Extrinsic vs Intrinsic Criticality in Systems with Many Components
Extrinsic vs Intrinsic Criticality in Systems with Many Components
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发表时间：
2023-09
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通讯作者：
Wave Ngampruetikorn;I. Nemenman;David J. Schwab
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作者：
Wave Ngampruetikorn;I. Nemenman;David J. Schwab
具有许多组成部分的生物系统往往表现出看似关键的行为，其特征是巨大的相关波动。然而，根本原因仍不清楚。在这里，我们定义和检查两种类型的关键性。内在临界性来自于系统内部的相互作用，这些相互作用被微调到临界点。相反，当可观测的自由度与不可观测的波动变量相耦合时，不需要微调就可以出现外临界。我们使用学习和信息论的语言统一了这两种类型的关键性。我们表明，关键的相关性，内在的或外在的，导致发散系统的两半之间的互信息，是学习问题的一个特点，其中未观察到的波动推断从可观察到的自由度。我们认为，外在的临界性是等同于标准的推理，而内在的临界性描述分数学习，其中要学习的量取决于系统的大小。我们进一步表明，这两种类型的临界是在同一个连续体，连接一个平滑的交叉。此外，我们调查的可观测性齐普夫定律，幂律秩频率分布经常被用作经验签名的临界。我们发现，齐普夫定律是一个强大的功能，外在的临界性，但可以是非平凡的观察一些内在的临界系统，包括临界平均场模型。我们进一步证明，模型与全球动态，如振荡模型，可以产生可观察的齐普夫定律，而不依赖于外部波动或微调。我们的研究结果表明，虽然在理论上是可能的，但微调并不是唯一的，也不是最有可能的，对具有许多组件的生物系统中明显普遍存在的临界性的解释。我们的工作提供了另一种解释，其中的关键性，特别是外在的关键性，从集体行为的适应外部刺激的结果。
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. Intrinsic criticality arises from interactions within the system which are fine-tuned to a critical point. Extrinsic 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 fractional learning, 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.