Experimentalists are often tempted to sample their study systems as densely as possible. But for systems where local mixing or diffusion can occur — such as gas within a chamber, chemical mixing within fluids, isotope concentrations within polar ice cores — too-frequent sampling can mask the underlying signal by temporarily shuffling/mixing the observations.
In a paper published in the American Physical Society’s Physical Review E, Michael Neuder, a participant in SFI’s Undergraduate Complexity Research program, along with SFI External Professor Elizabeth Bradley, SFI Applied Complexity Fellow Joshua Garland, and other coauthors present a solution to this challenge faced by experimentalists from a wide range of fields. “Leveraging the time-delay parameter in the permutation entropy (PE) calculation and studying the resulting relationship between successive PE estimates allows us to identify local mixing scales within the data and identify the maximum frequency for data reporting,” explains Garland. “This lets practitioners squeeze every drop of information out of their study system without oversampling—and thereby obfuscating—the signal of interest. Critically, this approach is model-free and requires no prior knowledge of the underlying dynamics or the system being measured.”
Read the paper, "Detection of local mixing in time-series data using permutation entropy," in Physical Review E (February 26, 2021)