The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ-oscillations

Barkhausen noise in disordered striplike ferromagnets: Experiment versus simulations

In this work, we present a systematic comparison of the results obtained from the low-frequency Barkhausen noise recordings in nanocrystalline samples with those from the numerical simulations of the random-field Ising model systems. We performed measurements at room temperature on a field-driven metallic glass stripe made of VITROPERM 800 R, a nanocrystalline iron-based material with an excellent combination of soft and magnetic properties, making it a cutting-edge material for a wide range of applications. Given that the Barkhausen noise emissions emerging along a hysteresis curve are stochastic and depend in general on a variety of factors (such as distribution of disorder due to impurities or defects, varied size of crystal grains, type of domain structure, driving rate of the external magnetic field, sample shape and temperature, etc.), adequate theoretical modeling is essential for their interpretation and prediction. Here the Random field Ising model, specifically its athermal nonequilibrium version with the finite driving rate, stands out as an appropriate choice due to the material's nanocrystalline structure and high Curie temperature. We performed a systematic analysis of the signal properties and magnetization avalanches comparing the outcomes of the numerical model and experiments carried out in a two-decade-wide range of the external magnetic field driving rates. Our results reveal that with a suitable choice of parameters, a considerable match with the experimental results is achieved, indicating that this model can accurately describe the Barkhausen noise features in nanocrystalline samples.

Beyond pulsed inhibition: Alpha oscillations modulate attenuation and amplification of neural activity in the awake resting state

Alpha oscillations are a distinctive feature of the awake resting state of the human brain. However, their functional role in resting-state neuronal dynamics remains poorly understood. Here we show that, during resting wakefulness, alpha oscillations drive an alternation of attenuation and amplification bouts in neural activity. Our analysis indicates that inhibition is activated in pulses that last for a single alpha cycle and gradually suppress neural activity, while excitation is successively enhanced over a few alpha cycles to amplify neural activity. Furthermore, we show that long-term alpha amplitude fluctuations-the "waxing and waning" phenomenon-are an attenuation-amplification mechanism described by a power-law decay of the activity rate in the "waning" phase. Importantly, we do not observe such dynamics during non-rapid eye movement (NREM) sleep with marginal alpha oscillations. The results suggest that alpha oscillations modulate neural activity not only through pulses of inhibition (pulsed inhibition hypothesis) but also by timely enhancement of excitation (or disinhibition).

Criticality of neuronal avalanches in human sleep and their relationship with sleep macro- and micro-architecture

Sleep plays a key role in preserving brain function, keeping brain networks in a state that ensures optimal computation. Empirical evidence indicates that this state is consistent with criticality, where scale-free neuronal avalanches emerge. However, the connection between sleep architecture and brain tuning to criticality remains poorly understood. Here, we characterize the critical behavior of avalanches and study their relationship with sleep macro- and micro-architectures, in particular, the cyclic alternating pattern (CAP). We show that avalanches exhibit robust scaling behaviors, with exponents obeying scaling relations consistent with the mean-field directed percolation universality class. We demonstrate that avalanche dynamics is modulated by the NREM-REM cycles and that, within NREM sleep, avalanche occurrence correlates with CAP activation phases-indicating a potential link between CAP and brain tuning to criticality. The results open new perspectives on the collective dynamics underlying CAP function, and on the relationship between sleep architecture, avalanches, and self-organization to criticality.

Unconventional criticality, scaling breakdown, and diverse universality classes in the Wilson-Cowan model of neural dynamics

The Wilson-Cowan model constitutes a paradigmatic approach to understanding the collective dynamics of networks of excitatory and inhibitory units. It has been profusely used in the literature to analyze the possible phases of neural networks at a mean-field level, e.g., assuming large fully connected networks. Moreover, its stochastic counterpart allows one to study fluctuation-induced phenomena, such as avalanches. Here we revisit the stochastic Wilson-Cowan model paying special attention to the possible phase transitions between quiescent and active phases. We unveil eight possible types of such transitions, including continuous ones with scaling behavior belonging to known universality classes-such as directed percolation and tricritical directed percolation-as well as six distinct ones. In particular, we show that under some special circumstances, at a so-called "Hopf tricritical directed percolation" transition, rather unconventional behavior is observed, including the emergence of scaling breakdown. Other transitions are discontinuous and show different types of anomalies in scaling and/or exhibit mixed features of continuous and discontinuous transitions. These results broaden our knowledge of the possible types of critical behavior in networks of excitatory and inhibitory units and are, thus, of relevance to understanding avalanche dynamics in actual neuronal recordings. From a more general perspective, these results help extend the theory of nonequilibrium phase transitions into quiescent or absorbing states.

Parabolic avalanche scaling in the synchronization of cortical cell assemblies

Neurons in the cerebral cortex fire coincident action potentials during ongoing activity and in response to sensory inputs. These synchronized cell assemblies are fundamental to cortex function, yet basic dynamical aspects of their size and duration are largely unknown. Using 2-photon imaging of neurons in the superficial cortex of awake mice, we show that synchronized cell assemblies organize as scale-invariant avalanches that quadratically grow with duration. The quadratic avalanche scaling was only found for correlated neurons, required temporal coarse-graining to compensate for spatial subsampling of the imaged cortex, and suggested cortical dynamics to be critical as demonstrated in simulations of balanced E/I-networks. The corresponding time course of an inverted parabola with exponent of χ = 2 described cortical avalanches of coincident firing for up to 5 s duration over an area of 1 mm². These parabolic avalanches maximized temporal complexity in the ongoing activity of prefrontal and somatosensory cortex and in visual responses of primary visual cortex. Our results identify a scale-invariant temporal order in the synchronization of highly diverse cortical cell assemblies in the form of parabolic avalanches.

Bistability and criticality in the stochastic Wilson-Cowan model

We study a stochastic version of the Wilson-Cowan model of neural dynamics, where the response function of neurons grows faster than linearly above the threshold. The model shows a region of parameters where two attractive fixed points of the dynamics exist simultaneously. One fixed point is characterized by lower activity and scale-free critical behavior, while the second fixed point corresponds to a higher (supercritical) persistent activity, with small fluctuations around a mean value. When the number of neurons is not too large, the system can switch between these two different states with a probability depending on the parameters of the network. Along with alternation of states, the model displays a bimodal distribution of the avalanches of activity, with a power-law behavior corresponding to the critical state, and a bump of very large avalanches due to the high-activity supercritical state. The bistability is due to the presence of a first-order (discontinuous) transition in the phase diagram, and the observed critical behavior is connected with the line where the low-activity state becomes unstable (spinodal line).

Power spectrum and critical exponents in the 2D stochastic Wilson-Cowan model

The power spectrum of brain activity is composed by peaks at characteristic frequencies superimposed to a background that decays as a power law of the frequency, [Formula: see text], with an exponent [Formula: see text] close to 1 (pink noise). This exponent is predicted to be connected with the exponent [Formula: see text] related to the scaling of the average size with the duration of avalanches of activity. "Mean field" models of neural dynamics predict exponents [Formula: see text] and [Formula: see text] equal or near 2 at criticality (brown noise), including the simple branching model and the fully-connected stochastic Wilson-Cowan model. We here show that a 2D version of the stochastic Wilson-Cowan model, where neuron connections decay exponentially with the distance, is characterized by exponents [Formula: see text] and [Formula: see text] markedly different from those of mean field, respectively around 1 and 1.3. The exponents [Formula: see text] and [Formula: see text] of avalanche size and duration distributions, equal to 1.5 and 2 in mean field, decrease respectively to [Formula: see text] and [Formula: see text]. This seems to suggest the possibility of a different universality class for the model in finite dimension.

Spontaneous neuronal avalanches as a correlate of access consciousness

Decades of research have advanced our understanding of the biophysical mechanisms underlying consciousness. However, an overarching framework bridging between models of consciousness and the large-scale organization of spontaneous brain activity is still missing. Based on the observation that spontaneous brain activity dynamically switches between epochs of segregation and large-scale integration of information, we hypothesize a brain-state dependence of conscious access, whereby the presence of either segregated or integrated states marks distinct modes of information processing. We first review influential works on the neuronal correlates of consciousness, spontaneous resting-state brain activity and dynamical system theory. Then, we propose a test experiment to validate our hypothesis that conscious access occurs in aperiodic cycles, alternating windows where new incoming information is collected but not experienced, to punctuated short-lived integration events, where conscious access to previously collected content occurs. In particular, we suggest that the integration events correspond to neuronal avalanches, which are collective bursts of neuronal activity ubiquitously observed in electrophysiological recordings. If confirmed, the proposed framework would link the physics of spontaneous cortical dynamics, to the concept of ignition within the global neuronal workspace theory, whereby conscious access manifest itself as a burst of neuronal activity.

Interplay of disorder and type of driving in disordered ferromagnetic systems

We investigate the effects of adiabatic, quasistatic, and finite-rate types of driving on the evolution of disordered three-dimensional ferromagnetic systems, studied within the frame of the nonequilibrium athermal random field Ising model. The effects were examined in all three domains of disorder (low, high, and transitional) for all types of driving, and in a wide range of driving rates for quasistatic and finite-rate driving, providing an extensive overview and comparison of the joint effects that the disorder, type of driving, and rate regime have on the system's behavior.

Addressing skepticism of the critical brain hypothesis

The hypothesis that living neural networks operate near a critical phase transition point has received substantial discussion. This “criticality hypothesis” is potentially important because experiments and theory show that optimal information processing and health are associated with operating near the critical point. Despite the promise of this idea, there have been several objections to it. While earlier objections have been addressed already, the more recent critiques of Touboul and Destexhe have not yet been fully met. The purpose of this paper is to describe their objections and offer responses. Their first objection is that the well-known Brunel model for cortical networks does not display a peak in mutual information near its phase transition, in apparent contradiction to the criticality hypothesis. In response I show that it does have such a peak near the phase transition point, provided it is not strongly driven by random inputs. Their second objection is that even simple models like a coin flip can satisfy multiple criteria of criticality. This suggests that the emergent criticality claimed to exist in cortical networks is just the consequence of a random walk put through a threshold. In response I show that while such processes can produce many signatures criticality, these signatures (1) do not emerge from collective interactions, (2) do not support information processing, and (3) do not have long-range temporal correlations. Because experiments show these three features are consistently present in living neural networks, such random walk models are inadequate. Nevertheless, I conclude that these objections have been valuable for refining research questions and should always be welcomed as a part of the scientific process.

How critical is brain criticality?

Criticality is the singular state of complex systems poised at the brink of a phase transition between order and randomness. Such systems display remarkable information-processing capabilities, evoking the compelling hypothesis that the brain may itself be critical. This foundational idea is now drawing renewed interest thanks to high-density data and converging cross-disciplinary knowledge. Together, these lines of inquiry have shed light on the intimate link between criticality, computation, and cognition. Here, we review these emerging trends in criticality neuroscience, highlighting new data pertaining to the edge of chaos and near-criticality, and making a case for the distance to criticality as a useful metric for probing cognitive states and mental illness. This unfolding progress in the field contributes to establishing criticality theory as a powerful mechanistic framework for studying emergent function and its efficiency in both biological and artificial neural networks.

Turing's cascade instability supports the coordination of the mind, brain, and behavior

Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor-that of the cascade. The time has come to confront Turing's cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing's cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.

Scaling of avalanche shape and activity power spectrum in neuronal networks

Many systems in nature exhibit avalanche dynamics with scale-free features. A general scaling theory has been proposed for critical avalanche profiles in crackling noise, predicting the collapse onto a universal avalanche shape, as well as the scaling behavior of the activity power spectrum as Brown noise. Recently, much attention has been given to the profile of neuronal avalanches, measured in neuronal systems in vitro and in vivo. Although a universal profile was evidenced, confirming the validity of the general scaling theory, the parallel study of the power spectrum scaling under the same conditions was not performed. The puzzling observation is that in the majority of healthy neuronal systems the power spectrum exhibits a behavior close to 1/f, rather than Brown, noise. Here we perform a numerical study of the scaling behavior of the avalanche shape and the power spectrum for a model of integrate and fire neurons with a short-term plasticity parameter able to tune the system to criticality. We confirm that, at criticality, the average avalanche size and the avalanche profile fulfill the general avalanche scaling theory. However, the power spectrum consistently exhibits Brown noise behavior, for both fully excitatory networks and systems with 30% inhibitory networks. Conversely, a behavior closer to 1/f noise is observed in systems slightly off criticality. Results suggest that the power spectrum is a good indicator to determine how close neuronal activity is to criticality.

Critical Spatial-Temporal Dynamics and Prominent Shape Collapse of Calcium Waves Observed in Human hNT Astrocytes in Vitro

Networks of neurons are typically studied in the field of Criticality. However, the study of astrocyte networks in the brain has been recently lauded to be of equal importance to that of the neural networks. To date criticality assessments have only been performed on networks astrocytes from healthy rats, and astrocytes from cultured dissociated resections of intractable epilepsy. This work, for the first time, presents studies of the critical dynamics and shape collapse of calcium waves observed in cultures of healthy human astrocyte networks in vitro, derived from the human hNT cell line. In this article, we demonstrate that avalanches of spontaneous calcium waves display strong critical dynamics, including power-laws in both the size and duration distributions. In addition, the temporal profiles of avalanches displayed self-similarity, leading to shape collapse of the temporal profiles. These findings are significant as they suggest that cultured networks of healthy human hNT astrocytes self-organize to a critical point, implying that healthy astrocytic networks operate at a critical point to process and transmit information. Furthermore, this work can serve as a point of reference to which other astrocyte criticality studies can be compared.

Scale-specific dynamics of high-amplitude bursts in EEG capture behaviorally meaningful variability

Cascading high-amplitude bursts in neural activity, termed avalanches, are thought to provide insight into the complex spatially distributed interactions in neural systems. In human neuroimaging, for example, avalanches occurring during resting-state show scale-invariant dynamics, supporting the hypothesis that the brain operates near a critical point that enables long range spatial communication. In fact, it has been suggested that such scale-invariant dynamics, characterized by a power-law distribution in these avalanches, are universal in neural systems and emerge through a common mechanism. While the analysis of avalanches and subsequent criticality is increasingly seen as a framework for using complex systems theory to understand brain function, it is unclear how the framework would account for the omnipresent cognitive variability, whether across individuals or tasks. To address this, we analyzed avalanches in the EEG activity of healthy humans during rest as well as two distinct task conditions that varied in cognitive demands and produced behavioral measures unique to each individual. In both rest and task conditions we observed that avalanche dynamics demonstrate scale-invariant characteristics, but differ in their specific features, demonstrating individual variability. Using a new metric we call normalized engagement, which estimates the likelihood for a brain region to produce high-amplitude bursts, we also investigated regional features of avalanche dynamics. Normalized engagement showed not only the expected individual and task dependent variability, but also scale-specificity that correlated with individual behavior. Our results suggest that the study of avalanches in human brain activity provides a tool to assess cognitive variability. Our findings expand our understanding of avalanche features and are supportive of the emerging theoretical idea that the dynamics of an active human brain operate close to a critical-like region and not a singular critical-state.

Long-term stability of avalanche scaling and integrative network organization in prefrontal and premotor cortex

Ongoing neuronal activity in the brain establishes functional networks that reflect normal and pathological brain function. Most estimates of these functional networks suffer from low spatiotemporal resolution and indirect measures of neuronal population activity, limiting the accuracy and reliability in their reconstruction over time. Here, we studied the stability of neuronal avalanche dynamics and corresponding reconstructed functional networks in the adult brain. Using chronically implanted high-density microelectrode arrays, the local field potential (LFP) of resting-state activity was recorded in prefrontal and premotor cortex of awake nonhuman primates. Avalanche dynamics revealed stable scaling exhibiting an inverted parabolic profile and collapse exponent of 2 in line with a critical branching process over many days and weeks. Functional networks were based on a Bayesian-derived estimator and demonstrated stable integrative properties characterized by nontrivial high neighborhood overlap between strongly connected nodes and robustness to weak-link pruning. Entropy-based mixing analysis revealed significant changes in strong link weights over weeks. The long-term stability in avalanche scaling and integrative network organization in the face of individual link weight changes should support the development of noninvasive biomarkers to characterize normal and abnormal brain states in the adult brain.

The brain is spontaneously active even in the absence of specific sensations or movements. This ongoing activity arises from the interactions among hundreds of thousands of neurons, which has been captured by a variety of distinct functional networks predictive of healthy and pathological brain functions. The global dynamical states and overarching network principles that underlie such ongoing brain activity are not well understood. Here we identify avalanche dynamics and “friendship” networks as two major features of ongoing activity in the frontal cortex of nonhuman primates. We demonstrate their stability over weeks in the face of local network changes. Deviation from avalanche dynamics and “friendship” organization might provide robust biomarkers to identify normal and pathological brain states.

Neural field theory of neural avalanche exponents

The power-law exponents of observed size and lifetime distributions of near-critical neural avalanches are calculated from neural field theory using diagrammatic methods. This brings neural avalanches within the ambit of neural field theory, which has also previously explained near-critical 1/f spectra and many other observed features of neural activity. This strengthens the case for near-criticality of the brain and opens the way for these other phenomena to be interrelated with avalanches and their dynamics.

Percolation theory of self-exciting temporal processes

We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of microscopic events produced by a self-exciting Hawkes process, and leverage a percolation framework to study the formation of macroscopic bursts of activity as a function of the resolution parameter. We find that the very same process may result in different distributions of avalanche size and duration, which are understood in terms of the competition between the 1D percolation and the branching process universality class. Pure regimes for the individual classes are observed at specific values of the resolution parameter corresponding to the critical points of the percolation diagram. A regime of crossover characterized by a mixture of the two universal behaviors is observed in a wide region of the diagram. The hybrid scaling appears to be a likely outcome for an analysis of the time series based on a reasonably chosen, but not precisely adjusted, value of the resolution parameter.

Criticality, Connectivity, and Neural Disorder: A Multifaceted Approach to Neural Computation

It has been hypothesized that the brain optimizes its capacity for computation by self-organizing to a critical point. The dynamical state of criticality is achieved by striking a balance such that activity can effectively spread through the network without overwhelming it and is commonly identified in neuronal networks by observing the behavior of cascades of network activity termed "neuronal avalanches." The dynamic activity that occurs in neuronal networks is closely intertwined with how the elements of the network are connected and how they influence each other's functional activity. In this review, we highlight how studying criticality with a broad perspective that integrates concepts from physics, experimental and theoretical neuroscience, and computer science can provide a greater understanding of the mechanisms that drive networks to criticality and how their disruption may manifest in different disorders. First, integrating graph theory into experimental studies on criticality, as is becoming more common in theoretical and modeling studies, would provide insight into the kinds of network structures that support criticality in networks of biological neurons. Furthermore, plasticity mechanisms play a crucial role in shaping these neural structures, both in terms of homeostatic maintenance and learning. Both network structures and plasticity have been studied fairly extensively in theoretical models, but much work remains to bridge the gap between theoretical and experimental findings. Finally, information theoretical approaches can tie in more concrete evidence of a network's computational capabilities. Approaching neural dynamics with all these facets in mind has the potential to provide a greater understanding of what goes wrong in neural disorders. Criticality analysis therefore holds potential to identify disruptions to healthy dynamics, granted that robust methods and approaches are considered.

Selective Participation of Single Cortical Neurons in Neuronal Avalanches

Neuronal avalanches are scale-invariant neuronal population activity patterns in the cortex that emerge in vivo in the awake state and in vitro during balanced excitation and inhibition. Theory and experiments suggest that avalanches indicate a state of cortex that improves numerous aspects of information processing by allowing for the transient and selective formation of local as well as system-wide spanning neuronal groups. If avalanches are indeed involved with information processing, one might expect that single neurons would participate in avalanche patterns selectively. Alternatively, all neurons could participate proportionally to their own activity in each avalanche as would be expected for a population rate code. Distinguishing these hypotheses, however, has been difficult as robust avalanche analysis requires technically challenging measures of their intricate organization in space and time at the population level, while also recording sub- or suprathreshold activity from individual neurons with high temporal resolution. Here, we identify repeated avalanches in the ongoing local field potential (LFP) measured with high-density microelectrode arrays in the cortex of awake nonhuman primates and in acute cortex slices from young and adult rats. We studied extracellular unit firing in vivo and intracellular responses of pyramidal neurons in vitro. We found that single neurons participate selectively in specific LFP-based avalanche patterns. Furthermore, we show in vitro that manipulating the balance of excitation and inhibition abolishes this selectivity. Our results support the view that avalanches represent the selective, scale-invariant formation of neuronal groups in line with the idea of Hebbian cell assemblies underlying cortical information processing.

Scale-Free Dynamics in Animal Groups and Brain Networks

Collective phenomena fascinate by the emergence of order in systems composed of a myriad of small entities. They are ubiquitous in nature and can be found over a vast range of scales in physical and biological systems. Their key feature is the seemingly effortless emergence of adaptive collective behavior that cannot be trivially explained by the properties of the system's individual components. This perspective focuses on recent insights into the similarities of correlations for two apparently disparate phenomena: flocking in animal groups and neuronal ensemble activity in the brain. We first will summarize findings on the spontaneous organization in bird flocks and macro-scale human brain activity utilizing correlation functions and insights from critical dynamics. We then will discuss recent experimental findings that apply these approaches to the collective response of neurons to visual and motor processing, i.e., to local perturbations of neuronal networks at the meso- and microscale. We show how scale-free correlation functions capture the collective organization of neuronal avalanches in evoked neuronal populations in nonhuman primates and between neurons during visual processing in rodents. These experimental findings suggest that the coherent collective neural activity observed at scales much larger than the length of the direct neuronal interactions is demonstrative of a phase transition and we discuss the experimental support for either discontinuous or continuous phase transitions. We conclude that at or near a phase-transition neuronal information can propagate in the brain with similar efficiency as proposed to occur in the collective adaptive response observed in some animal groups.

Subsampled Directed-Percolation Models Explain Scaling Relations Experimentally Observed in the Brain

Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations point to critical exponents whose values differ from those of a branching process, which has been the canonical model employed to understand brain criticality. This suggested that a different model, with a different phase transition, might be required to explain the data. Here we show that this is not necessarily the case. By employing two different models belonging to the same universality class as the branching process (mean-field directed percolation) and treating the simulation data exactly like experimental data, we reproduce most of the experimental results. We find that subsampling the model and adjusting the time bin used to define avalanches (as done with experimental data) are sufficient ingredients to change the apparent exponents of the critical point. Moreover, experimental data is only reproduced within a very narrow range in parameter space around the phase transition.

Hopf Bifurcation in Mean Field Explains Critical Avalanches in Excitation-Inhibition Balanced Neuronal Networks: A Mechanism for Multiscale Variability

Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) balanced neuronal network with biologically realistic synaptic kinetics. It can maintain irregular spiking dynamics with different levels of synchrony and critical avalanches emerge near the synchronous transition point. We propose a novel semi-analytical mean-field theory to derive the field equations governing the network macroscopic dynamics. It reveals that the E-I balanced state of the network manifesting irregular individual spiking is characterized by a macroscopic stable state, which can be either a fixed point or a periodic motion and the transition is predicted by a Hopf bifurcation in the macroscopic field. Furthermore, by analyzing public data, we find the coexistence of irregular spiking and critical avalanches in the spontaneous spiking activities of mouse cortical slice in vitro, indicating the universality of the observed phenomena. Our theory unveils the mechanism that permits complex neural activities in different spatiotemporal scales to coexist and elucidates a possible origin of the criticality of neural systems. It also provides a novel tool for analyzing the macroscopic dynamics of E-I balanced networks and its relationship to the microscopic counterparts, which can be useful for large-scale modeling and computation of cortical dynamics.

Visual effort moderates postural cascade dynamics

Standing still and focusing on a visible target in front of us is a preamble to many coordinated behaviors (e.g., reaching an object). Hiding behind its apparent simplicity is a deep layering of texture at many scales. The task of standing still laces together activities at multiple scales: from ensuring that a few photoreceptors on the retina cover the target in the visual field on an extremely fine scale to synergies spanning the limbs and joints at smaller scales to the mechanical layout of the ground underfoot and optic flow in the visual field on the coarser scales. Here, we used multiscale probability density function (PDF) analysis to show that postural fluctuations exhibit similar statistical signatures of cascade dynamics as found in fluid flow. In participants asked to stand quietly, the oculomotor strain of visually fixating at different distances moderated postural cascade dynamics. Visually fixating at a comfortable viewing distance elicited posture with a similar cascade dynamics as posture with eyes closed. Greater viewing distances known to stabilize posture showed more diminished cascade dynamics. In contrast, nearest and farthest viewing distances requiring greater oculomotor strain to focus on targets elicited a dramatic strengthening of postural cascade dynamics, reflecting active postural adjustments. Critically, these findings suggest that vision stabilizes posture by reconfiguring the prestressed poise that prepares the body to interact with different spatial layouts.

Postural constraints recruit shorter-timescale processes into the non-Gaussian cascade processes

Healthy human postural sway exhibits strong intermittency, reflecting a richly interactive foundation of postural control. From a linear perspective, intermittent fluctuations might be interpreted as engagement and disengagement of complementary control processes at distinct timescales or from a nonlinear perspective, as cascade-like interactions across many timescales at once. The diverse control processes entailed by cascade-like multiplicative dynamics suggest specific non-Gaussian distributional properties at different timescales. Multiscale probability density function (PDF) analysis showed that when standing quietly while balancing a sand-filled tube with the two arms elicited non-Gaussianity profiles showing a negative-quadratic crossover between short and long timescales. A more stringent task of balancing a water-filled tube elicited simpler monotonic decreases in non-Gaussianity, that is, a positive-quadratic cancellation of the negative-quadratic crossover. Multiple known indices of postural sway governed the appearance or disappearance of the crossover. Finally, both tasks elicited lognormal distributions over progressively larger timescales. These results provide the first evidence that more stringent postural constraints recruit shorter-timescale processes into the non-Gaussian cascade processes, that indices of postural sway moderate this recruitment, and that more stringent postural constraints show stronger statistical hallmarks of cascade structure.

Cognitive function: holarchy or holacracy?

Cognition is the most complex function of the brain. When exploring the inner workings of cognitive processes, it is crucial to understand the complexity of the brain's dynamics. This paper aims to describe the integrated framework of the cognitive function, seen as the result of organization and interactions between several systems and subsystems. We briefly describe several organizational concepts, spanning from the reductionist hierarchical approach, up to the more dynamic theory of open complex systems. The homeostatic regulation of the mechanisms responsible for cognitive processes is showcased as a dynamic interplay between several anticorrelated mechanisms, which can be found at every level of the brain's organization, from molecular and cellular level to large-scale networks (e.g., excitation-inhibition, long-term plasticity-long-term depression, synchronization-desynchronization, segregation-integration, order-chaos). We support the hypothesis that cognitive function is the consequence of multiple network interactions, integrating intricate relationships between several systems, in addition to neural circuits.

Time-dependent branching processes: a model of oscillating neuronal avalanches

Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitative comparison to available experimental results.