Signatures of criticality arise in simple neural population models with correlations

Large-scale recordings of neuronal activity make it possible to gain insights into the collective activity of neural ensembles. It has been hypothesized that neural populations might be optimized to operate at a 'thermodynamic critical point', and that this property has implications for information processing. Support for this notion has come from a series of studies which identified statistical signatures of criticality in the ensemble activity of retinal ganglion cells. What are the underlying mechanisms that give rise to these observations? Here we show that signatures of criticality arise even in simple feed-forward models of retinal population activity. In particular, they occur whenever neural population data exhibits correlations, and is randomly sub-sampled during data analysis. These results show that signatures of criticality are not necessarily indicative of an optimized coding strategy, and challenge the utility of analysis approaches based on equilibrium thermodynamics for understanding partially observed biological systems.Comment: 36 pages, LaTeX; added journal reference on page 1, added link to code repositor

Assessing criticality in pre-seizure single-neuron activity of human epileptic cortex

Epileptic seizures are characterized by abnormal and excessive neural activity, where cortical network dynamics seem to become unstable. However, most of the time, during seizure-free periods, cortex of epilepsy patients shows perfectly stable dynamics. This raises the question of how recurring instability can arise in the light of this stable default state. In this work, we examine two potential scenarios of seizure generation: (i) epileptic cortical areas might generally operate closer to instability, which would make epilepsy patients generally more susceptible to seizures, or (ii) epileptic cortical areas might drift systematically towards instability before seizure onset. We analyzed single-unit spike recordings from both the epileptogenic (focal) and the nonfocal cortical hemispheres of 20 epilepsy patients. We quantified the distance to instability in the framework of criticality, using a novel estimator, which enables an unbiased inference from a small set of recorded neurons. Surprisingly, we found no evidence for either scenario: Neither did focal areas generally operate closer to instability, nor were seizures preceded by a drift towards instability. In fact, our results from both pre-seizure and seizure-free intervals suggest that despite epilepsy, human cortex operates in the stable, slightly subcritical regime, just like cortex of other healthy mammalians.Comment: 19 pages, 8 Figure

Ensemble Inhibition and Excitation in the Human Cortex: an Ising Model Analysis with Uncertainties

The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance is unclear due to lack of reliable error estimates. We therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive Markov Chain Monte Carlo after the convergence of the main optimization algorithm. We apply our method to the spiking patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake-sleep cycle. Our analysis shows that the Ising model captures neuronal collective behavior much better than the independent model during wakefulness, light sleep, and deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled; ignoring the inhibitory effects of I-neurons dramatically overestimates synchrony among E-neurons. Furthermore, information-theoretic measures reveal that the Ising model explains about 80%-95% of the correlations, depending on sleep state and neuron type. Thermodynamic measures show signatures of criticality, although we take this with a grain of salt as it may be merely a reflection of long-range neural correlations.Comment: 17 pages, 8 figure

Extrinsic vs Intrinsic Criticality in Systems with Many Components

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.Comment: 13 pages, 9 figure

The Cortex and the Critical Point

How the cerebral cortex operates near a critical phase transition point for optimum performance. Individual neurons have limited computational powers, but when they work together, it is almost like magic. Firing synchronously and then breaking off to improvise by themselves, they can be paradoxically both independent and interdependent. This happens near the critical point: when neurons are poised between a phase where activity is damped and a phase where it is amplified, where information processing is optimized, and complex emergent activity patterns arise. The claim that neurons in the cortex work best when they operate near the critical point is known as the criticality hypothesis. In this book John Beggs—one of the pioneers of this hypothesis—offers an introduction to the critical point and its relevance to the brain. Drawing on recent experimental evidence, Beggs first explains the main ideas underlying the criticality hypotheses and emergent phenomena. He then discusses the critical point and its two main consequences—first, scale-free properties that confer optimum information processing; and second, universality, or the idea that complex emergent phenomena, like that seen near the critical point, can be explained by relatively simple models that are applicable across species and scale. Finally, Beggs considers future directions for the field, including research on homeostatic regulation, quasicriticality, and the expansion of the cortex and intelligence. An appendix provides technical material; many chapters include exercises that use freely available code and data sets