Parity and time-reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks
| Autor: | Rozum, Jordan C., Zañudo, Jorge Gómez Tejeda, Gan, Xiao, Deritei, Dávid, Albert, Réka |
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| Rok vydání: | 2020 |
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| Zdroj: | Sci. Adv. 7, eabf8124 (2021) |
| Druh dokumentu: | Working Paper |
| Popis: | We present new applications of parity inversion and time-reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal construction efficiently reveal discrete analogs of stable and unstable manifolds. We demonstrate their predictive power by studying decision-making in systems biology and statistical physics models. These applications underpin a novel attractor identification algorithm implemented for Boolean networks under stochastic dynamics. Its speed enables resolving a longstanding open question of how attractor count in critical random Boolean networks scales with network size, and whether the scaling matches biological observations. Via 80-fold improvement in probed network size ($N=16,384$), we find the surprisingly low scaling exponent of $0.12\pm 0.05$ -- approximately one tenth the analytical upper bound. We demonstrate a general principle: a system's relationship to its time-reversal and state-space inversion constrains its repertoire of emergent behaviors. Comment: The IPython Notebook referenced in supplemental information, along with other reproduction materials, is available at https://github.com/jcrozum/StableMotifs/tree/master/Random%20Boolean%20Network%20Application |
| Databáze: | arXiv |
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