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. 2021 Apr 26;11:8909. doi: 10.1038/s41598-021-87779-7

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© The Author(s) 2021

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Left: Singular value vector, $u_{ℓ_{1} t}$ , computed by HOSVD applied to $x_{t j t^{'} j^{'}}$ . Open black circles: 1st, (0.61) open red triangles: 2nd (− 0.77), green crosses: 3rd (− 0.41), blue crosses: 4th PC loading (0.48). The numbers in parentheses are the Pearson’s correlation coefficients. Hours (horizontal axis) represent the duration after the treatments. Horizontal magenta broken line indicates baseline (zero). Middle: singular value vector, $u_{ℓ_{3} t^{'}}$ , computed by HOSVD applied to $x_{t j t^{'} j^{'}}$ . Open black circles: 1st (0.78). open red triangles: 2nd (− 0.70), green crosses: 3rd (− 0.47), blue crosses: 4th PC loading (0.52). The numbers in parentheses are the Pearson’s correlation coefficients. Hours (horizontal axis) represent the duration after the treatments. Horizontal magenta broken line indicates baseline (zero). Right: scatter plot between $u_{2 t}$ (horizontal axis) and $u_{2 t^{'}}$ (vertical axis). The red broken line indicates $u_{2 t} = u_{2 t^{'}}$ .