Information-theoretical analysis of statistical measures for multiscale dynamics Article Swipe

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Naoki Asuke , Tomoki Yamagami , Takatomo Mihana , André Röhm , Ryoichi Horisaki , Makoto Naruse ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2301.01930

Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as clocks and lasers, ranging from short to long time scales. Although these two statistical measures were developed independently for different purposes in different fields in the literature, their interest is to examine multiscale temporal structures of physical phenomena under study. We show that, from an information-theoretical perspective, they share some foundations and exhibit similar tendencies. We experimentally confirmed that similar properties of the MSE and Allan variance can be observed in low-frequency fluctuations (LFF) in chaotic lasers and physiological heartbeat data. Furthermore, we calculated the condition under which this consistency between the MSE and Allan variance exists, which is related to certain conditional probabilities. Heuristically, physical systems in nature including the aforementioned LFF and heartbeat data mostly satisfy this condition, and hence the MSE and Allan variance demonstrate similar properties. As a counterexample, an artificially constructed random sequence is demonstrated, for which the MSE and Allan variance exhibit different trends.

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Allan variance Statistical physics Heartbeat Variance (accounting) Stability (learning theory) Chaotic Entropy (arrow of time) Nonlinear system Mathematics Statistics Computer science Algorithm Artificial intelligence Physics Standard deviation Machine learning Accounting Quantum mechanics Computer security Business

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2301.01930
PDF: https://arxiv.org/pdf/2301.01930
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DOI: https://doi.org/10.48550/arxiv.2301.01930

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Title: Information-theoretical analysis of statistical measures for multiscale dynamics

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Publication year: 2023

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Publication date: 2023-01-05

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Authors: Naoki Asuke, Tomoki Yamagami, Takatomo Mihana, André Röhm, Ryoichi Horisaki, Makoto Naruse

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Landing page: https://arxiv.org/abs/2301.01930

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Concepts: Allan variance, Statistical physics, Heartbeat, Variance (accounting), Stability (learning theory), Chaotic, Entropy (arrow of time), Nonlinear system, Mathematics, Statistics, Computer science, Algorithm, Artificial intelligence, Physics, Standard deviation, Machine learning, Accounting, Quantum mechanics, Computer security, Business

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abstract_inverted_index.Furthermore,	116
abstract_inverted_index.artificially	169
abstract_inverted_index.fluctuations	107
abstract_inverted_index.oscillators,	32
abstract_inverted_index.perspective,	81
abstract_inverted_index.demonstrated,	174
abstract_inverted_index.independently	52
abstract_inverted_index.low-frequency	106
abstract_inverted_index.physiological	113
abstract_inverted_index.Heuristically,	139
abstract_inverted_index.aforementioned	146
abstract_inverted_index.experimentally	91
abstract_inverted_index.probabilities.	138
abstract_inverted_index.counterexample,	167
abstract_inverted_index.information-theoretical	80
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	6
citation_normalized_percentile.value	0.00362416
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False