Parity and time reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks

Jordan C. Rozum, Jorge Gómez Tejeda Zañudo, Xiao Gan, Dávid Deritei, Réka Albert

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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 long-standing 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 unexpectedly low scaling exponent of 0.12 ± 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.

Original languageEnglish (US)
Article numbereabf8124
JournalScience Advances
Volume7
Issue number29
DOIs
StatePublished - Jul 2021

All Science Journal Classification (ASJC) codes

  • General

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