Characterisation of the elementary cellular automata in terms of their maximum sensitivity to all possible asynchronous updates

Ruivo, Eurico L. P.; Montalva-Medel, Marco; Oliveira, Pedro Paulo Balbi de; Perrot, Kévin

doi:10.1016/j.chaos.2018.06.004

Cited by 9 publications

(2 citation statements)

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“…We will analyze its dynamical behavior through a detailed study of all its different dynamics by using the algorithms developed in [22] that, roughly speaking, list all the sets of schemes that generate exactly the same dynamics, significantly reducing the number of dynamics to analyze. These algorithms have been shown to be effective in obtaining new and relevant information for the study of concrete biological networks [34,35] as well as in the field of the cellular automata theory [36][37][38][39][40][41].…”

Section: Lemmamentioning

confidence: 99%

Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

et al. 2021

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In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the lac operon in Escherichia coli capable of reproducing the operon being OFF, ON and bistable for three (low, medium and high) and two (low and high) parameters, representing the concentration ranges of lactose and glucose, respectively. Of these 6 possible combinations of parameters, 5 produce results that match with the biological experiments of Ozbudak et al. 2004. In the remaining one, the models predict the operon being OFF while biological experiments show a bistable behavior. In this paper, we first explore the robustness of two such models in the sense of how much its attractors change against any deterministic update schedule. We prove mathematically that, in cases where there is no bistability, all the dynamics in both models lack limit cycles while, when bistability appears, one model presents 30% of its dynamics with limit cycles while the other only 23%. Secondly, we propose two alternative improvements consisting of biologically supported modifications; one in which both models match with Ozbudak et al. 2004 in all 6 combinations of parameters and, the other one, where we increase the number of parameters to 9, matching in all these cases with the biological experiments of Ozbudak et al. 2004.

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Section: Lemmamentioning

confidence: 99%

Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

et al. 2021

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“…In recent studies, it has been shown that synchronous updating is not in accordance with many real processes (Baetens et al, ; Bandman, ; Barreira‐González et al, ; Cornforth, Green, & Newth, ; Kim, ; Lee, Adachi, Peper, & Morita, ; O'Sullivan & Torrens, ; Ruivo, Montalva‐Medel, Paulo Balbi de Oliveira, & Perrot, ; Schönfisch & de Roos, ) and therefore, due to the temporal nature of entities, asynchronous CA is more realistic than synchronous CA and achieves more accurate results (Ke et al, ). Schönfisch and de Roos () compared several updating methods for CA.…”

Section: Introductionmentioning

confidence: 99%

Assessing the effect of temporal dynamics on urban growth simulation: Towards an asynchronous cellular automata

Abolhasani

Taleai

2019

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Time is a fundamental dimension in urban dynamics, but the effect of various definitions of time on urban growth models has rarely been evaluated. In urban growth models such as cellular automata (CA), time has typically been defined as a sequence of discrete time steps. However, most urban growth processes such as land‐use changes are asynchronous. The aim of this study is to examine the effect of various temporal dynamics scenarios on urban growth simulation, in terms of urban land‐use planning, and to introduce an asynchronous parcel‐based cellular automata (AParCA) model. In this study, eight different scenarios were generated to investigate the impact of temporal dynamics on CA‐based urban growth models, and their outputs were evaluated using various urban planning indicators. The obtained results show that different degrees of temporal dynamics lead to various patterns appearing in urban growth CA models, and the application of asynchronous (event‐driven) CA models achieves better simulation results than synchronous models.

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