Abstract: This talk explores innovative methods for understanding complex systems, highlighting three distinct yet complementary approaches. First, we address the decoupling problem and explore its connections to tensor-based techniques, emphasizing recent advancements and open challenges in decoupling multivariate functions. Next, we investigate signal decomposition using Hankel matrices and tensors, which provide powerful tools for separating signal components while preserving interpretability. Finally, we connect these methods to recurrence plots, a valuable technique for visually capturing dynamic behaviors and periodicities in time-series data. Throughout, we will highlight both the theoretical foundations and practical applications of these approaches.
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