Inferring Coupled Oscillatory Dynamics From Data - IPAM at UCLA
Explore the intricacies of inferring coupled oscillatory dynamics from data in this 52-minute lecture by Arkady Pikovsky from Universität Potsdam. Delve into the analysis of oscillatory processes, focusing on phase estimation and a novel approach to phase demodulation using iterated Hilbert transforms. Examine the method's effectiveness in purely phase-modulated signals and its limitations when amplitude modulation is present. Discover techniques for transforming a generic protophase of an oscillatory signal into a "true phase." Investigate network reconstruction via phase dynamics, cardiorespiratory interaction, and higher-order couplings. Gain insights into the phase demodulation problem and iterative Hilbert transform embeddings, concluding with an exploration of error evolution in simple waveforms with strong modulation.