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Mathematical and Technical Tools

  • Mathematical analysis of brain electrical and magnetic activity within the framework of nonlinear spatiotemporal dynamics (Individual Lyapunov exponents, Cross-Lyapunov exponents, Transfer of Entropy, dynamical coupling/entrainment)
  • Use of Global Optimization techniques in signal processing. Recent application of such methods to EEG analysis has resulted to a deeper understanding and improvement of epileptogenic focus localization and seizure prediction.
  • Theory of chaos for strongly coupled and spatially distributed mathematical, physical and biological systems (e.g. coupled nonlinear maps, coupled laser arrays and networks of neurons respectively). Identification of the critical parameters and controllability of the phase transitions of these systems.
  • Development of fast digital signal processing algorithms for real time estimation of indices of chaoticity and complexity of complex signals.
  • Advanced multi-dimensional digital signal processing techniques for analysis of nonstationary signals and images (e.g. Time-Frequency and Wavelet transforms, Kalman filtering, KL transform).
  • Analysis of single-trial evoked potentials and event responses of the nervous system to visual, auditory, electrical and mechanical stimuli at the macroscopic and microscopic level. Issue of nonstationarity.
  • Design of biomedical (implanted or portable) devices (BioMEMS) for: a) measurement, b) amplification, c) analysis of biological and clinical signals of interest (e.g. EEG, MEG, MRI, ultrasound) and d) control and intervention for therapeutic purposes (e.g. via electromagnetic stimulators).