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How to compute suitable vicinity parameter and sampling time of recurrence analysis

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Abstract

We show how the maximum of recurrence-microstates entropy configures a new way to properly compute appropriate recurrence vicinity parameter and time sampling to perform recurrence analysis of continuous data. For experimental data, we show the same procedure may be used to find the optimum sampling or to perform down-sampling of the data, preserving recurrence meaning and adjusting the ideal sampling. The new method retrieves results obtained using traditional methods with the advantage of being independent of any free parameter, since all parameter dependencies are automatically set. Our results are also less sensitive to noise when experimental data are used. Due to the automatized way to capture suitable recurrence parameters, the method is adequate for using in autonomous numerical algorithms, allowing the recovery of relevant recurrence information embedded in time series (including over-sampled data), rationalizing the process of data acquisition and allowing only relevant data to be collected.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. The SGAMP database containing single-unit neuronal recordings of North Atlantic squid (Loligo pealei) giant axons in response to stochastic stimulus currents is provided by PhysioNet [10, 23]. The data are open and free available at https://physionet.org/content/sgamp/1.0.0/.

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Funding

We thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq—Brazil, grant numbers 308441/2021-4, 307907/2019-8, and 308621/2019-0 and Financiadora de Estudos e Projetos (FINEP) for financial support (LCPAD, CtInfra project).

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Authors and Affiliations

  1. Departamento de Física, Universidade Federal do Paraná, Curitiba, PR, 81531-980, Brazil

    Thiago de Lima Prado, Vandertone Santos Machado & Sergio Roberto Lopes

  2. Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil

    Gilberto Corso

  3. Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil

    Gustavo Zampier dos Santos Lima

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  1. Thiago de Lima Prado
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  2. Vandertone Santos Machado
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  3. Gilberto Corso
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  4. Gustavo Zampier dos Santos Lima
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  5. Sergio Roberto Lopes
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Contributions

TLP was involved in the conceptualization; data curation; formal analysis; investigation; methodology; project administration; validation; and visualization. VSN contributed to the investigation and supporting. GC assisted in the investigation and supporting. GZSL contributed to the investigation and supporting. SRL contributed to the conceptualization; formal analysis; investigation; methodology; supervision; writing—original draft; writing—review & editing.

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Correspondence to Sergio Roberto Lopes.

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de Lima Prado, T., Machado, V.S., Corso, G. et al. How to compute suitable vicinity parameter and sampling time of recurrence analysis. Nonlinear Dyn 112, 1141–1152 (2024). https://doi.org/10.1007/s11071-023-09063-9

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