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.

Intro
Network reconstruction via the phase dynamics
Theory of the phase dynamics
Theoretical framework: Phase equations
Protophase vs the true phase
Step 1: Protophase-to-phase transformation
Step 2: Reconstruction of the phase equations
protophases vs phases
Example 2: Cardiorespiratory interaction
Coupling function for cardiorespiratory interaction
Remarks about higher-order couplings and hypernetworks
Conclusions to this part
Phase demodulation problem
Iterative Hilbert transform embeddings
Evolution of the error
Simple waveform, strong modulation