periodic sequence of Gaussian pulses on a chimera state in a ring of coupled FitzHugh-Nagumo systems. We found that on the way to complete spatial synchronization, one can observe a number of variations of chimera states that are not typical for the parameter range under consideration. For example, the following modes were found: breathing chimera, chimera with intermittency in the incoherent part, traveling chimera with strong intermittency, and others. For comparison, here we also consider the impact of a harmonic influence on the same chimera, and to preserve the generality of the conclusions, we compare the regimes caused by both a purely positive harmonic influence and a positive-negative one.
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Affiliation(s)
- E Rybalova
- Radiophysics and Nonlinear Dynamics Department, Institute of Physics, Saratov State University, Astrakhanskaya str. 83, Saratov 410012, Russia
| | - N Semenova
- Radiophysics and Nonlinear Dynamics Department, Institute of Physics, Saratov State University, Astrakhanskaya str. 83, Saratov 410012, Russia
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2
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Curic D, Singh S, Nazari M, Mohajerani MH, Davidsen J. Spatial-Temporal Analysis of Neural Desynchronization in Sleeplike States Reveals Critical Dynamics. PHYSICAL REVIEW LETTERS 2024; 132:218403. [PMID: 38856286 DOI: 10.1103/physrevlett.132.218403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 02/26/2024] [Accepted: 04/10/2024] [Indexed: 06/11/2024]
Abstract
Sleep is characterized by nonrapid eye movement sleep, originating from widespread neuronal synchrony, and rapid eye movement sleep, with neuronal desynchronization akin to waking behavior. While these were thought to be global brain states, recent research suggests otherwise. Using time-frequency analysis of mesoscopic voltage-sensitive dye recordings of mice in a urethane-anesthetized model of sleep, we find transient neural desynchronization occurring heterogeneously across the cortex within a background of synchronized neural activity, in a manner reminiscent of a critical spreading process and indicative of an "edge-of-synchronization" phase transition.
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Affiliation(s)
- Davor Curic
- Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
| | - Surjeet Singh
- Canadian Centre for Behavioral Neuroscience, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada
| | - Mojtaba Nazari
- Canadian Centre for Behavioral Neuroscience, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada
| | - Majid H Mohajerani
- Canadian Centre for Behavioral Neuroscience, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada
| | - Jörn Davidsen
- Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
- Hotchkiss Brain Institute, University of Calgary, Calgary, Alberta T2N 4N1, Canada
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3
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Wang H, Zhu Z, Bi H, Jiang Z, Cao Y, Wang S, Zou L. Changes in Community Structure of Brain Dynamic Functional Connectivity States in Mild Cognitive Impairment. Neuroscience 2024; 544:1-11. [PMID: 38423166 DOI: 10.1016/j.neuroscience.2024.02.026] [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: 09/08/2023] [Revised: 01/22/2024] [Accepted: 02/24/2024] [Indexed: 03/02/2024]
Abstract
Recent researches have noted many changes of short-term dynamic modalities in mild cognitive impairment (MCI) patients' brain functional networks. In this study, the dynamic functional brain networks of 82 MCI patients and 85 individuals in the normal control (NC) group were constructed using the sliding window method and Pearson correlation. The window size was determined using single-scale time-dependent (SSTD) method. Subsequently, k-means was applied to cluster all window samples, identifying three dynamic functional connectivity (DFC) states. Collective sparse symmetric non-negative matrix factorization (cssNMF) was then used to perform community detection on these states and quantify differences in brain regions. Finally, metrics such as within-community connectivity strength, community strength, and node diversity were calculated for further analysis. The results indicated high similarity between the two groups in state 2, with no significant differences in optimal community quantity and functional segregation (p < 0.05). However, for state 1 and state 3, the optimal community quantity was smaller in MCI patients compared to the NC group. In state 1, MCI patients had lower within-community connectivity strength and overall strength than the NC group, whereas state 3 showed results opposite to state 1. Brain regions with statistical difference included MFG.L, ORBinf.R, STG.R, IFGtriang.L, CUN.L, CUN.R, LING.R, SOG.L, and PCUN.R. This study on DFC states explores changes in the brain functional networks of patients with MCI from the perspective of alterations in the community structures of DFC states. The findings could provide new insights into the pathological changes in the brains of MCI patients.
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Affiliation(s)
- Hongwei Wang
- School of Computer Science and Artificial Intelligence, Aliyun School of Big Data, School of Software, Changzhou University, Changzhou, Jiangsu 213164, China
| | - Zhihao Zhu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, Jiangsu 213164, China
| | - Hui Bi
- School of Computer Science and Artificial Intelligence, Aliyun School of Big Data, School of Software, Changzhou University, Changzhou, Jiangsu 213164, China
| | - Zhongyi Jiang
- School of Computer Science and Artificial Intelligence, Aliyun School of Big Data, School of Software, Changzhou University, Changzhou, Jiangsu 213164, China
| | - Yin Cao
- The Affiliated Changzhou Second People's Hospital of Nanjing Medical University, Changzhou, Jiangsu 213164, China
| | - Suhong Wang
- Clinical Psychology, The Third Affiliated Hospital of Soochow University, Juqian Road No. 185, Changzhou, Jiangsu 213164, China
| | - Ling Zou
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, Jiangsu 213164, China; The Key Laboratory of Brain Machine Collaborative Intelligence Foundation of Zhejiang Province, Hangzhou, Zhejiang 310018, China.
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4
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Manos T, Diaz-Pier S, Fortel I, Driscoll I, Zhan L, Leow A. Enhanced simulations of whole-brain dynamics using hybrid resting-state structural connectomes. Front Comput Neurosci 2023; 17:1295395. [PMID: 38188355 PMCID: PMC10770256 DOI: 10.3389/fncom.2023.1295395] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2023] [Accepted: 12/05/2023] [Indexed: 01/09/2024] Open
Abstract
The human brain, composed of billions of neurons and synaptic connections, is an intricate network coordinating a sophisticated balance of excitatory and inhibitory activities between brain regions. The dynamical balance between excitation and inhibition is vital for adjusting neural input/output relationships in cortical networks and regulating the dynamic range of their responses to stimuli. To infer this balance using connectomics, we recently introduced a computational framework based on the Ising model, which was first developed to explain phase transitions in ferromagnets, and proposed a novel hybrid resting-state structural connectome (rsSC). Here, we show that a generative model based on the Kuramoto phase oscillator can be used to simulate static and dynamic functional connectomes (FC) with rsSC as the coupling weight coefficients, such that the simulated FC aligns well with the observed FC when compared with that simulated traditional structural connectome.
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Affiliation(s)
- Thanos Manos
- ETIS, ENSEA, CNRS, UMR8051, CY Cergy-Paris University, Cergy, France
- Laboratoire de Physique Théorique et Modélisation, UMR 8089, CNRS, Cergy-Pontoise, CY Cergy Paris Université, Cergy, France
| | - Sandra Diaz-Pier
- Simulation and Data Lab Neuroscience, Institute for Advanced Simulation, Jülich Supercomputing Centre (JSC), JARA, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Igor Fortel
- Department of Biomedical Engineering, University of Illinois at Chicago, Chicago, IL, United States
| | - Ira Driscoll
- Department of Psychology, University of Wisconsin-Milwaukee, Milwaukee, WI, United States
| | - Liang Zhan
- Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, PA, United States
| | - Alex Leow
- Department of Biomedical Engineering, University of Illinois at Chicago, Chicago, IL, United States
- Department of Psychiatry, University of Illinois at Chicago, Chicago, IL, United States
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5
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Bollt E, Fish J, Kumar A, Roque Dos Santos E, Laurienti PJ. Fractal basins as a mechanism for the nimble brain. Sci Rep 2023; 13:20860. [PMID: 38012212 PMCID: PMC10682042 DOI: 10.1038/s41598-023-45664-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 10/22/2023] [Indexed: 11/29/2023] Open
Abstract
An interesting feature of the brain is its ability to respond to disparate sensory signals from the environment in unique ways depending on the environmental context or current brain state. In dynamical systems, this is an example of multi-stability, the ability to switch between multiple stable states corresponding to specific patterns of brain activity/connectivity. In this article, we describe chimera states, which are patterns consisting of mixed synchrony and incoherence, in a brain-inspired dynamical systems model composed of a network with weak individual interactions and chaotic/periodic local dynamics. We illustrate the mechanism using synthetic time series interacting on a realistic anatomical brain network derived from human diffusion tensor imaging. We introduce the so-called vector pattern state (VPS) as an efficient way of identifying chimera states and mapping basin structures. Clustering similar VPSs for different initial conditions, we show that coexisting attractors of such states reveal intricately "mingled" fractal basin boundaries that are immediately reachable. This could explain the nimble brain's ability to rapidly switch patterns between coexisting attractors.
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Affiliation(s)
- Erik Bollt
- Department of Electrical and Computer Engineering, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA.
- Clarkson Center for Complex Systems Science, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA.
| | - Jeremie Fish
- Department of Electrical and Computer Engineering, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
- Clarkson Center for Complex Systems Science, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
| | - Anil Kumar
- Department of Electrical and Computer Engineering, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
- Clarkson Center for Complex Systems Science, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
| | - Edmilson Roque Dos Santos
- Department of Electrical and Computer Engineering, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
- Clarkson Center for Complex Systems Science, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
- Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, Av. Trab. São Carlense, 400, São Carlos, SP, 13566-590, Brazil
| | - Paul J Laurienti
- Department of Radiology, Wake Forest University School of Medicine, 475 Vine Street, Winston-Salem, NC, 27101, USA
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6
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Kumar P, Gangopadhyay G. Nonequilibrium thermodynamic signatures of collective dynamical states around chimera in a chemical reaction network. Phys Rev E 2023; 108:044218. [PMID: 37978606 DOI: 10.1103/physreve.108.044218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Accepted: 10/03/2023] [Indexed: 11/19/2023]
Abstract
Different dynamical states ranging from coherent, incoherent to chimera, multichimera, and related transitions are addressed in a globally coupled nonlinear continuum chemical oscillator system by implementing a modified complex Ginzburg-Landau equation. Besides dynamical identifications of observed states using standard qualitative metrics, we systematically acquire nonequilibrium thermodynamic characterizations of these states obtained via coupling parameters. The nonconservative work profiles in collective dynamics qualitatively reflect the time-integrated concentration of the activator, and the majority of the nonconservative work contributes to the entropy production over the spatial dimension. It is illustrated that the evolution of spatial entropy production and semigrand Gibbs free-energy profiles associated with each state are connected yet completely out of phase, and these thermodynamic signatures are extensively elaborated to shed light on the exclusiveness and similarities of these states. Moreover, a relationship between the proper nonequilibrium thermodynamic potential and the variance of activator concentration is established by exhibiting both quantitative and qualitative similarities between a Fano factor like entity, derived from the activator concentration, and the Kullback-Leibler divergence associated with the transition from a nonequilibrium homogeneous state to an inhomogeneous state. Quantifying the thermodynamic costs for collective dynamical states would aid in efficiently controlling, manipulating, and sustaining such states to explore the real-world relevance and applications of these states.
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Affiliation(s)
- Premashis Kumar
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Gautam Gangopadhyay
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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7
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Liu Z, Han F, Wang Q. Task-relevant brain dynamics among cognitive subsystems induced by regional stimulation in a whole-brain computational model. Phys Rev E 2023; 108:044402. [PMID: 37978611 DOI: 10.1103/physreve.108.044402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Accepted: 09/11/2023] [Indexed: 11/19/2023]
Abstract
Cognition involves the global integration of distributed brain regions that are known to work cohesively as cognitive subsystems during brain functioning. Empirical evidence has suggested that spatiotemporal phase relationships between brain regions, measured as synchronization and metastability, may encode important task-relevant information. However, it remains largely unknown how phase relationships aggregate at the level of cognitive subsystems under different cognitive processing. Here, we probe this question by simulating task-relevant brain dynamics through regional stimulation of a whole-brain dynamical network model operating in the resting-state dynamical regime. The model is constructed with structurally embedded Stuart-Laudon oscillators and then fitted with human resting-state functional magnetic resonance imaging data. Based on this framework, we first demonstrate the plausibility of introducing the cognitive system partition into the modeling analysis framework by showing that the clustering of regions across functional networks is better circumscribed by the predefined partition. At the cognitive subsystem level, we focus on how task-relevant phase dynamics are organized in terms of synchronization and metastability. We found that patterns of cognitive synchronization are more task specific, whereas patterns of cognitive metastability are more consistent across different states, suggesting it may encode a more task-general property during cognitive processing, an inherent property conferred by brain organization. This consistent network architecture in cognitive metastability may be related to the distinct functional responses of realistic cognitive systems. We also provide empirical evidence to partially support our computational results. Our paper may provide insights for the mechanisms underlying task-relevant brain dynamics, and establish a model-based link between brain structure, dynamics, and cognition, a fundamental step for computationally aided brain interventions.
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Affiliation(s)
- Zilu Liu
- Department of Dynamics and Control, Beihang University, Beijing 100191, China
| | - Fang Han
- College of Information Science and Technology, Donghua University, Shanghai 200051, China
| | - Qingyun Wang
- Department of Dynamics and Control, Beihang University, Beijing 100191, China
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8
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Rybalova E, Nechaev V, Schöll E, Strelkova G. Chimera resonance in networks of chaotic maps. CHAOS (WOODBURY, N.Y.) 2023; 33:093138. [PMID: 37748485 DOI: 10.1063/5.0164008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 09/05/2023] [Indexed: 09/27/2023]
Abstract
We explore numerically the impact of additive Gaussian noise on the spatiotemporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the Henon map. 2D distributions of the probability of observing chimera states are constructed in terms of the coupling strength and the noise intensity and for several choices of the local dynamics parameters. It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance.
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Affiliation(s)
- Elena Rybalova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - Vasilii Nechaev
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
| | - Galina Strelkova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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9
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Phillips ET. The synchronizing role of multiplexing noise: Exploring Kuramoto oscillators and breathing chimeras. CHAOS (WOODBURY, N.Y.) 2023; 33:073140. [PMID: 37463090 DOI: 10.1063/5.0135528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2022] [Accepted: 06/02/2023] [Indexed: 07/20/2023]
Abstract
The synchronization of spatiotemporal patterns in a two-layer multiplex network of identical Kuramoto phase oscillators is studied, where each layer is a non-locally coupled ring. Particular focus is on the role played by a noisy inter-layer communication. It is shown that modulating the inter-layer coupling strength by uncommon noise has a significant impact on the dynamics of the network, in particular, that modulating the interlayer coupling by noise can counter-intuitively induce synchronization in networks. It is further shown that increasing the noise intensity has many other analogous effects to that of increasing the interlayer coupling strength. For example, the noise intensity can also induce state transitions in a similar way, in some cases causing the layers to completely synchronize within themselves. It is discussed how such disturbances may in many cases be beneficial to multilayer systems. These effects are demonstrated both for white noise and for other kinds of colored noise. A "floating" breathing chimera state is also discovered in this system.
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10
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Chen D, Yang Z, Xiao Q, Liu Z. Sensitive dynamics of brain cognitive networks and its resource constraints. CHAOS (WOODBURY, N.Y.) 2023; 33:063139. [PMID: 37318341 DOI: 10.1063/5.0145734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 05/24/2023] [Indexed: 06/16/2023]
Abstract
It is well known that brain functions are closely related to the synchronization of brain networks, but the underlying mechanisms are still not completely understood. To study this problem, we here focus on the synchronization of cognitive networks, in contrast to that of a global brain network, as individual brain functions are in fact performed by different cognitive networks but not the global network. In detail, we consider four different levels of brain networks and two approaches, i.e., either with or without resource constraints. For the case of without resource constraints, we find that global brain networks have fundamentally different behaviors from that of the cognitive networks; i.e., the former has a continuous synchronization transition, while the latter shows a novel transition of oscillatory synchronization. This feature of oscillation comes from the sparse links among the communities of cognitive networks, resulting in coupling sensitive dynamics of brain cognitive networks. While for the case of resource constraints, we find that at the global level, the synchronization transition becomes explosive, in contrast to the continuous synchronization for the case of without resource constraints. At the level of cognitive networks, the transition also becomes explosive and the coupling sensitivity is significantly reduced, thus guaranteeing the robustness and fast switch of brain functions. Moreover, a brief theoretical analysis is provided.
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Affiliation(s)
- Dehua Chen
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, People's Republic of China
| | - Zhiyin Yang
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, People's Republic of China
| | - Qin Xiao
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, People's Republic of China
- College of Science, Shanghai Institute of Technology, Shanghai 201418, People's Republic of China
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, People's Republic of China
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11
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Lu X, Wang T, Ye M, Huang S, Wang M, Zhang J. Study on characteristic of epileptic multi-electroencephalograph base on Hilbert-Huang transform and brain network dynamics. Front Neurosci 2023; 17:1117340. [PMID: 37214385 PMCID: PMC10192695 DOI: 10.3389/fnins.2023.1117340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 04/11/2023] [Indexed: 05/24/2023] Open
Abstract
Lots of studies have been carried out on characteristic of epileptic Electroencephalograph (EEG). However, traditional EEG characteristic research methods lack exploration of spatial information. To study the characteristics of epileptic EEG signals from the perspective of the whole brain,this paper proposed combination methods of multi-channel characteristics from time-frequency and spatial domains. This paper was from two aspects: Firstly, signals were converted into 2D Hilbert Spectrum (HS) images which reflected the time-frequency characteristics by Hilbert-Huang Transform (HHT). These images were identified by Convolutional Neural Network (CNN) model whose sensitivity was 99.8%, accuracy was 98.7%, specificity was 97.4%, F1-score was 98.7%, and AUC-ROC was 99.9%. Secondly, the multi-channel signals were converted into brain networks which reflected the spatial characteristics by Symbolic Transfer Entropy (STE) among different channels EEG. And the results show that there are different network properties between ictal and interictal phase and the signals during the ictal enter the synchronization state more quickly, which was verified by Kuramoto model. To summarize, our results show that there was different characteristics among channels for the ictal and interictal phase, which can provide effective physical non-invasive indicators for the identification and prediction of epileptic seizures.
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Affiliation(s)
- Xiaojie Lu
- School of Physics and Electronic Information, Anhui Normal University, Wuhu, China
- Research Center of Health Big Data Mining and Applications, School of Medicine Information, Wan Nan Medical College, Wuhu, China
| | - Tingting Wang
- Research Center of Health Big Data Mining and Applications, School of Medicine Information, Wan Nan Medical College, Wuhu, China
| | - Mingquan Ye
- Research Center of Health Big Data Mining and Applications, School of Medicine Information, Wan Nan Medical College, Wuhu, China
| | - Shoufang Huang
- School of Physics and Electronic Information, Anhui Normal University, Wuhu, China
| | - Maosheng Wang
- School of Physics and Electronic Information, Anhui Normal University, Wuhu, China
| | - Jiqian Zhang
- School of Physics and Electronic Information, Anhui Normal University, Wuhu, China
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12
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Andrzejak RG, Espinoso A. Chimera states in multiplex networks: Chameleon-like across-layer synchronization. CHAOS (WOODBURY, N.Y.) 2023; 33:2890080. [PMID: 37163994 DOI: 10.1063/5.0146550] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 04/19/2023] [Indexed: 05/12/2023]
Abstract
Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.
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Affiliation(s)
- Ralph G Andrzejak
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
| | - Anaïs Espinoso
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
- Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology, Carrer Baldiri Reixac 10-12, 08028 Barcelona, Catalonia, Spain
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13
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Zheng Y, Tang S, Zheng H, Wang X, Liu L, Yang Y, Zhen Y, Zheng Z. Noise improves the association between effects of local stimulation and structural degree of brain networks. PLoS Comput Biol 2023; 19:e1010866. [PMID: 37167331 PMCID: PMC10205011 DOI: 10.1371/journal.pcbi.1010866] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2023] [Revised: 05/23/2023] [Accepted: 04/20/2023] [Indexed: 05/13/2023] Open
Abstract
Stimulation to local areas remarkably affects brain activity patterns, which can be exploited to investigate neural bases of cognitive function and modify pathological brain statuses. There has been growing interest in exploring the fundamental action mechanisms of local stimulation. Nevertheless, how noise amplitude, an essential element in neural dynamics, influences stimulation-induced brain states remains unknown. Here, we systematically examine the effects of local stimulation by using a large-scale biophysical model under different combinations of noise amplitudes and stimulation sites. We demonstrate that noise amplitude nonlinearly and heterogeneously tunes the stimulation effects from both regional and network perspectives. Furthermore, by incorporating the role of the anatomical network, we show that the peak frequencies of unstimulated areas at different stimulation sites averaged across noise amplitudes are highly positively related to structural connectivity. Crucially, the association between the overall changes in functional connectivity as well as the alterations in the constraints imposed by structural connectivity with the structural degree of stimulation sites is nonmonotonically influenced by the noise amplitude, with the association increasing in specific noise amplitude ranges. Moreover, the impacts of local stimulation of cognitive systems depend on the complex interplay between the noise amplitude and average structural degree. Overall, this work provides theoretical insights into how noise amplitude and network structure jointly modulate brain dynamics during stimulation and introduces possibilities for better predicting and controlling stimulation outcomes.
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Affiliation(s)
- Yi Zheng
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
| | - Shaoting Tang
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R. China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
| | - Hongwei Zheng
- Beijing Academy of Blockchain and Edge Computing (BABEC), Beijing, China
| | - Xin Wang
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R. China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
| | - Longzhao Liu
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R. China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
| | - Yaqian Yang
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
| | - Yi Zhen
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
| | - Zhiming Zheng
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R. China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
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14
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Nakuci J, Wasylyshyn N, Cieslak M, Elliott JC, Bansal K, Giesbrecht B, Grafton ST, Vettel JM, Garcia JO, Muldoon SF. Within-subject reproducibility varies in multi-modal, longitudinal brain networks. Sci Rep 2023; 13:6699. [PMID: 37095180 PMCID: PMC10126005 DOI: 10.1038/s41598-023-33441-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Accepted: 04/12/2023] [Indexed: 04/26/2023] Open
Abstract
Network neuroscience provides important insights into brain function by analyzing complex networks constructed from diffusion Magnetic Resonance Imaging (dMRI), functional MRI (fMRI) and Electro/Magnetoencephalography (E/MEG) data. However, in order to ensure that results are reproducible, we need a better understanding of within- and between-subject variability over long periods of time. Here, we analyze a longitudinal, 8 session, multi-modal (dMRI, and simultaneous EEG-fMRI), and multiple task imaging data set. We first confirm that across all modalities, within-subject reproducibility is higher than between-subject reproducibility. We see high variability in the reproducibility of individual connections, but observe that in EEG-derived networks, during both rest and task, alpha-band connectivity is consistently more reproducible than connectivity in other frequency bands. Structural networks show a higher reliability than functional networks across network statistics, but synchronizability and eigenvector centrality are consistently less reliable than other network measures across all modalities. Finally, we find that structural dMRI networks outperform functional networks in their ability to identify individuals using a fingerprinting analysis. Our results highlight that functional networks likely reflect state-dependent variability not present in structural networks, and that the type of analysis should depend on whether or not one wants to take into account state-dependent fluctuations in connectivity.
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Affiliation(s)
- Johan Nakuci
- Neuroscience Program, University at Buffalo, SUNY, Buffalo, NY, 14260, USA.
- School of Psychology, Georgia Institute of Technology, Atlanta, GA, 14260, USA.
| | - Nick Wasylyshyn
- U.S. CCDC Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, 21005, USA
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | - Matthew Cieslak
- Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA, 93106, USA
| | - James C Elliott
- Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA, 93106, USA
| | - Kanika Bansal
- U.S. CCDC Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, 21005, USA
- Department of Biomedical Engineering, Columbia University, New York, NY, 10027, USA
| | - Barry Giesbrecht
- Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA, 93106, USA
- Institute for Collaborative Biotechnologies, University of California, Santa Barbara, CA, 93106, USA
| | - Scott T Grafton
- Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA, 93106, USA
- Institute for Collaborative Biotechnologies, University of California, Santa Barbara, CA, 93106, USA
| | - Jean M Vettel
- U.S. CCDC Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, 21005, USA
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, 19104, USA
- Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA, 93106, USA
| | - Javier O Garcia
- U.S. CCDC Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, 21005, USA
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | - Sarah F Muldoon
- Neuroscience Program, University at Buffalo, SUNY, Buffalo, NY, 14260, USA.
- Department of Mathematics and CDSE Program, University at Buffalo, SUNY, Buffalo, NY, 14260, USA.
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15
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Kurtin DL, Giunchiglia V, Vohryzek J, Cabral J, Skeldon AC, Violante IR. Moving from phenomenological to predictive modelling: Progress and pitfalls of modelling brain stimulation in-silico. Neuroimage 2023; 272:120042. [PMID: 36965862 DOI: 10.1016/j.neuroimage.2023.120042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Revised: 02/06/2023] [Accepted: 03/16/2023] [Indexed: 03/27/2023] Open
Abstract
Brain stimulation is an increasingly popular neuromodulatory tool used in both clinical and research settings; however, the effects of brain stimulation, particularly those of non-invasive stimulation, are variable. This variability can be partially explained by an incomplete mechanistic understanding, coupled with a combinatorial explosion of possible stimulation parameters. Computational models constitute a useful tool to explore the vast sea of stimulation parameters and characterise their effects on brain activity. Yet the utility of modelling stimulation in-silico relies on its biophysical relevance, which needs to account for the dynamics of large and diverse neural populations and how underlying networks shape those collective dynamics. The large number of parameters to consider when constructing a model is no less than those needed to consider when planning empirical studies. This piece is centred on the application of phenomenological and biophysical models in non-invasive brain stimulation. We first introduce common forms of brain stimulation and computational models, and provide typical construction choices made when building phenomenological and biophysical models. Through the lens of four case studies, we provide an account of the questions these models can address, commonalities, and limitations across studies. We conclude by proposing future directions to fully realise the potential of computational models of brain stimulation for the design of personalized, efficient, and effective stimulation strategies.
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Affiliation(s)
- Danielle L Kurtin
- Neuromodulation Laboratory, School of Psychology, University of Surrey, Guildford, GU2 7XH, United Kingdom; Department of Brain Sciences, Imperial College London, London, United Kingdom.
| | | | - Jakub Vohryzek
- Centre for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain; Centre for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, UK
| | - Joana Cabral
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, Portugal
| | - Anne C Skeldon
- Department of Mathematics, Centre for Mathematical and Computational Biology, University of Surrey, Guildford, United Kingdom
| | - Ines R Violante
- Neuromodulation Laboratory, School of Psychology, University of Surrey, Guildford, GU2 7XH, United Kingdom
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16
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Feng P, Yang J, Wu Y, Liu Z. Alternating chimera states in complex networks with modular structures. CHAOS (WOODBURY, N.Y.) 2023; 33:033136. [PMID: 37003804 DOI: 10.1063/5.0132072] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 02/28/2023] [Indexed: 06/19/2023]
Abstract
Chimera, the coexistence state of synchronization and non-synchronization, widely exists in complex networks. It has a great potentially explanatory power for the unihemispheric sleep of birds and some mammals, in which the synchronizations of the hemispheres of the cerebral cortex are evolving alternately. In this study, a coupled nonlinear oscillator system with a topology of the modular complex network was constructed to simulate the left and right hemispheres of the brain. The results showed that a stable chimera, an alternating chimera, and a breathing chimera were produced when the coupling strength and connection probability of the left and right hemispheres were changed. Further, we studied the effect of noise on rich synchronous patterns and found that the alternating chimera was robust to Gaussian white noise when the strength was not very large. Finally, our study was extended to a complex network with three sub-networks, and an alternating chimera could exist in two or three sub-networks. Our research provides a deeper insight into the mechanism of brain function like unihemispheric sleep.
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Affiliation(s)
- Peihua Feng
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Jiayi Yang
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Ying Wu
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Zhilong Liu
- Hefei General Machinery Research Institute, State Key Laboratory of Compressor Technology, Hefei 230031, People's Republic of China
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17
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Provata A. From Turing patterns to chimera states in the 2D Brusselator model. CHAOS (WOODBURY, N.Y.) 2023; 33:033133. [PMID: 37003796 DOI: 10.1063/5.0130539] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 02/23/2023] [Indexed: 06/19/2023]
Abstract
The Brusselator has been used as a prototype model for autocatalytic reactions and, in particular, for the Belousov-Zhabotinsky reaction. When coupled at the diffusive limit, the Brusselator undergoes a Turing bifurcation resulting in the formation of classical Turing patterns, such as spots, stripes, and spirals in two spatial dimensions. In the present study, we use generic nonlocally coupled Brusselators and show that in the limit of the coupling range R→1 (diffusive limit), the classical Turing patterns are recovered, while for intermediate coupling ranges and appropriate parameter values, chimera states are produced. This study demonstrates how the parameters of a typical nonlinear oscillator can be tuned so that the coupled system passes from spatially stable Turing structures to dynamical spatiotemporal chimera states.
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Affiliation(s)
- A Provata
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15341 Athens, Greece
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18
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Ansarinasab S, Parastesh F, Ghassemi F, Rajagopal K, Jafari S, Ghosh D. Synchronization in functional brain networks of children suffering from ADHD based on Hindmarsh-Rose neuronal model. Comput Biol Med 2022. [DOI: 10.1016/j.compbiomed.2022.106461] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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19
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Chekroun MD, Koren I, Liu H, Liu H. Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations. SCIENCE ADVANCES 2022; 8:eabq7137. [PMID: 36399565 PMCID: PMC9674290 DOI: 10.1126/sciadv.abq7137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 10/17/2022] [Indexed: 06/16/2023]
Abstract
Nonlinear time delay systems produce inherently delay-induced periodic oscillations, which are, however, too idealistic compared to observations. We exhibit a unified stochastic framework to systematically rectify such oscillations into oscillatory patterns with enriched temporal variabilities through generic, nonlinear responses to stochastic perturbations. Two paradigms of noise-driven chaos in high dimension are identified, fundamentally different from chaos triggered by parameter-space noise. Noteworthy is a low-dimensional stretch-and-fold mechanism, leading to stochastic strange attractors exhibiting horseshoe-like structures mirroring turbulent transport of passive tracers. The other is high-dimensional , with noise acting along the critical eigendirection and transmitted to "deeper" stable modes through nonlinearity, leading to stochastic attractors exhibiting swarm-like behaviors with power-law and scale break properties. The theory is applied to cloud delay models to parameterize missing physics such as intermittent rain and Lagrangian turbulent effects. The stochastically rectified model reproduces with fidelity complex temporal variabilities of open-cell oscillations exhibited by high-end cloud simulations.
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Affiliation(s)
- Mickaël D. Chekroun
- Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 76100, Israel
- Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, CA 90095, USA
| | - Ilan Koren
- Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Honghu Liu
- Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
| | - Huan Liu
- Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 76100, Israel
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20
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Li B, Uchida N. Effect of mobility on collective phase dynamics of nonlocally coupled oscillators with a phase lag. Phys Rev E 2022; 106:054210. [PMID: 36559432 DOI: 10.1103/physreve.106.054210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2022] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
Nonlocally coupled oscillators with a phase lag self-organize into various patterns, such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, whereas it destroys coherence for a repulsive coupling. The transition behaviors are discussed in terms of the timescales of synchronization and diffusion of the oscillators. We also find a novel spatiotemporal pattern at the border between coherent and incoherent states.
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Affiliation(s)
- Bojun Li
- Department of Physics, Tohoku University, Sendai 980-8578, Japan
| | - Nariya Uchida
- Department of Physics, Tohoku University, Sendai 980-8578, Japan
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21
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Li Q, Larosz KC, Han D, Ji P, Kurths J. Basins of attraction of chimera states on networks. Front Physiol 2022; 13:959431. [PMID: 36160849 PMCID: PMC9493443 DOI: 10.3389/fphys.2022.959431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 08/02/2022] [Indexed: 11/13/2022] Open
Abstract
Networks of identical coupled oscillators display a remarkable spatiotemporal pattern, the chimera state, where coherent oscillations coexist with incoherent ones. In this paper we show quantitatively in terms of basin stability that stable and breathing chimera states in the original two coupled networks typically have very small basins of attraction. In fact, the original system is dominated by periodic and quasi-periodic chimera states, in strong contrast to the model after reduction, which can not be uncovered by the Ott-Antonsen ansatz. Moreover, we demonstrate that the curve of the basin stability behaves bimodally after the system being subjected to even large perturbations. Finally, we investigate the emergence of chimera states in brain network, through inducing perturbations by stimulating brain regions. The emerged chimera states are quantified by Kuramoto order parameter and chimera index, and results show a weak and negative correlation between these two metrics.
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Affiliation(s)
- Qiang Li
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
- Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai, China
- MOE Frontiers Center for Brain Science, Fudan University, Shanghai, China
| | - Kelly C. Larosz
- University Center UNIFATEB, Telêmaco Borba, Brazil
- Graduate Program in Chemical Engineering Federal Technological University of Paraná, Ponta Grossa, Brazil
- Physics Institute, University of São Paulo, Oscillation Control Group, São Paulo, Brazil
| | - Dingding Han
- School of Information Science and Technology, Fudan University, Shanghai, China
- *Correspondence: Dingding Han, ; Peng Ji,
| | - Peng Ji
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
- Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai, China
- MOE Frontiers Center for Brain Science, Fudan University, Shanghai, China
- *Correspondence: Dingding Han, ; Peng Ji,
| | - Jürgen Kurths
- Research Institute of Intelligent Complex Systems, Fudan University, Shanghai, China
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
- Humboldt University, Berlin, Germany
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22
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Functional control of oscillator networks. Nat Commun 2022; 13:4721. [PMID: 35953467 PMCID: PMC9372149 DOI: 10.1038/s41467-022-31733-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Accepted: 06/28/2022] [Indexed: 11/11/2022] Open
Abstract
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators’ parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion of functional pattern, which encodes the pairwise relationships between the oscillators’ phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids. In network systems governed by oscillatory activity, such as brain networks or power grids, configurations of synchrony may define network functions. The authors introduce a control approach for the formation of desired synchrony patterns through optimal interventions on the network parameters.
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23
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Botha AE, Ansariara M, Emadi S, Kolahchi MR. Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses. Front Comput Neurosci 2022; 16:888019. [PMID: 35814347 PMCID: PMC9260432 DOI: 10.3389/fncom.2022.888019] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2022] [Accepted: 05/30/2022] [Indexed: 11/13/2022] Open
Abstract
The union of the Kuramoto–Sakaguchi model and the Hebb dynamics reproduces the Lisman switch through a bistability in synchronized states. Here, we show that, within certain ranges of the frustration parameter, the chimera pattern can emerge, causing a different, time-evolving, distribution in the Hebbian synaptic strengths. We study the stability range of the chimera as a function of the frustration (phase-lag) parameter. Depending on the range of the frustration, two different types of chimeras can appear spontaneously, i.e., from randomized initial conditions. In the first type, the oscillators in the coherent region rotate, on average, slower than those in the incoherent region; while in the second type, the average rotational frequencies of the two regions are reversed, i.e., the coherent region runs, on average, faster than the incoherent region. We also show that non-stationary behavior at finite N can be controlled by adjusting the natural frequency of a single pacemaker oscillator. By slowly cycling the frequency of the pacemaker, we observe hysteresis in the system. Finally, we discuss how we can have a model for learning and memory.
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Affiliation(s)
- A. E. Botha
- Department of Physics, Science Campus, University of South Africa, Private Bag X6, Johannesburg, South Africa
| | - M. Ansariara
- Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
| | - S. Emadi
- Department of Biological Sciences, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
| | - M. R. Kolahchi
- Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
- *Correspondence: M. R. Kolahchi
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24
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Shi JY, Cai LM, Lin JH, Zou ZY, Zhang XH, Chen HJ. Dynamic Alterations in Functional Connectivity Density in Amyotrophic Lateral Sclerosis: A Resting-State Functional Magnetic Resonance Imaging Study. Front Aging Neurosci 2022; 14:827500. [PMID: 35370623 PMCID: PMC8967369 DOI: 10.3389/fnagi.2022.827500] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2021] [Accepted: 02/14/2022] [Indexed: 11/13/2022] Open
Abstract
Background and Aims Current knowledge on the temporal dynamics of the brain functional organization in amyotrophic lateral sclerosis (ALS) is limited. This is the first study on alterations in the patterns of dynamic functional connection density (dFCD) involving ALS. Methods We obtained resting-state functional magnetic resonance imaging (fMRI) data from 50 individuals diagnosed with ALS and 55 healthy controls (HCs). We calculated the functional connectivity (FC) between a given voxel and all other voxels within the entire brain and yield the functional connection density (FCD) value per voxel. dFCD was assessed by sliding window correlation method. In addition, the standard deviation (SD) of dFCD across the windows was computed voxel-wisely to measure dFCD variability. The difference in dFCD variability between the two groups was compared using a two-sample t-test following a voxel-wise manner. The receiver operating characteristic (ROC) curve was used to assess the between-group recognition performance of the dFCD variability index. Results The dFCD variability was significantly reduced in the bilateral precentral and postcentral gyrus compared with the HC group, whereas a marked increase was observed in the left middle frontal gyrus of ALS patients. dFCD variability exhibited moderate potential (areas under ROC curve = 0.753–0.837, all P < 0.001) in distinguishing two groups. Conclusion ALS patients exhibit aberrant dynamic property in brain functional architecture. The dFCD evaluation improves our understanding of the pathological mechanisms underlying ALS and may assist in its diagnosis.
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Affiliation(s)
- Jia-Yan Shi
- Department of Radiology, Fujian Medical University Union Hospital, Fuzhou, China
| | - Li-Min Cai
- Department of Radiology, Fujian Medical University Union Hospital, Fuzhou, China
| | - Jia-Hui Lin
- Department of Radiology, Fujian Medical University Union Hospital, Fuzhou, China
| | - Zhang-Yu Zou
- Department of Neurology, Fujian Medical University Union Hospital, Fuzhou, China
| | - Xiao-Hong Zhang
- Department of Radiology, Fujian Medical University Union Hospital, Fuzhou, China
| | - Hua-Jun Chen
- Department of Radiology, Fujian Medical University Union Hospital, Fuzhou, China
- *Correspondence: Hua-Jun Chen,
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25
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Kumar P, Gangopadhyay G. Nonequilibrium thermodynamic characterization of chimeras in a continuum chemical oscillator system. Phys Rev E 2022; 105:034208. [PMID: 35428096 DOI: 10.1103/physreve.105.034208] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 03/04/2022] [Indexed: 06/14/2023]
Abstract
The emergence of the chimera state as the counterintuitive spatial coexistence of synchronous and asynchronous regimes is addressed here in a continuum chemical oscillator system by implementing a relevant complex Ginzburg-Landau equation with global coupling. This study systematically acquires and characterizes the evolution of nonequilibrium thermodynamic entities corresponding to the chimera state. The temporal evolution of the entropy production rate exhibits a beat pattern with a series of equidistant spectral lines in the frequency domain. Symmetric profiles associated with the incoherent regime appear in descriptions of the dynamics and thermodynamics of the chimera. It is shown that identifying the semigrand Gibbs free energy of the state as the Gabor elementary function can reveal the guiding role of the information uncertainty principle in shaping the chimera energetics.
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Affiliation(s)
- Premashis Kumar
- S. N. Bose National Centre for Basic Sciences, Salt Lake, Kolkata 700 106, India
| | - Gautam Gangopadhyay
- S. N. Bose National Centre for Basic Sciences, Salt Lake, Kolkata 700 106, India
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26
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Goodfellow M, Andrzejak RG, Masoller C, Lehnertz K. What Models and Tools can Contribute to a Better Understanding of Brain Activity? FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:907995. [PMID: 36926061 PMCID: PMC10013030 DOI: 10.3389/fnetp.2022.907995] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 06/06/2022] [Indexed: 12/18/2022]
Abstract
Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.
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Affiliation(s)
- Marc Goodfellow
- Living Systems Institute, University of Exeter, Exeter, United Kingdom
| | - Ralph G Andrzejak
- Department of Information and Communication Technologies, University Pompeu Fabra, Barcelona, Spain
| | - Cristina Masoller
- Department of Physics, Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany.,Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
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27
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Yang L, Wei J, Li Y, Wang B, Guo H, Yang Y, Xiang J. Test–Retest Reliability of Synchrony and Metastability in Resting State fMRI. Brain Sci 2021; 12:brainsci12010066. [PMID: 35053813 PMCID: PMC8773904 DOI: 10.3390/brainsci12010066] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Revised: 12/23/2021] [Accepted: 12/28/2021] [Indexed: 11/16/2022] Open
Abstract
In recent years, interest has been growing in dynamic characteristic of brain signals from resting-state functional magnetic resonance imaging (rs-fMRI). Synchrony and metastability, as neurodynamic indexes, are considered as one of methods for analyzing dynamic characteristics. Although much research has studied the analysis of neurodynamic indices, few have investigated its reliability. In this paper, the datasets from the Human Connectome Project have been used to explore the test–retest reliabilities of synchrony and metastability from multiple angles through intra-class correlation (ICC). The results showed that both of these indexes had fair test–retest reliability, but they are strongly affected by the field strength, the spatial resolution, and scanning interval, less affected by the temporal resolution. Denoising processing can help improve their ICC values. In addition, the reliability of neurodynamic indexes was affected by the node definition strategy, but these effects were not apparent. In particular, by comparing the test–retest reliability of different resting-state networks, we found that synchrony of different networks was basically stable, but the metastability varied considerably. Among these, DMN and LIM had a relatively higher test–retest reliability of metastability than other networks. This paper provides a methodological reference for exploring the brain dynamic neural activity by using synchrony and metastability in fMRI signals.
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Affiliation(s)
| | | | | | | | | | | | - Jie Xiang
- Correspondence: ; Tel.: +86-186-0351-1178
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28
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Kachhara S, Ambika G. Frequency chimera state induced by differing dynamical timescales. Phys Rev E 2021; 104:064214. [PMID: 35030851 DOI: 10.1103/physreve.104.064214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2021] [Accepted: 12/04/2021] [Indexed: 06/14/2023]
Abstract
We report the occurrence of a self-emerging frequency chimera state in spatially extended systems of coupled oscillators, where the coherence and incoherence are defined with respect to the emergent frequency of the oscillations. This is generated by the local coupling among nonlinear oscillators evolving under differing dynamical timescales starting from random initial conditions. We show how they self-organize to structured patterns with spatial domains of coherence that are in frequency synchronization, coexisting with domains that are incoherent in frequencies. Our study has relevance in understanding such patterns observed in real-world systems like neuronal systems, power grids, social and ecological networks, where differing dynamical timescales is natural and realistic among the interacting systems.
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Affiliation(s)
- Sneha Kachhara
- Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India
| | - G Ambika
- Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India
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29
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Orsucci F. Human Synchronization Maps-The Hybrid Consciousness of the Embodied Mind. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1569. [PMID: 34945875 PMCID: PMC8700702 DOI: 10.3390/e23121569] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 11/01/2021] [Accepted: 11/18/2021] [Indexed: 11/17/2022]
Abstract
We examine the theoretical implications of empirical studies developed over recent years. These experiments have explored the biosemiotic nature of communication streams from emotional neuroscience and embodied mind perspectives. Information combinatorics analysis enabled a deeper understanding of the coupling and decoupling dynamics of biosemiotics streams. We investigated intraindividual and interpersonal relations as coevolution dynamics of hybrid couplings, synchronizations, and desynchronizations. Cluster analysis and Markov chains produced evidence of chimaera states and phase transitions. A probabilistic and nondeterministic approach clarified the properties of these hybrid dynamics. Thus, multidimensional theoretical models can represent the hybrid nature of human interactions.
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Affiliation(s)
- Franco Orsucci
- Department of Psychology, University College London, London WC1E 6BT, UK;
- Norfolk and Suffolk NHS Foundation Trust, Drayton High Road, Norwich NR6 5BE, UK
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30
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Parkes L, Moore TM, Calkins ME, Cieslak M, Roalf DR, Wolf DH, Gur RC, Gur RE, Satterthwaite TD, Bassett DS. Network Controllability in Transmodal Cortex Predicts Positive Psychosis Spectrum Symptoms. Biol Psychiatry 2021; 90:409-418. [PMID: 34099190 PMCID: PMC8842484 DOI: 10.1016/j.biopsych.2021.03.016] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Revised: 02/11/2021] [Accepted: 03/15/2021] [Indexed: 01/31/2023]
Abstract
BACKGROUND The psychosis spectrum (PS) is associated with structural dysconnectivity concentrated in transmodal cortex. However, understanding of this pathophysiology has been limited by an overreliance on examining direct interregional connectivity. Using network control theory, we measured variation in both direct and indirect connectivity to a region to gain new insights into the pathophysiology of the PS. METHODS We used psychosis symptom data and structural connectivity in 1068 individuals from the Philadelphia Neurodevelopmental Cohort. Applying a network control theory metric called average controllability, we estimated each brain region's capacity to leverage its direct and indirect structural connections to control linear brain dynamics. Using nonlinear regression, we determined the accuracy with which average controllability could predict PS symptoms in out-of-sample testing. We also examined the predictive performance of regional strength, which indexes only direct connections to a region, as well as several graph-theoretic measures of centrality that index indirect connectivity. Finally, we assessed how the prediction performance for PS symptoms varied over the functional hierarchy spanning unimodal to transmodal cortex. RESULTS Average controllability outperformed all other connectivity features at predicting positive PS symptoms and was the only feature to yield above-chance predictive performance. Improved prediction for average controllability was concentrated in transmodal cortex, whereas prediction performance for strength was uniform across the cortex, suggesting that indexing indirect connections through average controllability is crucial in association cortex. CONCLUSIONS Examining interindividual variation in direct and indirect structural connections to transmodal cortex is crucial for accurate prediction of positive PS symptoms.
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Affiliation(s)
- Linden Parkes
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, Pennsylvania
| | - Tyler M Moore
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania; Lifespan Brain Institute, University of Pennsylvania & Children's Hospital of Philadelphia, Philadelphia
| | - Monica E Calkins
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania; Lifespan Brain Institute, University of Pennsylvania & Children's Hospital of Philadelphia, Philadelphia
| | - Matthew Cieslak
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania; Lifespan Brain Institute, University of Pennsylvania & Children's Hospital of Philadelphia, Philadelphia; Center for Biomedical Image Computing and Analytics, Perelman School of Medicine, Philadelphia, Pennsylvania
| | - David R Roalf
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania; Lifespan Brain Institute, University of Pennsylvania & Children's Hospital of Philadelphia, Philadelphia
| | - Daniel H Wolf
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania; Lifespan Brain Institute, University of Pennsylvania & Children's Hospital of Philadelphia, Philadelphia; Center for Biomedical Image Computing and Analytics, Perelman School of Medicine, Philadelphia, Pennsylvania
| | - Ruben C Gur
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania; Lifespan Brain Institute, University of Pennsylvania & Children's Hospital of Philadelphia, Philadelphia; Department of Neurology, Perelman School of Medicine, Philadelphia, Pennsylvania; Department of Radiology, Perelman School of Medicine, Philadelphia, Pennsylvania
| | - Raquel E Gur
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania; Lifespan Brain Institute, University of Pennsylvania & Children's Hospital of Philadelphia, Philadelphia; Department of Neurology, Perelman School of Medicine, Philadelphia, Pennsylvania; Department of Radiology, Perelman School of Medicine, Philadelphia, Pennsylvania
| | - Theodore D Satterthwaite
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania; Lifespan Brain Institute, University of Pennsylvania & Children's Hospital of Philadelphia, Philadelphia; Center for Biomedical Image Computing and Analytics, Perelman School of Medicine, Philadelphia, Pennsylvania
| | - Danielle S Bassett
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, Pennsylvania; Department of Electrical & Systems Engineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, Pennsylvania; Department of Physics & Astronomy, College of Arts & Sciences, University of Pennsylvania, Philadelphia, Pennsylvania; Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania; Department of Neurology, Perelman School of Medicine, Philadelphia, Pennsylvania; Santa Fe Institute, Santa Fe, New Mexico.
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31
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Widespread plasticity of cognition-related brain networks in single-sided deafness revealed by randomized window-based dynamic functional connectivity. Med Image Anal 2021; 73:102163. [PMID: 34303170 DOI: 10.1016/j.media.2021.102163] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2020] [Revised: 06/07/2021] [Accepted: 07/02/2021] [Indexed: 11/22/2022]
Abstract
As an extreme type of partial auditory deprivation, single-sided deafness (SSD) has been demonstrated to lead to extensive neural plasticity according to multimodal neuroimaging studies. Among them, resting-state functional magnetic resonance imaging (rs-fMRI) offers valuable information on functional connectivities (FCs). However, most previous SSD rs-fMRI studies assumed that the extracted FC remains stationary during the entire fMRI scan and neglected dynamic functional activities. Existing fixed window-based dynamic FC analysis also ignores dynamic functional activities under different temporal terms. Additionally, due to the cost constraints of using MRI machines, using data-driven methods for unbiased hypothesis investigations may require more effective sample data augmentation techniques. To tackle these challenges and problems together, in this study, we proposed a dynamic window with a random length and position to extract participants' dynamic characteristics under different temporal terms and to extract more information from the dataset. Then, we proposed a nodal efficiency-based correlation matrix to describe the relationships of synergism between regions as features and applied a linear support vector machine (SVM) model to learn the importance of the features, which helped to identify SSD patients and healthy controls. A total of 68 participants (including 23 with left SSD, 20 with right SSD and 25 healthy controls) were enrolled. Our proposed approach with a random window showed clear improvement compared with traditional static and fixed window-based dynamic FC by using the linear SVM model. FCs related to the frontoparietal, somatomotor, dorsal attention, limbic and default mode networks played significant roles in differentiating SSD patients from healthy controls. Additionally, FCs between the somatomotor and frontoparietal networks made the greatest contribution to the classification model. Regarding brain regions, FCs related to the superior frontal gyrus, superior parietal lobule, superior temporal gyrus, amygdala, and orbital gyrus played significant roles. These findings suggest that networks and regions related to higher-order cognitive functions showed the most significant FC alterations in SSD, which may represent a compensatory collaboration of cognitive resources in SSD.
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32
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Shen Q, Liu Z. Remote firing propagation in the neural network of C. elegans. Phys Rev E 2021; 103:052414. [PMID: 34134291 DOI: 10.1103/physreve.103.052414] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2021] [Accepted: 05/10/2021] [Indexed: 11/07/2022]
Abstract
Understanding the mechanisms of firing propagation in brain networks has been a long-standing problem in the fields of nonlinear dynamics and network science. In general, it is believed that a specific firing in a brain network may be gradually propagated from a source node to its neighbors and then to the neighbors' neighbors and so on. Here, we explore firing propagation in the neural network of Caenorhabditis elegans and surprisingly find an abnormal phenomenon, i.e., remote firing propagation between two distant and indirectly connected nodes with the intermediate nodes being inactivated. This finding is robust to source nodes but depends on the topology of network such as the unidirectional couplings and heterogeneity of network. Further, a brief theoretical analysis is provided to explain its mechanism and a principle for remote firing propagation is figured out. This finding provides insights for us to understand how those cognitive subnetworks emerge in a brain network.
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Affiliation(s)
- Qiwei Shen
- School of Physics and Electronic Science, East China Normal University, Shanghai 200062, People's Republic of China
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai 200062, People's Republic of China
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33
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Wang Z, Liu Z. Effect of remote signal propagation in an empirical brain network. CHAOS (WOODBURY, N.Y.) 2021; 31:063126. [PMID: 34241283 DOI: 10.1063/5.0054296] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Accepted: 05/28/2021] [Indexed: 06/13/2023]
Abstract
Increasing evidence has shown that brain functions are seriously influenced by the heterogeneous structure of a brain network, but little attention has been paid to the aspect of signal propagation. We here study how a signal is propagated from a source node to other nodes on an empirical brain network by a model of bistable oscillators. We find that the unique structure of the brain network favors signal propagation in contrast to other heterogeneous networks and homogeneous random networks. Surprisingly, we find an effect of remote propagation where a signal is not successfully propagated to the neighbors of the source node but to its neighbors' neighbors. To reveal its underlying mechanism, we simplify the heterogeneous brain network into a heterogeneous chain model and find that the accumulation of weak signals from multiple channels makes a strong input signal to the next node, resulting in remote propagation. Furthermore, a theoretical analysis is presented to explain these findings.
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Affiliation(s)
- Zhenhua Wang
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, People's Republic of China
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, People's Republic of China
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34
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Wein S, Deco G, Tomé AM, Goldhacker M, Malloni WM, Greenlee MW, Lang EW. Brain Connectivity Studies on Structure-Function Relationships: A Short Survey with an Emphasis on Machine Learning. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2021; 2021:5573740. [PMID: 34135951 PMCID: PMC8177997 DOI: 10.1155/2021/5573740] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 05/06/2021] [Indexed: 12/12/2022]
Abstract
This short survey reviews the recent literature on the relationship between the brain structure and its functional dynamics. Imaging techniques such as diffusion tensor imaging (DTI) make it possible to reconstruct axonal fiber tracks and describe the structural connectivity (SC) between brain regions. By measuring fluctuations in neuronal activity, functional magnetic resonance imaging (fMRI) provides insights into the dynamics within this structural network. One key for a better understanding of brain mechanisms is to investigate how these fast dynamics emerge on a relatively stable structural backbone. So far, computational simulations and methods from graph theory have been mainly used for modeling this relationship. Machine learning techniques have already been established in neuroimaging for identifying functionally independent brain networks and classifying pathological brain states. This survey focuses on methods from machine learning, which contribute to our understanding of functional interactions between brain regions and their relation to the underlying anatomical substrate.
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Affiliation(s)
- Simon Wein
- CIML, Biophysics, University of Regensburg, Regensburg 93040, Germany
- Experimental Psychology, University of Regensburg, Regensburg 93040, Germany
| | - Gustavo Deco
- Center for Brain and Cognition, Department of Technology and Information, University Pompeu Fabra, Carrer Tanger, 122-140, Barcelona 08018, Spain
- Institució Catalana de la Recerca i Estudis Avançats, University Barcelona, Passeig Lluís Companys 23, Barcelona 08010, Spain
| | - Ana Maria Tomé
- IEETA/DETI, University de Aveiro, Aveiro 3810-193, Portugal
| | - Markus Goldhacker
- CIML, Biophysics, University of Regensburg, Regensburg 93040, Germany
- Experimental Psychology, University of Regensburg, Regensburg 93040, Germany
| | - Wilhelm M. Malloni
- Experimental Psychology, University of Regensburg, Regensburg 93040, Germany
| | - Mark W. Greenlee
- Experimental Psychology, University of Regensburg, Regensburg 93040, Germany
| | - Elmar W. Lang
- CIML, Biophysics, University of Regensburg, Regensburg 93040, Germany
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35
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Yin D, Kaiser M. Understanding neural flexibility from a multifaceted definition. Neuroimage 2021; 235:118027. [PMID: 33836274 DOI: 10.1016/j.neuroimage.2021.118027] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Revised: 01/19/2021] [Accepted: 03/27/2021] [Indexed: 11/19/2022] Open
Abstract
Flexibility is a hallmark of human intelligence. Emerging studies have proposed several flexibility measurements at the level of individual regions, to produce a brain map of neural flexibility. However, flexibility is usually inferred from separate components of brain activity (i.e., intrinsic/task-evoked), and different definitions are used. Moreover, recent studies have argued that neural processing may be more than a task-driven and intrinsic dichotomy. Therefore, the understanding to neural flexibility is still incomplete. To address this issue, we propose a multifaceted definition of neural flexibility according to three key features: broad cognitive engagement, distributed connectivity, and adaptive connectome dynamics. For these three features, we first review the advances in computational approaches, their functional relevance, and their potential pitfalls. We then suggest a set of metrics that can help us assign a flexibility rating to each region. Subsequently, we present an emergent probabilistic view for further understanding the functional operation of individual regions in the unified framework of intrinsic and task-driven states. Finally, we highlight several areas related to the multifaceted definition of neural flexibility for future research. This review not only strengthens our understanding of flexible human brain, but also suggests that the measure of neural flexibility could bridge the gap between understanding intrinsic and task-driven brain function dynamics.
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Affiliation(s)
- Dazhi Yin
- Key Laboratory of Brain Functional Genomics (Ministry of Education and Shanghai), School of Psychology and Cognitive Science, East China Normal University, Shanghai 200062, China.
| | - Marcus Kaiser
- School of Computing, Newcastle University, Newcastle upon Tyne NE4 5TG, UK; School of Medicine, University of Nottingham, Nottingham NG7 2UH, UK; Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China.
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36
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Abrego L, Gordleeva S, Kanakov O, Krivonosov M, Zaikin A. Estimating integrated information in bidirectional neuron-astrocyte communication. Phys Rev E 2021; 103:022410. [PMID: 33736090 DOI: 10.1103/physreve.103.022410] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 01/04/2021] [Indexed: 01/14/2023]
Abstract
There is growing evidence that suggests the importance of astrocytes as elements for neural information processing through the modulation of synaptic transmission. A key aspect of this problem is understanding the impact of astrocytes in the information carried by compound events in neurons across time. In this paper, we investigate how the astrocytes participate in the information integrated by individual neurons in an ensemble through the measurement of "integrated information." We propose a computational model that considers bidirectional communication between astrocytes and neurons through glutamate-induced calcium signaling. Our model highlights the role of astrocytes in information processing through dynamical coordination. Our findings suggest that the astrocytic feedback promotes synergetic influences in the neural communication, which is maximized when there is a balance between excess correlation and spontaneous spiking activity. The results were further linked with additional measures such as net synergy and mutual information. This result reinforces the idea that astrocytes have integrative properties in communication among neurons.
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Affiliation(s)
- Luis Abrego
- Department of Mathematics, University College London, London, United Kingdom
| | - Susanna Gordleeva
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia.,Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Oleg Kanakov
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Mikhail Krivonosov
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Alexey Zaikin
- Department of Mathematics, University College London, London, United Kingdom.,Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia.,Institute for Women's Health, University College London, London WC1E 6BT, United Kingdom.,Centre for Analysis of Complex Systems, Sechenov First Moscow State Medical University (Sechenov University), Moscow, Russia
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37
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Xiong K, Yan Z, Xie Y, Liu Z. Regulating heat conduction of complex networks by distributed nodes masses. Sci Rep 2021; 11:5501. [PMID: 33750886 PMCID: PMC7943792 DOI: 10.1038/s41598-021-85011-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Accepted: 02/15/2021] [Indexed: 01/31/2023] Open
Abstract
Developing efficient strategy to regulate heat conduction is a challenging problem, with potential implication in the field of thermal materials. We here focus on a potential thermal material, i.e. complex networks of nanowires and nanotubes, and propose a model where the mass of each node is assigned proportional to its degree with [Formula: see text], to investigate how distributed nodes masses can impact the heat flow in a network. We find that the heat conduction of complex network can be either increased or decreased, depending on the controlling parameter [Formula: see text]. Especially, there is an optimal heat conduction at [Formula: see text] and it is independent of network topologies. Moreover, we find that the temperature distribution within a complex network is also strongly influenced by the controlling parameter [Formula: see text]. A brief theoretical analysis is provided to explain these results. These findings may open up appealing applications in the cases of demanding either increasing or decreasing heat conduction, and our approach of regulating heat conduction by distributed nodes masses may be also valuable to the challenge of controlling waste heat dissipation in highly integrated and miniaturized modern devices.
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Affiliation(s)
- Kezhao Xiong
- College of Science, Xi'an University of Science and Technology, Xi'an, 710054, People's Republic of China.
- Department of Physics, Fudan University, Shanghai, 200433, People's Republic of China.
| | - Zhengxin Yan
- College of Science, Xi'an University of Science and Technology, Xi'an, 710054, People's Republic of China
| | - You Xie
- College of Science, Xi'an University of Science and Technology, Xi'an, 710054, People's Republic of China
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai, 200062, People's Republic of China.
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38
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Zhang Y, Motter AE. Mechanism for Strong Chimeras. PHYSICAL REVIEW LETTERS 2021; 126:094101. [PMID: 33750176 DOI: 10.1103/physrevlett.126.094101] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2020] [Revised: 11/23/2020] [Accepted: 01/27/2021] [Indexed: 06/12/2023]
Abstract
Chimera states have attracted significant attention as symmetry-broken states exhibiting the unexpected coexistence of coherence and incoherence. Despite the valuable insights gained from analyzing specific systems, an understanding of the general physical mechanism underlying the emergence of chimeras is still lacking. Here, we show that many stable chimeras arise because coherence in part of the system is sustained by incoherence in the rest of the system. This mechanism may be regarded as a deterministic analog of noise-induced synchronization and is shown to underlie the emergence of strong chimeras. These are chimera states whose coherent domain is formed by identically synchronized oscillators. Recognizing this mechanism offers a new meaning to the interpretation that chimeras are a natural link between coherence and incoherence.
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Affiliation(s)
- Yuanzhao Zhang
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | - Adilson E Motter
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
- Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA
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39
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Itabashi K, Tran QH, Hasegawa Y. Evaluating the phase dynamics of coupled oscillators via time-variant topological features. Phys Rev E 2021; 103:032207. [PMID: 33862823 DOI: 10.1103/physreve.103.032207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Accepted: 02/22/2021] [Indexed: 06/12/2023]
Abstract
By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient for identifying more specific behaviors. To improve this situation, we propose a topological approach that constructs the quantitative features describing the phase evolution of oscillators. Here, the phase data are mapped into a high-dimensional space at each time, and the topological features describing the shape of the data are subsequently extracted from the mapped points. These features are extended to time-variant topological features by adding the evolution time as an extra dimension in the topological feature space. The time-variant features provide crucial insights into the evolution of phase dynamics. Combining these features with the kernel method, we characterize the multiclustered synchronized dynamics during the early evolution stages. Finally, we demonstrate that our method can qualitatively explain chimera states. The experimental results confirmed the superiority of our method over those based on order parameters, especially when the available data are limited to the early-stage dynamics.
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Affiliation(s)
- Kazuha Itabashi
- Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Quoc Hoan Tran
- Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoshihiko Hasegawa
- Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
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40
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Huo S, Tian C, Zheng M, Guan S, Zhou C, Liu Z. Spatial multi-scaled chimera states of cerebral cortex network and its inherent structure-dynamics relationship in human brain. Natl Sci Rev 2021; 8:nwaa125. [PMID: 34691552 PMCID: PMC8288421 DOI: 10.1093/nsr/nwaa125] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2019] [Revised: 04/01/2020] [Accepted: 05/21/2020] [Indexed: 11/20/2022] Open
Abstract
Human cerebral cortex displays various dynamics patterns under different states, however the mechanism how such diverse patterns can be supported by the underlying brain network is still not well understood. Human brain has a unique network structure with different regions of interesting to perform cognitive tasks. Using coupled neural mass oscillators on human cortical network and paying attention to both global and local regions, we observe a new feature of chimera states with multiple spatial scales and a positive correlation between the synchronization preference of local region and the degree of symmetry of the connectivity of the region in the network. Further, we use the concept of effective symmetry in the network to build structural and dynamical hierarchical trees and find close matching between them. These results help to explain the multiple brain rhythms observed in experiments and suggest a generic principle for complex brain network as a structure substrate to support diverse functional patterns.
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Affiliation(s)
- Siyu Huo
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
| | - Changhai Tian
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
- School of Data Science, Tongren University, Tongren 554300, China
| | - Muhua Zheng
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
| | - Shuguang Guan
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
| | - Changsong Zhou
- Department of Physics, Centre for Nonlinear Studies and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Institute of Computational and Theoretical Studies, Hong Kong Baptist University, China
- Department of Physics, Zhejiang University, Hangzhou 310058, China
| | - Zonghua Liu
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
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41
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Woo JH, Honey CJ, Moon JY. Phase and amplitude dynamics of coupled oscillator systems on complex networks. CHAOS (WOODBURY, N.Y.) 2020; 30:121102. [PMID: 33380037 PMCID: PMC7714526 DOI: 10.1063/5.0031031] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2020] [Accepted: 11/05/2020] [Indexed: 06/12/2023]
Abstract
We investigated locking behaviors of coupled limit-cycle oscillators with phase and amplitude dynamics. We focused on how the dynamics are affected by inhomogeneous coupling strength and by angular and radial shifts in coupling functions. We performed mean-field analyses of oscillator systems with inhomogeneous coupling strength, testing Gaussian, power-law, and brain-like degree distributions. Even for oscillators with identical intrinsic frequencies and intrinsic amplitudes, we found that the coupling strength distribution and the coupling function generated a wide repertoire of phase and amplitude dynamics. These included fully and partially locked states in which high-degree or low-degree nodes would phase-lead the network. The mean-field analytical findings were confirmed via numerical simulations. The results suggest that, in oscillator systems in which individual nodes can independently vary their amplitude over time, qualitatively different dynamics can be produced via shifts in the coupling strength distribution and the coupling form. Of particular relevance to information flows in oscillator networks, changes in the non-specific drive to individual nodes can make high-degree nodes phase-lag or phase-lead the rest of the network.
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42
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Ruzzene G, Omelchenko I, Sawicki J, Zakharova A, Schöll E, Andrzejak RG. Remote pacemaker control of chimera states in multilayer networks of neurons. Phys Rev E 2020; 102:052216. [PMID: 33327161 DOI: 10.1103/physreve.102.052216] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Accepted: 10/30/2020] [Indexed: 06/12/2023]
Abstract
Networks of coupled nonlinear oscillators allow for the formation of nontrivial partially synchronized spatiotemporal patterns, such as chimera states, in which there are coexisting coherent (synchronized) and incoherent (desynchronized) domains. These complementary domains form spontaneously, and it is impossible to predict where the synchronized group will be positioned within the network. Therefore, possible ways to control the spatial position of the coherent and incoherent groups forming the chimera states are of high current interest. In this work we investigate how to control chimera patterns in multiplex networks of FitzHugh-Nagumo neurons, and in particular we want to prove that it is possible to remotely control chimera states exploiting the multiplex structure. We introduce a pacemaker oscillator within the network: this is an oscillator that does not receive input from the rest of the network but is sending out information to its neighbors. The pacemakers can be positioned in one or both layers. Their presence breaks the spatial symmetry of the layer in which they are introduced and allows us to control the position of the incoherent domain. We demonstrate how the remote control is possible for both uni- and bidirectional coupling between the layers. Furthermore we show which are the limitations of our control mechanisms when it is generalized from single-layer to multilayer networks.
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Affiliation(s)
- Giulia Ruzzene
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
| | - Iryna Omelchenko
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Jakub Sawicki
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Ralph G Andrzejak
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
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Srivastava P, Nozari E, Kim JZ, Ju H, Zhou D, Becker C, Pasqualetti F, Pappas GJ, Bassett DS. Models of communication and control for brain networks: distinctions, convergence, and future outlook. Netw Neurosci 2020; 4:1122-1159. [PMID: 33195951 PMCID: PMC7655113 DOI: 10.1162/netn_a_00158] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 07/21/2020] [Indexed: 12/13/2022] Open
Abstract
Recent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white-matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work.
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Affiliation(s)
- Pragya Srivastava
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA USA
| | - Erfan Nozari
- Department of Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, PA USA
| | - Jason Z. Kim
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA USA
| | - Harang Ju
- Neuroscience Graduate Group, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA USA
| | - Dale Zhou
- Neuroscience Graduate Group, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA USA
| | - Cassiano Becker
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA USA
| | - Fabio Pasqualetti
- Department of Mechanical Engineering, University of California, Riverside, CA USA
| | - George J. Pappas
- Department of Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, PA USA
| | - Danielle S. Bassett
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA USA
- Department of Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, PA USA
- Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, PA USA
- Department of Neurology, University of Pennsylvania, Philadelphia, PA USA
- Department of Psychiatry, University of Pennsylvania, Philadelphia, PA USA
- Santa Fe Institute, Santa Fe, NM USA
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Koulierakis I, Verganelakis DA, Omelchenko I, Zakharova A, Schöll E, Provata A. Structural anomalies in brain networks induce dynamical pacemaker effects. CHAOS (WOODBURY, N.Y.) 2020; 30:113137. [PMID: 33261325 DOI: 10.1063/5.0006207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/29/2020] [Accepted: 10/22/2020] [Indexed: 06/12/2023]
Abstract
Dynamical effects on healthy brains and brains affected by tumor are investigated via numerical simulations. The brains are modeled as multilayer networks consisting of neuronal oscillators whose connectivities are extracted from Magnetic Resonance Imaging (MRI) data. The numerical results demonstrate that the healthy brain presents chimera-like states where regions with high white matter concentrations in the direction connecting the two hemispheres act as the coherent domain, while the rest of the brain presents incoherent oscillations. To the contrary, in brains with destructed structures, traveling waves are produced initiated at the region where the tumor is located. These areas act as the pacemaker of the waves sweeping across the brain. The numerical simulations are performed using two neuronal models: (a) the FitzHugh-Nagumo model and (b) the leaky integrate-and-fire model. Both models give consistent results regarding the chimera-like oscillations in healthy brains and the pacemaker effect in the tumorous brains. These results are considered a starting point for further investigation in the detection of tumors with small sizes before becoming discernible on MRI recordings as well as in tumor development and evolution.
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Affiliation(s)
- I Koulierakis
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15341 Athens, Greece
| | - D A Verganelakis
- Nuclear Medicine Unit, Oncology Clinic "Marianna V. Vardinoyiannis-ELPIDA," Childrens' Hospital "A. Sofia," 11527 Athens, Greece
| | - I Omelchenko
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - A Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - E Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - A Provata
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15341 Athens, Greece
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45
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Kumar S, Williams RS, Wang Z. Third-order nanocircuit elements for neuromorphic engineering. Nature 2020; 585:518-523. [PMID: 32968256 DOI: 10.1038/s41586-020-2735-5] [Citation(s) in RCA: 49] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 08/03/2020] [Indexed: 11/09/2022]
Abstract
Current hardware approaches to biomimetic or neuromorphic artificial intelligence rely on elaborate transistor circuits to simulate biological functions. However, these can instead be more faithfully emulated by higher-order circuit elements that naturally express neuromorphic nonlinear dynamics1-4. Generating neuromorphic action potentials in a circuit element theoretically requires a minimum of third-order complexity (for example, three dynamical electrophysical processes)5, but there have been few examples of second-order neuromorphic elements, and no previous demonstration of any isolated third-order element6-8. Using both experiments and modelling, here we show how multiple electrophysical processes-including Mott transition dynamics-form a nanoscale third-order circuit element. We demonstrate simple transistorless networks of third-order elements that perform Boolean operations and find analogue solutions to a computationally hard graph-partitioning problem. This work paves a way towards very compact and densely functional neuromorphic computing primitives, and energy-efficient validation of neuroscientific models.
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Lilienkamp T, Parlitz U. Susceptibility of transient chimera states. Phys Rev E 2020; 102:032219. [PMID: 33075925 DOI: 10.1103/physreve.102.032219] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Accepted: 08/26/2020] [Indexed: 11/07/2022]
Abstract
Chaotic dynamics of a dynamical system is not necessarily persistent. If there is (without any active intervention from outside) a transition towards a (possibly nonchaotic) attractor, this phenomenon is called transient chaos, which can be observed in a variety of systems, e.g., in chemical reactions, population dynamics, neuronal activity, or cardiac dynamics. Also, chimera states, which show coherent and incoherent dynamics in spatially distinct regions of the system, are often chaotic transients. In many practical cases, the control of the chaotic dynamics (either the termination or the preservation of the chaotic dynamics) is desired. Although the self-termination typically occurs quite abruptly and can so far in general not be properly predicted, previous studies showed that in many systems a 'terminal transient phase" (TTP) prior to the self-termination existed, where the system was less susceptible against small but finite perturbations in different directions in state space. In this study, we show that, in the specific case of chimera states, these susceptible directions can be related to the structure of the chimera, which we divide into the coherent part, the incoherent part and the boundary in between. That means, in practice, if self-termination is close we can identify the direction of perturbation which is likely to maintain the chaotic dynamics (the chimera state). This finding improves the general understanding of the state space structure during the TTP, and could contribute also to practical applications like future control strategies of epileptic seizures which have been recently related to the collapse of chimera states.
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Affiliation(s)
- Thomas Lilienkamp
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany.,German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Robert-Koch-Straße 42a, 37075 Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany.,German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Robert-Koch-Straße 42a, 37075 Göttingen, Germany.,Institut für Dynamik komplexer Systeme, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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Papadopoulos L, Lynn CW, Battaglia D, Bassett DS. Relations between large-scale brain connectivity and effects of regional stimulation depend on collective dynamical state. PLoS Comput Biol 2020; 16:e1008144. [PMID: 32886673 PMCID: PMC7537889 DOI: 10.1371/journal.pcbi.1008144] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2020] [Revised: 10/06/2020] [Accepted: 07/12/2020] [Indexed: 01/09/2023] Open
Abstract
At the macroscale, the brain operates as a network of interconnected neuronal populations, which display coordinated rhythmic dynamics that support interareal communication. Understanding how stimulation of different brain areas impacts such activity is important for gaining basic insights into brain function and for further developing therapeutic neurmodulation. However, the complexity of brain structure and dynamics hinders predictions regarding the downstream effects of focal stimulation. More specifically, little is known about how the collective oscillatory regime of brain network activity—in concert with network structure—affects the outcomes of perturbations. Here, we combine human connectome data and biophysical modeling to begin filling these gaps. By tuning parameters that control collective system dynamics, we identify distinct states of simulated brain activity and investigate how the distributed effects of stimulation manifest at different dynamical working points. When baseline oscillations are weak, the stimulated area exhibits enhanced power and frequency, and due to network interactions, activity in this excited frequency band propagates to nearby regions. Notably, beyond these linear effects, we further find that focal stimulation causes more distributed modifications to interareal coherence in a band containing regions’ baseline oscillation frequencies. Importantly, depending on the dynamical state of the system, these broadband effects can be better predicted by functional rather than structural connectivity, emphasizing a complex interplay between anatomical organization, dynamics, and response to perturbation. In contrast, when the network operates in a regime of strong regional oscillations, stimulation causes only slight shifts in power and frequency, and structural connectivity becomes most predictive of stimulation-induced changes in network activity patterns. In sum, this work builds upon and extends previous computational studies investigating the impacts of stimulation, and underscores the fact that both the stimulation site, and, crucially, the regime of brain network dynamics, can influence the network-wide responses to local perturbations. Stimulation can be used to alter brain activity and is a therapeutic option for certain neurological conditions. However, predicting the distributed effects of local perturbations is difficult. Previous studies show that responses to stimulation depend on anatomical (or structural) coupling. In addition to structure, here we consider how stimulation effects also depend on the brain’s collective dynamical (or functional) state, arising from the coordination of rhythmic activity across large-scale networks. In a whole-brain computational model, we show that global responses to regional stimulation can indeed be contingent upon and differ across various dynamical working points. Notably, depending on the network’s oscillatory regime, stimulation can accelerate the activity of the stimulated site, and lead to widespread effects at both the new, excited frequency, as well as in a much broader frequency range including areas’ baseline frequencies. While structural connectivity is a good predictor of “excited band” changes, in some states “baseline band” effects can be better predicted by functional connectivity, which depends upon the system’s oscillatory regime. By integrating and extending past efforts, our results thus indicate that dynamical—in additional to structural—brain organization plays a role in governing how focal stimulation modulates interactions between distributed network elements.
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Affiliation(s)
- Lia Papadopoulos
- Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
| | - Christopher W. Lynn
- Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
| | - Demian Battaglia
- Université Aix-Marseille, INSERM UMR 1106, Institut de Neurosciences des Systèmes, F-13005, Marseille, France
| | - Danielle S. Bassett
- Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
- Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
- Department of Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
- Department of Neurology, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
- Department of Psychiatry, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
- Santa Fe Institute, Santa Fe, New Mexico, United States of America
- * E-mail:
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48
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Wang Z, Baruni S, Parastesh F, Jafari S, Ghosh D, Perc M, Hussain I. Chimeras in an adaptive neuronal network with burst-timing-dependent plasticity. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.083] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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49
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Vadivasova TE, Slepnev AV, Zakharova A. Control of inter-layer synchronization by multiplexing noise. CHAOS (WOODBURY, N.Y.) 2020; 30:091101. [PMID: 33003909 DOI: 10.1063/5.0023071] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2020] [Accepted: 08/25/2020] [Indexed: 06/11/2023]
Abstract
We study the synchronization of spatio-temporal patterns in a two-layer network of coupled chaotic maps, where each layer is represented by a nonlocally coupled ring. In particular, we focus on noisy inter-layer communication that we call multiplexing noise. We show that noisy modulation of inter-layer coupling strength has a significant impact on the dynamics of the network and specifically on the degree of synchronization of spatio-temporal patterns of interacting layers initially (in the absence of interaction) exhibiting chimera states. Our goal is to develop control strategies based on multiplexing noise for both identical and non-identical layers. We find that for the appropriate choice of intensity and frequency characteristics of parametric noise, complete or partial synchronization of the layers can be observed. Interestingly, for achieving inter-layer synchronization through multiplexing noise, it is crucial to have colored noise with intermediate spectral width. In the limit of white noise, the synchronization is destroyed. These results are the first step toward understanding the role of noisy inter-layer communication for the dynamics of multilayer networks.
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Affiliation(s)
- T E Vadivasova
- Department of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - A V Slepnev
- Department of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - A Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
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50
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Frolov N, Maksimenko V, Majhi S, Rakshit S, Ghosh D, Hramov A. Chimera-like behavior in a heterogeneous Kuramoto model: The interplay between attractive and repulsive coupling. CHAOS (WOODBURY, N.Y.) 2020; 30:081102. [PMID: 32872824 DOI: 10.1063/5.0019200] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Accepted: 07/22/2020] [Indexed: 06/11/2023]
Abstract
Interaction within an ensemble of coupled nonlinear oscillators induces a variety of collective behaviors. One of the most fascinating is a chimera state that manifests the coexistence of spatially distinct populations of coherent and incoherent elements. Understanding of the emergent chimera behavior in controlled experiments or real systems requires a focus on the consideration of heterogeneous network models. In this study, we explore the transitions in a heterogeneous Kuramoto model under the monotonical increase of the coupling strength and specifically find that this system exhibits a frequency-modulated chimera-like pattern during the explosive transition to synchronization. We demonstrate that this specific dynamical regime originates from the interplay between (the evolved) attractively and repulsively coupled subpopulations. We also show that the above-mentioned chimera-like state is induced under weakly non-local, small-world, and sparse scale-free coupling and suppressed in globally coupled, strongly rewired, and dense scale-free networks due to the emergence of the large-scale connections.
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Affiliation(s)
- Nikita Frolov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
| | - Vladimir Maksimenko
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
| | - Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Alexander Hramov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
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