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A model of artificial biological time series generation

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Abstract

This paper presents a novel model of artificial biological time series generation. We employed a cellular automata (CA) system that comprises self-replicating and mutually competing loops. Our self-replicating system is an advanced version of Chou & Reggia’s system (Physica D 110, 252–276). The complex self-replicating CA loops were developed using a construction scheme in which we introduce a unique measure of the CA to quantify the activity of the loops. By summing the loop activities globally and observing the time evolution of the sum, we obtain an artificial time series. The power spectrum of the resulting time series exhibits \({1 \mathord{\left/ {\vphantom {1 {f^{\alpha } }}} \right. \kern-\nulldelimiterspace} {f^{\alpha } }}\) scaling behavior. The exponent \(\alpha\) in the \({1 \mathord{\left/ {\vphantom {1 {f^{\alpha } }}} \right. \kern-\nulldelimiterspace} {f^{\alpha } }}\) power spectrum of the unconstrained self-replicating system is \(\alpha \approx 1.5\). Constraints on loop dynamics, leading to larger-scale death in the loop colonies, are implemented in our CA. With the application of the constraints, the value of \(\alpha\) is lowered to nearly 1. The results show that self-replication and death in the CA space play the roles of excitatory and inhibitory synaptic functions, respectively, in a neuronal network. The self-replication/death balance control in our study could modulate the scaling exponent \(\alpha\) in the power spectrum, similar to the activation/inhibition balance control in neural networks and local field potential (LFP) simulations in recent studies. The calculation of the largest Lyapunov exponent, L1, shows the chaotic nature of the time series. The form of our CA system resembles that of neuronal potential transmission and replication to nearby neurons. The results of this study suggest another feasible concept for the origin of biological signals. Executable codes associated with this study are freely accessible.

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Acknowledgements

This work passed the internal review of MPI-PKS and was archived in the MPG edoc server (https://web.archive.org/web/20200609112257/http://edoc.mpg.de/330829). This study was presented in the 2020 KPS fall meeting as P1-bp.001. The work was supported by the 2020 Hannam University Research Fund. Any questions and executable code requests are welcomed by the author (hr_kim@hnu.kr; k52hr01@gmail.com)

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  1. School of Basic Sciences, Hannam University, 70 Hannamro, Daedeok-Gu, Daejeon, 34430, Republic of Korea

    Hyung-Rae Kim

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Kim, HR. A model of artificial biological time series generation. J. Korean Phys. Soc. 79, 412–427 (2021). https://doi.org/10.1007/s40042-021-00259-z

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