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Bröhl T, Rings T, Pukropski J, von Wrede R, Lehnertz K. The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 3:1338864. [PMID: 38293249 PMCID: PMC10825060 DOI: 10.3389/fnetp.2023.1338864] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Accepted: 12/19/2023] [Indexed: 02/01/2024]
Abstract
Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.
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Affiliation(s)
- Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Jan Pukropski
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Randi von Wrede
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - 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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Novitskaya Y, Dümpelmann M, Schulze-Bonhage A. Physiological and pathological neuronal connectivity in the living human brain based on intracranial EEG signals: the current state of research. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:1297345. [PMID: 38107334 PMCID: PMC10723837 DOI: 10.3389/fnetp.2023.1297345] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 11/17/2023] [Indexed: 12/19/2023]
Abstract
Over the past decades, studies of human brain networks have received growing attention as the assessment and modelling of connectivity in the brain is a topic of high impact with potential application in the understanding of human brain organization under both physiological as well as various pathological conditions. Under specific diagnostic settings, human neuronal signal can be obtained from intracranial EEG (iEEG) recording in epilepsy patients that allows gaining insight into the functional organisation of living human brain. There are two approaches to assess brain connectivity in the iEEG-based signal: evaluation of spontaneous neuronal oscillations during ongoing physiological and pathological brain activity, and analysis of the electrophysiological cortico-cortical neuronal responses, evoked by single pulse electrical stimulation (SPES). Both methods have their own advantages and limitations. The paper outlines available methodological approaches and provides an overview of current findings in studies of physiological and pathological human brain networks, based on intracranial EEG recordings.
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Affiliation(s)
- Yulia Novitskaya
- Epilepsy Center, Department of Neurosurgery, Medical Center—University of Freiburg, Faculty of Medicine, University of Freiburg, Freiburg, Germany
| | - Matthias Dümpelmann
- Epilepsy Center, Department of Neurosurgery, Medical Center—University of Freiburg, Faculty of Medicine, University of Freiburg, Freiburg, Germany
- Department of Microsystems Engineering (IMTEK), University of Freiburg, Freiburg, Germany
| | - Andreas Schulze-Bonhage
- Epilepsy Center, Department of Neurosurgery, Medical Center—University of Freiburg, Faculty of Medicine, University of Freiburg, Freiburg, Germany
- Center for Basics in NeuroModulation, Faculty of Medicine, University of Freiburg, Freiburg, Germany
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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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Sanz-García A, Perez-Romero M, Ortega GJ. Spectral and network characterization of focal seizure types and phases. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2022; 217:106704. [PMID: 35220198 DOI: 10.1016/j.cmpb.2022.106704] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Revised: 01/27/2022] [Accepted: 02/19/2022] [Indexed: 06/14/2023]
Abstract
BACKGROUND AND OBJECTIVE Currently, epileptic seizure characterization relies on several clinical features that allow their classification into different types. The present work aims to characterize both seizure types and phases based exclusively on electrophysiological characteristics. METHODS Based on the analysis of intracranial EEG recordings of 129 seizures from 22 patients obtained from the European Epilepsy Database, network and spectral measures were calculated in five-second temporal windows. Statistically significant differences between each window of the seizure phases (preictal, ictal, and postictal) and the interictal phase were used to identify/classify seizure types and their phases. A support vector machine (SVM) working on a multidimensional feature space of network and spectral measures was implemented for the classification of each seizure type; a traditional statistical approach was also conducted to highlight the underlying patterns to each seizure type or phase. RESULTS The percentage of correct classification of seizure types, corrected by chance, provided by the SVM exceeded 70%, considering all measures and the entire seizure (preictal + ictal + postictal). This percentage increased to more than 80% when all the measures during the ictal period for the depth electrodes or during the postictal for subdural electrodes were considered. Regarding the statistical approach, several measures presented a monotonic ascending and descending behavior with respect to seizure severity; these changes were observed during the ictal and postictal periods. Some measures were specific of each seizure type. CONCLUSIONS Our results provide a new framework to seizure characterization and reveal the possibility of an exclusively intracranial EEG-based classification. This could be used to build an automatic seizure classification system and provides new evidence of the network-related physiopathology of epilepsies. Thus, the novelty of this work is the possibility of differentiating seizure types based exclusively on the EEG recordings, providing evidence of the underlying patterns or characteristics to each seizure type and/or phase that would allow their optimal classification.
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Affiliation(s)
- Ancor Sanz-García
- Instituto de Investigación Sanitaria, Hospital Universitario de la Princesa, Diego de León 62, 9th floor, Madrid 28006, Spain.
| | - Miriam Perez-Romero
- Instituto de Investigación Sanitaria, Hospital Universitario de la Princesa, Diego de León 62, 9th floor, Madrid 28006, Spain
| | - Guillermo J Ortega
- Instituto de Investigación Sanitaria, Hospital Universitario de la Princesa, Diego de León 62, 9th floor, Madrid 28006, Spain; CONICET, National Scientific and Technical Research Council, Argentina; Universidad Nacional de Quilmes, Science and Technology Department, Argentina
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Saboo KV, Balzekas I, Kremen V, Varatharajah Y, Kucewicz M, Iyer RK, Worrell GA. Leveraging electrophysiologic correlates of word encoding to map seizure onset zone in focal epilepsy: Task-dependent changes in epileptiform activity, spectral features, and functional connectivity. Epilepsia 2021; 62:2627-2639. [PMID: 34536230 DOI: 10.1111/epi.17067] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Revised: 08/31/2021] [Accepted: 09/01/2021] [Indexed: 11/29/2022]
Abstract
OBJECTIVE Verbal memory dysfunction is common in focal, drug-resistant epilepsy (DRE). Unfortunately, surgical removal of seizure-generating brain tissue can be associated with further memory decline. Therefore, localization of both the circuits generating seizures and those underlying cognitive functions is critical in presurgical evaluations for patients who may be candidates for resective surgery. We used intracranial electroencephalographic (iEEG) recordings during a verbal memory task to investigate word encoding in focal epilepsy. We hypothesized that engagement in a memory task would exaggerate local iEEG feature differences between the seizure onset zone (SOZ) and neighboring tissue as compared to wakeful rest ("nontask"). METHODS Ten participants undergoing presurgical iEEG evaluation for DRE performed a free recall verbal memory task. We evaluated three iEEG features in SOZ and non-SOZ electrodes during successful word encoding and compared them with nontask recordings: interictal epileptiform spike (IES) rates, power in band (PIB), and relative entropy (REN; a functional connectivity measure). RESULTS We found a complex pattern of PIB and REN changes in SOZ and non-SOZ electrodes during successful word encoding compared to nontask. Successful word encoding was associated with a reduction in local electrographic functional connectivity (increased REN), which was most exaggerated in temporal lobe SOZ. The IES rates were reduced during task, but only in the non-SOZ electrodes. Compared with nontask, REN features during task yielded marginal improvements in SOZ classification. SIGNIFICANCE Previous studies have supported REN as a biomarker for epileptic brain. We show that REN differences between SOZ and non-SOZ are enhanced during a verbal memory task. We also show that IESs are reduced during task in non-SOZ, but not in SOZ. These findings support the hypothesis that SOZ and non-SOZ respond differently to task and warrant further exploration into the use of cognitive tasks to identify functioning memory circuits and localize SOZ.
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Affiliation(s)
- Krishnakant V Saboo
- Department of Electrical and Computer Engineering, University of Illinois, Urbana, Illinois, USA.,Bioelectronics, Neurophysiology, and Engineering Laboratory, Department of Neurology, Mayo Clinic, Rochester, Minnesota, USA.,Mayo Clinic Graduate School of Biomedical Sciences, Mayo Clinic School of Medicine and Mayo Clinic Medical Scientist Training Program, Mayo Clinic, Rochester, Minnesota, USA
| | - Irena Balzekas
- Bioelectronics, Neurophysiology, and Engineering Laboratory, Department of Neurology, Mayo Clinic, Rochester, Minnesota, USA.,Mayo Clinic Graduate School of Biomedical Sciences, Mayo Clinic School of Medicine and Mayo Clinic Medical Scientist Training Program, Mayo Clinic, Rochester, Minnesota, USA
| | - Vaclav Kremen
- Bioelectronics, Neurophysiology, and Engineering Laboratory, Department of Neurology, Mayo Clinic, Rochester, Minnesota, USA.,Czech Institute of Informatics, Robotics, and Cybernetics, Czech Technical University in Prague, Prague, Czech Republic
| | - Yogatheesan Varatharajah
- Department of Electrical and Computer Engineering, University of Illinois, Urbana, Illinois, USA.,Department of Bioengineering, University of Illinois, Urbana, Illinois, USA
| | - Michal Kucewicz
- Bioelectronics, Neurophysiology, and Engineering Laboratory, Department of Neurology, Mayo Clinic, Rochester, Minnesota, USA.,Faculty of Electronics, Telecommunications, and Informatics, Multimedia Systems Department, BioTechMed Center, Gdansk University of Technology, Gdansk, Poland.,Department of Physiology and Biomedical Engineering, Mayo Clinic, Rochester, Minnesota, USA
| | - Ravishankar K Iyer
- Department of Electrical and Computer Engineering, University of Illinois, Urbana, Illinois, USA
| | - Gregory A Worrell
- Bioelectronics, Neurophysiology, and Engineering Laboratory, Department of Neurology, Mayo Clinic, Rochester, Minnesota, USA
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Bernabei JM, Arnold TC, Shah P, Revell A, Ong IZ, Kini LG, Stein JM, Shinohara RT, Lucas TH, Davis KA, Bassett DS, Litt B. Electrocorticography and stereo EEG provide distinct measures of brain connectivity: implications for network models. Brain Commun 2021; 3:fcab156. [PMID: 34396112 PMCID: PMC8361393 DOI: 10.1093/braincomms/fcab156] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Revised: 04/19/2021] [Accepted: 05/31/2021] [Indexed: 01/01/2023] Open
Abstract
Brain network models derived from graph theory have the potential to guide functional neurosurgery, and to improve rates of post-operative seizure freedom for patients with epilepsy. A barrier to applying these models clinically is that intracranial EEG electrode implantation strategies vary by centre, region and country, from cortical grid & strip electrodes (Electrocorticography), to purely stereotactic depth electrodes (Stereo EEG), to a mixture of both. To determine whether models derived from one type of study are broadly applicable to others, we investigate the differences in brain networks mapped by electrocorticography and stereo EEG in a cohort of patients who underwent surgery for temporal lobe epilepsy and achieved a favourable outcome. We show that networks derived from electrocorticography and stereo EEG define distinct relationships between resected and spared tissue, which may be driven by sampling bias of temporal depth electrodes in patients with predominantly cortical grids. We propose a method of correcting for the effect of internodal distance that is specific to electrode type and explore how additional methods for spatially correcting for sampling bias affect network models. Ultimately, we find that smaller surgical targets tend to have lower connectivity with respect to the surrounding network, challenging notions that abnormal connectivity in the epileptogenic zone is typically high. Our findings suggest that effectively applying computational models to localize epileptic networks requires accounting for the effects of spatial sampling, particularly when analysing both electrocorticography and stereo EEG recordings in the same cohort, and that future network studies of epilepsy surgery should also account for differences in focality between resection and ablation. We propose that these findings are broadly relevant to intracranial EEG network modelling in epilepsy and an important step in translating them clinically into patient care.
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Affiliation(s)
- John M Bernabei
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Center for Neuroengineering & Therapeutics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - T Campbell Arnold
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Center for Neuroengineering & Therapeutics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Preya Shah
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Center for Neuroengineering & Therapeutics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Andrew Revell
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Center for Neuroengineering & Therapeutics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Ian Z Ong
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Center for Neuroengineering & Therapeutics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Lohith G Kini
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Center for Neuroengineering & Therapeutics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Joel M Stein
- Department of Radiology, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Russell T Shinohara
- Department of Biostatistics, Epidemiology, & Informatics, University of Pennsylvania, Philadelphia, PA 19104, USA
- Statistics in Imaging and Visualization Center, University of Pennsylvania, Philadelphia, PA 19104, USA
- Center for Clinical Epidemiology and Biostatistics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Timothy H Lucas
- Department of Neurosurgery, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Kathryn A Davis
- Center for Neuroengineering & Therapeutics, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Neurology, Penn Epilepsy Center, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Danielle S Bassett
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Neurosurgery, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Neurology, Penn Epilepsy Center, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Psychiatry, University of Pennsylvania, Philadelphia, PA 19104, USA
- The Santa Fe Institute, Santa Fe, NM 87501, USA
| | - Brian Litt
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Center for Neuroengineering & Therapeutics, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Neurosurgery, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Neurology, Penn Epilepsy Center, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA
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Wang Q, Siok WT. Intracranial recording in patients with aphasia using nanomaterial-based flexible electronics: promises and challenges. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2021; 12:330-342. [PMID: 33889479 PMCID: PMC8042484 DOI: 10.3762/bjnano.12.27] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/31/2020] [Accepted: 03/18/2021] [Indexed: 06/12/2023]
Abstract
In recent years, researchers have studied how nanotechnology could enhance neuroimaging techniques. The application of nanomaterial-based flexible electronics has the potential to advance conventional intracranial electroencephalography (iEEG) by utilising brain-compatible soft nanomaterials. The resultant technique has significantly high spatial and temporal resolution, both of which enhance the localisation of brain functions and the mapping of dynamic language processing. This review presents findings on aphasia, an impairment in language and communication, and discusses how different brain imaging techniques, including positron emission tomography, magnetic resonance imaging, and iEEG, have advanced our understanding of the neural networks underlying language and reading processing. We then outline the strengths and weaknesses of iEEG in studying human cognition and the development of intracranial recordings that use brain-compatible flexible electrodes. We close by discussing the potential advantages and challenges of future investigations adopting nanomaterial-based flexible electronics for intracranial recording in patients with aphasia.
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Affiliation(s)
- Qingchun Wang
- Department of Linguistics, The University of Hong Kong, Hong Kong, China
| | - Wai Ting Siok
- Department of Linguistics, The University of Hong Kong, Hong Kong, China
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Reconfiguration of human evolving large-scale epileptic brain networks prior to seizures: an evaluation with node centralities. Sci Rep 2020; 10:21921. [PMID: 33318564 PMCID: PMC7736584 DOI: 10.1038/s41598-020-78899-7] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 11/30/2020] [Indexed: 01/01/2023] Open
Abstract
Previous research has indicated that temporal changes of centrality of specific nodes in human evolving large-scale epileptic brain networks carry information predictive of impending seizures. Centrality is a fundamental network-theoretical concept that allows one to assess the role a node plays in a network. This concept allows for various interpretations, which is reflected in a number of centrality indices. Here we aim to achieve a more general understanding of local and global network reconfigurations during the pre-seizure period as indicated by changes of different node centrality indices. To this end, we investigate—in a time-resolved manner—evolving large-scale epileptic brain networks that we derived from multi-day, multi-electrode intracranial electroencephalograpic recordings from a large but inhomogeneous group of subjects with pharmacoresistant epilepsies with different anatomical origins. We estimate multiple centrality indices to assess the various roles the nodes play while the networks transit from the seizure-free to the pre-seizure period. Our findings allow us to formulate several major scenarios for the reconfiguration of an evolving epileptic brain network prior to seizures, which indicate that there is likely not a single network mechanism underlying seizure generation. Rather, local and global aspects of the pre-seizure network reconfiguration affect virtually all network constituents, from the various brain regions to the functional connections between them.
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Stankovski T, Pereira T, McClintock PVE, Stefanovska A. Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20190039. [PMID: 31656134 PMCID: PMC6834002 DOI: 10.1098/rsta.2019.0039] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 08/13/2019] [Indexed: 06/10/2023]
Abstract
Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions-which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.
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Affiliation(s)
- Tomislav Stankovski
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
- Faculty of Medicine, Ss Cyril and Methodius University, Skopje 1000, Macedonia
| | - Tiago Pereira
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
- Institute of Mathematical and Computer Sciences, University of Sao Paulo, Sao Carlos 13566-590, Brazil
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Bröhl T, Lehnertz K. Centrality-based identification of important edges in complex networks. CHAOS (WOODBURY, N.Y.) 2019; 29:033115. [PMID: 30927842 DOI: 10.1063/1.5081098] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2018] [Accepted: 02/13/2019] [Indexed: 06/09/2023]
Abstract
Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify various, widely used centrality concepts for vertices to those for edges, in order to find which edges in a network are important between other pairs of vertices. Focusing on the importance of edges, we propose an edge-centrality-based network decomposition technique to identify a hierarchy of sets of edges, where each set is associated with a different level of importance. We evaluate the efficiency of our methods using various paradigmatic network models and apply the novel concepts to identify important edges and important sets of edges in a commonly used benchmark model in social network analysis, as well as in evolving epileptic brain networks.
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Affiliation(s)
- Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Sigmund-Freud-Straße 25, 53105 Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Sigmund-Freud-Straße 25, 53105 Bonn, Germany
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