论文标题
在经验模型中的奇偶校验和时间逆转阐明决策和关键布尔网络中的吸引子缩放
Parity and time-reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks
论文作者
论文摘要
我们向随机离散模型中简单的动力学规则出现了平价反转和时间反转的新应用。我们基于奇偶校验的因果关系和时间反转构造有效地揭示了稳定和不稳定的流形的离散类似物。我们通过研究系统生物学和统计物理模型中的决策来证明他们的预测能力。这些应用是在随机动力学下针对布尔网络实现的一种新型吸引子识别算法。它的速度可以解决一个长期以来的开放问题，即吸引者在关键的随机布尔网络中如何计数网络大小的尺度以及缩放量表是否与生物学观察相匹配。通过探测网络大小的80倍改进（$ n = 16,384 $），我们发现了令人惊讶的低标度指数为$ 0.12 \ pm 0.05 $ - 大约是分析上限的十分之一。我们证明了一个一般原则：系统与其时间逆转和状态空间倒置的关系限制了其紧急行为的曲目。
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.
