Ngampruetikorn Vudtiwat, Nemenman Ilya, Schwab David J
Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York 10016, USA.
Department of Physics, Department of Biology, and Initiative in Theory and Modeling of Living Systems, Emory University, Atlanta, Georgia 30322, USA.
ArXiv. 2023 Sep 25:arXiv:2309.13898v1.
Biological systems with many components often exhibit seemingly critical behaviors, characterized by atypically large correlated fluctuations. Yet the underlying causes remain unclear. Here we define and examine two types of criticality. criticality arises from interactions within the system which are fine-tuned to a critical point. criticality, in contrast, emerges without fine tuning when observable degrees of freedom are coupled to unobserved fluctuating variables. We unify both types of criticality using the language of learning and information theory. We show that critical correlations, intrinsic or extrinsic, lead to diverging mutual information between two halves of the system, and are a feature of learning problems, in which the unobserved fluctuations are inferred from the observable degrees of freedom. We argue that extrinsic criticality is equivalent to standard inference, whereas intrinsic criticality describes , in which the amount to be learned depends on the system size. We show further that both types of criticality are on the same continuum, connected by a smooth crossover. In addition, we investigate the observability of Zipf's law, a power-law rank-frequency distribution often used as an empirical signature of criticality. We find that Zipf's law is a robust feature of extrinsic criticality but can be nontrivial to observe for some intrinsically critical systems, including critical mean-field models We further demonstrate that models with global dynamics, such as oscillatory models, can produce observable Zipf's law without relying on either external fluctuations or fine tuning. Our findings suggest that while possible in theory, fine tuning is not the only, nor the most likely, explanation for the apparent ubiquity of criticality in biological systems with many components. Our work offers an alternative interpretation in which criticality, specifically extrinsic criticality, results from the adaptation of collective behavior to external stimuli.
具有许多组件的生物系统通常表现出看似关键的行为，其特征是具有异常大的相关波动。然而，其潜在原因仍不清楚。在这里，我们定义并研究了两种类型的临界性。一种临界性源于系统内部相互作用，这些相互作用被微调至临界点。相比之下，另一种临界性在可观测自由度与未观测到的波动变量耦合时，无需微调即可出现。我们使用学习和信息论的语言统一了这两种类型的临界性。我们表明，内在或外在的临界相关性会导致系统两半部分之间的互信息发散，并且是学习问题的一个特征，其中从可观测自由度推断未观测到的波动。我们认为外在临界性等同于标准推理，而内在临界性描述的是，其中要学习的量取决于系统大小。我们进一步表明，这两种类型的临界性处于同一连续统上，通过平滑过渡相连。此外，我们研究了齐普夫定律的可观测性，齐普夫定律是一种幂律秩 - 频率分布，常被用作临界性的经验特征。我们发现齐普夫定律是外在临界性的一个稳健特征，但对于一些内在临界系统，包括临界平均场模型，可能难以观测到。我们进一步证明，具有全局动力学的模型，如振荡模型，可以在不依赖外部波动或微调的情况下产生可观测的齐普夫定律。我们的研究结果表明，虽然在理论上是可能的，但微调并不是对具有许多组件的生物系统中临界性明显普遍存在的唯一解释，也不是最可能的解释。我们的工作提供了另一种解释，即临界性，特别是外在临界性，是集体行为适应外部刺激的结果。
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