Analysis of complex time series generated by nonlinear dynamic systems

PhD study program: Applied Mathematics
Akademic year: 2020-2021
Advisor: RNDr. Anna Krakovská, CSc. (krakovska@savba.sk)
External educational institution: Institute of Measurement Science SAS
Accepting university: Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Department of Applied Mathematics and Statistics

Annotation:
The topic concerns modern analysis of measured time series. Emphasis will be on reconstruction of the underlying dynamics and also on prediction, modeling, evaluation of fractal complexity and causal analysis. One of the goals will be to design a method of multivariate causal analysis that looks for the variables with the strongest influence. In practice, when measuring several observables of the system, the causality detection can help to select the measurements that represent the most useful source of information. The main application area will be multichannel electroencephalographic records from the human brain. It turns out that the connectivity between the brain regions is a potentially useful tool for classifying different brain states, recognizing neurological disorders, or characterizing cognitive abilities.
The thesis topic is suitable for a candidate with an interest in creative applications and design of the appropriate mathematical methods. Another requirement is knowledge of English and experience with software development and testing in the MatLab environment.
During the study, the PhD. student will extend his / her knowledge in the field of dynamic systems theory, including chaos and fractal theory and partly also in biomeasurements, statistics, information theory and mathematical optimization.

back