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Masoller C, Lehnertz K, Goodfellow M, Kugiumtzis D, Zochowski M. Editorial: Reviews in networks in the brain system. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 4:1403698. [PMID: 38840903 PMCID: PMC11151744 DOI: 10.3389/fnetp.2024.1403698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 05/08/2024] [Indexed: 06/07/2024]
Affiliation(s)
- 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
- nterdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
| | - Marc Goodfellow
- Living Systems Institute, University of Exeter, Exeter, United Kingdom
| | - Dimitris Kugiumtzis
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece
| | - Michal Zochowski
- Biophysics Program and Department of Physics, University of Michigan, Ann Arbor, MI, United States
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Mannone M, Fazio P, Marwan N. Modeling a neurological disorder as the result of an operator acting on the brain: A first sketch based on network channel modeling. CHAOS (WOODBURY, N.Y.) 2024; 34:053133. [PMID: 38781106 DOI: 10.1063/5.0199988] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2024] [Accepted: 05/06/2024] [Indexed: 05/25/2024]
Abstract
The brain is a complex network, and diseases can alter its structures and connections between regions. Therefore, we can try to formalize the action of diseases by using operators acting on the brain network. Here, we propose a conceptual model of the brain, seen as a multilayer network, whose intra-lobe interactions are formalized as the diagonal blocks of an adjacency matrix. We propose a general and abstract definition of disease as an operator altering the weights of the connections between neural agglomerates, that is, the elements of the brain matrix. As models, we consider examples from three neurological disorders: epilepsy, Alzheimer-Perusini's disease, and schizophrenia. The alteration of neural connections can be seen as alterations of communication pathways, and thus, they can be described with a new channel model.
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Affiliation(s)
- Maria Mannone
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
- DSMN, Ca' Foscari University of Venice, 30170 Venezia Mestre Italy
- Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, 14473 Potsdam, Germany
| | - Peppino Fazio
- DSMN, Ca' Foscari University of Venice, 30170 Venezia Mestre Italy
- VSB, Technical University of Ostrava, 708 00 Ostrava, Czechia
| | - Norbert Marwan
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
- Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, 14473 Potsdam, Germany
- Institute of Geosciences Potsdam, University of Potsdam, 14473 Potsdam, Germany
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Papo D, Buldú JM. Does the brain behave like a (complex) network? I. Dynamics. Phys Life Rev 2024; 48:47-98. [PMID: 38145591 DOI: 10.1016/j.plrev.2023.12.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 12/10/2023] [Indexed: 12/27/2023]
Abstract
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.
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Affiliation(s)
- D Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, Ferrara, Italy; Center for Translational Neurophysiology, Fondazione Istituto Italiano di Tecnologia, Ferrara, Italy.
| | - J M Buldú
- Complex Systems Group & G.I.S.C., Universidad Rey Juan Carlos, Madrid, Spain
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Niu X, Peng Y, Jiang Z, Huang S, Liu R, Zhu M, Shi L. Gamma-band-based dynamic functional connectivity in pigeon entopallium during sample presentation in a delayed color matching task. Cogn Neurodyn 2024; 18:37-47. [PMID: 38406198 PMCID: PMC10881935 DOI: 10.1007/s11571-022-09916-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Revised: 10/12/2022] [Accepted: 11/17/2022] [Indexed: 01/09/2023] Open
Abstract
Birds have developed visual cognitions, especially in discriminating colors due to their four types of cones in the retina. The entopallium of birds is thought to be involved in the processing of color information during visual cognition. However, there is a lack of understanding about how functional connectivity in the entopallium region of birds changes during color cognition, which is related to various input colors. We therefore trained pigeons to perform a delayed color matching task, in which two colors were randomly presented in sample stimuli phrases, and the neural activity at individual recording site and the gamma band functional connectivity among local population in entopallium during sample presentation were analyzed. Both gamma band energy and gamma band functional connectivity presented dynamics as the stimulus was presented and persisted. The response features in the early-stimulus phase were significantly different from those of baseline and the late-stimulus phase. Furthermore, gamma band energy showed significant differences between different colors during the early-stimulus phase, but the global feature of the gamma band functional network did not. Further decoding results showed that decoding accuracy was significantly enhanced by adding functional connectivity features, suggesting the global feature of the gamma band functional network did not directly contain color information, but was related to it. These results provided insight into information processing rules among local neuronal populations in the entopallium of birds during color cognition, which is important for their daily life.
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Affiliation(s)
- Xiaoke Niu
- Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, School of Electrical and Information Engineering, ZhengZhou University, Zhengzhou, 450001 China
| | - Yanyan Peng
- Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, School of Electrical and Information Engineering, ZhengZhou University, Zhengzhou, 450001 China
| | - Zhenyang Jiang
- Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, School of Electrical and Information Engineering, ZhengZhou University, Zhengzhou, 450001 China
| | - Shuman Huang
- Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, School of Electrical and Information Engineering, ZhengZhou University, Zhengzhou, 450001 China
| | - Ruibin Liu
- Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, School of Electrical and Information Engineering, ZhengZhou University, Zhengzhou, 450001 China
| | - Minjie Zhu
- Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, School of Electrical and Information Engineering, ZhengZhou University, Zhengzhou, 450001 China
| | - Li Shi
- Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, School of Electrical and Information Engineering, ZhengZhou University, Zhengzhou, 450001 China
- Department of Automation, Tsinghua University, Beijing, 100000 China
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Briggs JK, Gresch A, Marinelli I, Dwulet JM, Albers DJ, Kravets V, Benninger RKP. β-cell intrinsic dynamics rather than gap junction structure dictates subpopulations in the islet functional network. eLife 2023; 12:e83147. [PMID: 38018905 PMCID: PMC10803032 DOI: 10.7554/elife.83147] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Accepted: 11/27/2023] [Indexed: 11/30/2023] Open
Abstract
Diabetes is caused by the inability of electrically coupled, functionally heterogeneous β-cells within the pancreatic islet to provide adequate insulin secretion. Functional networks have been used to represent synchronized oscillatory [Ca2+] dynamics and to study β-cell subpopulations, which play an important role in driving islet function. The mechanism by which highly synchronized β-cell subpopulations drive islet function is unclear. We used experimental and computational techniques to investigate the relationship between functional networks, structural (gap junction) networks, and intrinsic β-cell dynamics in slow and fast oscillating islets. Highly synchronized subpopulations in the functional network were differentiated by intrinsic dynamics, including metabolic activity and KATP channel conductance, more than structural coupling. Consistent with this, intrinsic dynamics were more predictive of high synchronization in the islet functional network as compared to high levels of structural coupling. Finally, dysfunction of gap junctions, which can occur in diabetes, caused decreases in the efficiency and clustering of the functional network. These results indicate that intrinsic dynamics rather than structure drive connections in the functional network and highly synchronized subpopulations, but gap junctions are still essential for overall network efficiency. These findings deepen our interpretation of functional networks and the formation of functional subpopulations in dynamic tissues such as the islet.
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Affiliation(s)
- Jennifer K Briggs
- Department of Bioengineering, University of Colorado Anschutz Medical CampusAuroraUnited States
| | - Anne Gresch
- Department of Bioengineering, University of Colorado Anschutz Medical CampusAuroraUnited States
- Barbara Davis Center for Childhood Diabetes, University of Colorado Anschutz Medical CampusAuroraUnited States
| | - Isabella Marinelli
- Centre for Systems Modelling and Quantitative Biomedicine, University of BirminghamBirminghamUnited Kingdom
| | - JaeAnn M Dwulet
- Department of Bioengineering, University of Colorado Anschutz Medical CampusAuroraUnited States
| | - David J Albers
- Department of Bioengineering, University of Colorado Anschutz Medical CampusAuroraUnited States
- Department of Biomedical Informatics, University of Colorado Anschutz Medical CampusAuroraUnited States
| | - Vira Kravets
- Department of Bioengineering, University of Colorado Anschutz Medical CampusAuroraUnited States
| | - Richard KP Benninger
- Department of Bioengineering, University of Colorado Anschutz Medical CampusAuroraUnited States
- Barbara Davis Center for Childhood Diabetes, University of Colorado Anschutz Medical CampusAuroraUnited States
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Rosenblum M, Pikovsky A. Inferring connectivity of an oscillatory network via the phase dynamics reconstruction. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:1298228. [PMID: 38073862 PMCID: PMC10704096 DOI: 10.3389/fnetp.2023.1298228] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 11/13/2023] [Indexed: 06/10/2024]
Abstract
We review an approach for reconstructing oscillatory networks' undirected and directed connectivity from data. The technique relies on inferring the phase dynamics model. The central assumption is that we observe the outputs of all network nodes. We distinguish between two cases. In the first one, the observed signals represent smooth oscillations, while in the second one, the data are pulse-like and can be viewed as point processes. For the first case, we discuss estimating the true phase from a scalar signal, exploiting the protophase-to-phase transformation. With the phases at hand, pairwise and triplet synchronization indices can characterize the undirected connectivity. Next, we demonstrate how to infer the general form of the coupling functions for two or three oscillators and how to use these functions to quantify the directional links. We proceed with a different treatment of networks with more than three nodes. We discuss the difference between the structural and effective phase connectivity that emerges due to high-order terms in the coupling functions. For the second case of point-process data, we use the instants of spikes to infer the phase dynamics model in the Winfree form directly. This way, we obtain the network's coupling matrix in the first approximation in the coupling strength.
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Affiliation(s)
- Michael Rosenblum
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
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Bröhl T, Lehnertz K. A perturbation-based approach to identifying potentially superfluous network constituents. CHAOS (WOODBURY, N.Y.) 2023; 33:2894464. [PMID: 37276550 DOI: 10.1063/5.0152030] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 05/16/2023] [Indexed: 06/07/2023]
Abstract
Constructing networks from empirical time-series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks.
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Affiliation(s)
- Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
- Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany
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Elaeva M, Blanter E, Shnirman M, Shapoval A. Asymmetry in the Kuramoto model with nonidentical coupling. Phys Rev E 2023; 107:064201. [PMID: 37464665 DOI: 10.1103/physreve.107.064201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2022] [Accepted: 04/26/2023] [Indexed: 07/20/2023]
Abstract
Synchronization and desynchronization of coupled oscillators appear to be the key property of many physical systems. It is believed that to predict a synchronization (or desynchronization) event, the knowledge on the exact structure of the oscillatory network is required. However, natural sciences often deal with observations where the coupling coefficients are not available. In the present paper we suggest a way to characterize synchronization of two oscillators without the reconstruction of coupling. Our method is based on the Kuramoto chain with three oscillators with constant but nonidentical coupling. We characterize coupling in this chain by two parameters: the coupling strength s and disparity σ. We give an analytical expression of the boundary s_{max} of synchronization occurred when s>s_{max}. We propose asymmetry A of the generalized order parameter induced by the coupling disparity as a new characteristic of the synchronization between two oscillators. For the chain model with three oscillators we present the self-consistent inverse problem. We explore scaling properties of the asymmetry A constructed for the inverse problem. We demonstrate that the asymmetry A in the chain model is maximal when the coupling strength in the model reaches the boundary of synchronization s_{max}. We suggest that the asymmetry A may be derived from the phase difference of any two oscillators if one pretends that they are edges of an abstract chain with three oscillators. Performing such a derivation with the general three-oscillator Kuramoto model, we show that the crossover from the chain to general network of oscillators keeps the interrelation between the asymmetry A and synchronization. Finally, we apply the asymmetry A to describe synchronization of the solar magnetic field proxies and discuss its potential use for the forecast of solar cycle anomalies.
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Affiliation(s)
- M Elaeva
- Department of Higher Mathematics, HSE University, Moscow 109028, Russia
| | - E Blanter
- Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS, Moscow 117997, Russia
| | - M Shnirman
- Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS, Moscow 117997, Russia
| | - A Shapoval
- Department of Mathematics and Computer Science, University of Lodz, Lodz 90-238, Poland and Cybersecurity Center, Universidad Bernardo O'Higgins, Santiago 8370993, Chile
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Lehnertz K. Ordinal methods for a characterization of evolving functional brain networks. CHAOS (WOODBURY, N.Y.) 2023; 33:022101. [PMID: 36859225 DOI: 10.1063/5.0136181] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Accepted: 01/06/2023] [Indexed: 06/18/2023]
Abstract
Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a resulting loss of information, this approach captures meaningful information about the temporal structure of the underlying system dynamics as well as about properties of interactions between coupled systems. This-together with its conceptual simplicity and robustness against measurement noise-makes ordinal time series analysis well suited to improve characterization of the still poorly understood spatiotemporal dynamics of the human brain. This minireview briefly summarizes the state-of-the-art of uni- and bivariate ordinal time-series-analysis techniques together with applications in the neurosciences. It will highlight current limitations to stimulate further developments, which would be necessary to advance characterization of evolving functional brain networks.
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Affiliation(s)
- Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany; Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany; and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany
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