Transfer entropy in information theory was recently demonstrated [Basak et al., Phys. Rev. E 102, 012404 (2020)] to enable us to elucidate the interaction domain among interacting elements solely from an ensemble of trajectories. Therefore, only pairs of elements whose distances are shorter than some distance variable, termed cutoff distance, are taken into account in the computation of transfer entropies. The prediction performance in capturing the underlying interaction domain is subject to the noise level exerted on the elements and the sufficiency of statistics of the interaction events. In this paper, the dependence of the prediction performance is scrutinized systematically on noise level and the length of trajectories by using a modified Vicsek model. The larger the noise level and the shorter the time length of trajectories, the more the derivative of average transfer entropy fluctuates, which makes the identification of the interaction domain in terms of the position of global minimum of the derivative of average transfer entropy difficult. A measure to quantify the degree of strong convexity at the coarse-grained level is proposed. It is shown that the convexity score scheme can identify the interaction distance fairly well even while the position of the global minimum of the derivative of average transfer entropy does not. We also derive an analytical model to explain the relationship between the interaction domain and the change in transfer entropy that supports our cutoff distance technique to elucidate the underlying interaction domain from trajectories.
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21 January 2021
Research Article|
January 15 2021
An information-theoretic approach to infer the underlying interaction domain among elements from finite length trajectories in a noisy environment
Udoy S. Basak
;
Udoy S. Basak
1
Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University
, Kita 12, Nishi 6, Kita-ku, Sapporo 060-0812, Japan
2
Pabna University of Science and Technology
, Pabna 6600, Bangladesh
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Sulimon Sattari
;
Sulimon Sattari
3
Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University
, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan
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Md. Motaleb Hossain
;
Md. Motaleb Hossain
3
Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University
, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan
4
University of Dhaka
, Dhaka 1000, Bangladesh
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Kazuki Horikawa;
Kazuki Horikawa
5
Department of Optical Imaging, The Institute of Biomedical Sciences, Tokushima University Graduate School
, 3-18-15 Kuramoto-cho, Tokushima City, Tokushima 770-8503, Japan
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Tamiki Komatsuzaki
Tamiki Komatsuzaki
a)
1
Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University
, Kita 12, Nishi 6, Kita-ku, Sapporo 060-0812, Japan
3
Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University
, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan
6
Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University
, Kita 21 Nishi 10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan
7
Graduate School of Chemical Sciences and Engineering Materials Chemistry and Engineering Course, Hokkaido University
, Kita 13, Nishi 8, Kita-ku, Sapporo 060-0812, Japan
a)Author to whom correspondence should be addressed: [email protected]
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a)Author to whom correspondence should be addressed: [email protected]
J. Chem. Phys. 154, 034901 (2021)
Article history
Received:
October 21 2020
Accepted:
December 26 2020
Citation
Udoy S. Basak, Sulimon Sattari, Md. Motaleb Hossain, Kazuki Horikawa, Tamiki Komatsuzaki; An information-theoretic approach to infer the underlying interaction domain among elements from finite length trajectories in a noisy environment. J. Chem. Phys. 21 January 2021; 154 (3): 034901. https://doi.org/10.1063/5.0034467
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