Criticality and sampling in neural networks

Abstract

The brain is made of billions of functional units that interact and give raise to its collective properties. The criticality hypothesis states that many these properties emerge due to brain dynamics operating at the critical point of a phase transition. In models, the critical point maximizes potentially useful properties such as sensitivity, temporal integration, and correlation length. The hypothesis remains controversial, however, in part due to sampling effects: only a small fraction of the neurons in the brain can be recorded, leading to bias in the observed collective properties. In this Thesis we analyze how sampling effects can bias the assessment of criticality in neural networks. We explore sampling effects both in models with critical dynamics and in experimental results, and find a number of mechanisms that can result in bias. Chiefly, we develop a model of neuronal avalanches where activity is sampled in different levels (spikes and coarse signals), and show that coarse signals cannot differentiate between close to critical and very subcritical states. This unifies contradictory results in the literature, and argue in favor of a subcritical, reverberating state for dynamics in vivo. We also show that sampling can alter the spectra of neuronal activity, and thus explain its variability. Applying this mechanism to data, we find that flatter spectra observed in in vitro recordings suggest poorer sampling in that condition. Lastly, we also perform a literature review on the evidence of criticality in the brain. The picture that emerges is that evidence is largely ambiguous, mostly due to sampling effects. Nevertheless, a few key results offer strong evidence that criticality can emerge in neural networks. Coupled with the prospect of considerably improved experimental techniques in the near future, we argue that critical phenomena may become increasingly useful in the understanding of brain activity.