Dissecting evolving interaction networks: Which network components are important for the dynamics?

• Applicant: Professor Dr. Klaus Lehnertz
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 391934314

• Final Report Year: 2022

Final Report Abstract

Complex networks can be found in animate and inanimate nature on virtually all scales. Examples include interconnected cellular structures (e.g., the brain), communication (e.g., the Internet) and infrastructure networks (e.g., air traffic, power grid), social, and even climate networks. Interdisciplinary research into complex networks has advanced from a characterization of network properties on various scales to improving our understanding of collective dynamical phenomena by means of time-evolving interaction networks. Still, disentangling the complicated relationship between structure and dynamics remains a challenge, mostly because progress in identifying key constituents (nodes and links) of time-evolving interaction networks is limited by a number of factors. With our research programme, we targeted at improving (1) the identification of constituents that are important for the network’s structure and dynamics and (2) the characterization of properties of such key constituents. By means of application-oriented method developments, we modified various, widely-used and well-known centrality concepts for nodes to those for links, in order to find which links (or groups thereof) in a network are important between other pairs of nodes. With these concepts, importance of network constituents for structure and dynamics of the larger network can be assessed from different perspectives. We could verify the suitability of our novel approaches with computer simulations of a number of paradigmatic model networks under controlled conditions and could demonstrate their usefulness through applications to various real-world networks. With an eye to the analysis of empirical networks, where knowledge about and access to key network constituents is usually very limited, we investigated how well this information can be derived from incomplete observational data of a network’s dynamics. With quite extensive computer simulations, we identified possibilities and limitations of a data-driven identification of key constituents as well as characterization of other, more global network properties. Eventually, we employed our newly developed analysis concepts and methods to identify and characterize key constituents in so called functional brain networks from subjects with epilepsy. We derived these networks from long-lasting (days to weeks) electroencephalographic recordings that cover various dynamical regimes of the human brain and achieved novel insights into network mechanisms underlying epilepsy and the generation of seizures. These insights significantly contribute to further improve prediction and control of seizures. With our research findings, we could contribute to advancing our understanding of local aspects of the relationship between structure and dynamics in natural and man-made evolving interaction networks.

Publications

• Centrality-based identification of important edges in complex networks. Chaos 29, 033115
  Bröhl T, Lehnertz K
  
• Precursors of seizures due to specific spatial-temporal modifications of evolving large-scale epileptic brain networks. Scientific Reports 9, 10623
  Rings T, von Wrede R, Lehnertz K
  
• Identifying edges that facilitate the generation of extreme events in networked dynamical systems. Chaos 30, 073113
  Bröhl T, Lehnertz K
  
• Reconfiguration of human evolving large-scale epileptic brain networks prior to seizures: an evaluation with node centralities. Scientific Reports 10, 21921
  Fruengel R, Brohl T, Rings T, Lehnertz K
  
• The human organism as an integrated interaction network: recent conceptual and methodological challenges. Frontiers in Physiology 11, 598694
  Lehnertz K, Bröhl T, Rings T
  
• A straightforward edge centrality concept derived from generalizing degree and strength. Scientific Reports
  Bröhl T, Lehnertz K
  
• Impact of transcutaneous auricular vagus nerve stimulation on large-scale functional brain networks: from local to global. Frontiers in Physiology 12, 700261
  Rings T, von Wrede R, Bröhl T, Schach S, Helmstaedter C, Lehnertz K
  
• Time in brain: How biological rhythms impact on EEG signals and on EEG-derived brain networks. Frontiers in Network Physiology 1, 755016
  Lehnertz K, Rings T, Bröhl T
  
• Transcutaneous auricular vagus nerve stimulation induces stabilizing modifications in large-scale functional brain networks: towards understanding the effects of taVNS in subjects with epilepsy. Scientific Reports 11, 7906
  von Wrede R., Rings T, Schach S, Helmstaedter C, Lehnertz K