Struktura konektivity složitých dynamických systémů
| Thesis title in Czech: | Struktura konektivity složitých dynamických systémů |
|---|---|
| Thesis title in English: | Connectivity structure of complex dynamical systems |
| Key words: | komplexní sítě|dynamické systémy|konektivita|synchronizace|dynamické procesy |
| English key words: | complex networks|dynamical systems|connectivity|synchronization|dynamical processes |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Computer Science Institute of Charles University (32-IUUK) |
| Supervisor: | doc. Ing. et Ing. David Hartman, Ph.D. et Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 01.09.2021 |
| Date of assignment: | 01.09.2021 |
| Confirmed by Study dept. on: | 14.09.2021 |
| Advisors: | Ing. Mgr. Jaroslav Hlinka, Ph.D. |
| Guidelines |
| Complex real systems can often be represented as a system of mutually interconnected simpler dynamic subsystems. The behaviour of this system is determined both by the dynamics of the subsystems and by the coupling structure. The synchronization between subsystems provides so-called structural connectivity. Such connectivity represents a synchronization of subsystems as in the case of interconnected oscillators for modelling dynamical systems, e.g., modelling epileptic seizures in the human brain. Alternatively, this connectivity could serve as a model for the domain-specific exchange of information between subsystems enabling the whole dynamic, e.g., the higher-level modelling of disease spreading. Often, we can additionally measure quantities of the system corresponding to the behaviour of all subsystems. Statistical dependencies between these variables are called functional connectivity. The functional connectivity provides a network describing the behaviour of the system. This thesis aims to explore such types of systems from the viewpoint of their structural and functional connectivity. An example can be the long-standing open problem in dynamical systems to explain the relationship between these two connectivities. To achieve such a high-level goal, we need first to solve the robust determination of pairwise connectivity of network vertices. This task includes resolving the exponential time complexity of the corresponding computations determining the relationship of variables, or, more generally, understanding the influence of specific structural connectivity on the resulting functional connectivity. Providing solutions to problems like these can contribute to the characterization of various events or state for dynamical systems, such as neurodegenerative diseases in the brain. |
| References |
| Porter, M. A., Gleeson, J. P. Dynamical systems on networks. in Frontiers in Applied Dynamical Systems: Reviews and Tutorials, Springer, 2016.
S. Boccaletti, A. Pisarchik, C. Genio, and A. Amann. Synchronization: From Coupled Systems to Complex Networks. Cambridge University Press, 2018. Newmann, M.E.J. Networks: an introduction. Oxford University Press, 2018. T. M. Cover, J. A. Thomas. Elements of information theory. John Wiley & Sons, 2012. Holger Kantz, Thomas Schreiber. Nonlinear Time Series Analysis, Cambridge University Press, 2004. R. W. Yeung. Information Theory and Network Coding. Springer, 2008. Barrat, A., Barthelemy, M., & Vespignani, A. Dynamical processes on complex networks. Cambridge university press, 2008. J. Hlinka, S. Coombes. Using computational models to relate structural and functional brain connectivity. European Journal of Neuroscience 36 (2), 2137-2145. 2012 |