Hysteresis, neural avalanches, and critical behavior near a first-order transition of a spiking neural network

Inhibitory neurons and the asymmetric shape of neuronal avalanches

In the last twenty years neuronal avalanches have been deeply investigated, both experimentally and numerically, also framing the results in the context of the avalanche scaling theory. In particular the avalanche shape has recently received a wide attention, also because the existence of a universal shape is an indication of the brain acting at a critical point. Within this scope, the detection of the shape asymmetry and the understanding of the mechanisms leading to it can provide useful insights into brain activity. Experimental data evidence, either symmetric or leftward asymmetry in the shape, results are not confirmed by numerical studies. Here we analyze the role of inhibition, connectivity range, and short term plasticity in determining the avalanche shape in an integrate and fire model. Results indicate that, not only the physiological fraction of inhibitory neurons is crucial to observe leftward asymmetry, but also the different synaptic recovery rates between excitatory and inhibitory neurons, confirming the importance of a dynamic balance between excitation and inhibition in brain activity.

The recovery of parabolic avalanches in spatially subsampled neuronal networks at criticality

Scaling relationships are key in characterizing complex systems at criticality. In the brain, they are evident in neuronal avalanches-scale-invariant cascades of neuronal activity quantified by power laws. Avalanches manifest at the cellular level as cascades of neuronal groups that fire action potentials simultaneously. Such spatiotemporal synchronization is vital to theories on brain function yet avalanche synchronization is often underestimated when only a fraction of neurons is observed. Here, we investigate biases from fractional sampling within a balanced network of excitatory and inhibitory neurons with all-to-all connectivity and critical branching process dynamics. We focus on how mean avalanche size scales with avalanche duration. For parabolic avalanches, this scaling is quadratic, quantified by the scaling exponent, χ = 2, reflecting rapid spatial expansion of simultaneous neuronal firing over short durations. However, in networks sampled fractionally, χ is significantly lower. We demonstrate that applying temporal coarse-graining and increasing a minimum threshold for coincident firing restores χ = 2, even when as few as 0.1% of neurons are sampled. This correction crucially depends on the network being critical and fails for near sub- and supercritical branching dynamics. Using cellular 2-photon imaging, our approach robustly identifies χ = 2 over a wide parameter regime in ongoing neuronal activity from frontal cortex of awake mice. In contrast, the common 'crackling noise' approach fails to determine χ under similar sampling conditions at criticality. Our findings overcome scaling bias from fractional sampling and demonstrate rapid, spatiotemporal synchronization of neuronal assemblies consistent with scale-invariant, parabolic avalanches at criticality.

Collective dynamics and long-range order in thermal neuristor networks

In the pursuit of scalable and energy-efficient neuromorphic devices, recent research has unveiled a novel category of spiking oscillators, termed "thermal neuristors." These devices function via thermal interactions among neighboring vanadium dioxide resistive memories, emulating biological neuronal behavior. Here, we show that the collective dynamical behavior of networks of these neurons showcases a rich phase structure, tunable by adjusting the thermal coupling and input voltage. Notably, we identify phases exhibiting long-range order that, however, does not arise from criticality, but rather from the time non-local response of the system. In addition, we show that these thermal neuristor arrays achieve high accuracy in image recognition and time series prediction through reservoir computing, without leveraging long-range order. Our findings highlight a crucial aspect of neuromorphic computing with possible implications on the functioning of the brain: criticality may not be necessary for the efficient performance of neuromorphic systems in certain computational tasks.

The recovery of parabolic avalanches in spatially subsampled neuronal networks at criticality

Scaling relationships are key in characterizing complex systems at criticality. In the brain, they are evident in neuronal avalanches-scale-invariant cascades of neuronal activity quantified by power laws. Avalanches manifest at the cellular level as cascades of neuronal groups that fire action potentials simultaneously. Such spatiotemporal synchronization is vital to theories on brain function yet avalanche synchronization is often underestimated when only a fraction of neurons is observed. Here, we investigate biases from fractional sampling within a balanced network of excitatory and inhibitory neurons with all-to-all connectivity and critical branching process dynamics. We focus on how mean avalanche size scales with avalanche duration. For parabolic avalanches, this scaling is quadratic, quantified by the scaling exponent, χ = 2 , reflecting rapid spatial expansion of simultaneous neuronal firing over short durations. However, in networks sampled fractionally, χ is significantly lower. We demonstrate that applying temporal coarse-graining and increasing a minimum threshold for coincident firing restores χ = 2 , even when as few as 0.1% of neurons are sampled. This correction crucially depends on the network being critical and fails for near sub- and supercritical branching dynamics. Using cellular 2-photon imaging, our approach robustly identifies χ = 2 over a wide parameter regime in ongoing neuronal activity from frontal cortex of awake mice. In contrast, the common 'crackling noise' approach fails to determine χ under similar sampling conditions at criticality. Our findings overcome scaling bias from fractional sampling and demonstrate rapid, spatiotemporal synchronization of neuronal assemblies consistent with scale-invariant, parabolic avalanches at criticality.

Neuronal avalanche dynamics regulated by spike-timing-dependent plasticity under different topologies and heterogeneities

Neuronal avalanches, a critical state of network self-organization, have been widely observed in electrophysiological records at different signal levels and spatial scales of the brain, which has significant influence on information transmission and processing in the brain. In this paper, the collective behavior of neuron firing is studied based on Leaky Integrate-and-Fire model and we induce spike-timing-dependent plasticity (STDP) to update the connection weight through competition between adjacent neurons in different network topologies. The result shows that STDP can facilitate the synchronization of the network and increase the probability of large-scale neuron avalanche obviously. Moreover, both the structure of STDP and network connection density can affect the generation of avalanche critical states, specifically, learning rate has positive correlation effect on the slope of power-law distribution and time constant has negative correction on it. However, when we the increase of heterogeneity in network, STDP can only has obvious promotion in synchrony under suitable level of heterogeneity. And we find that the process of long-term potentiation is sensitive to the adjustment of time constant and learning rate, unlike long-term depression, which is only sensitive to learning rate in heterogeneity network. It is suggested that presented results could facilitate our understanding on synchronization in various neural networks under the effect of STDP learning rules.

Critical-like Brain Dynamics in a Continuum from Second- to First-Order Phase Transition

The classic brain criticality hypothesis postulates that the brain benefits from operating near a continuous second-order phase transition. Slow feedback regulation of neuronal activity could, however, lead to a discontinuous first-order transition and thereby bistable activity. Observations of bistability in awake brain activity have nonetheless remained scarce and its functional significance unclear. Moreover, there is no empirical evidence to support the hypothesis that the human brain could flexibly operate near either a first- or second-order phase transition despite such a continuum being common in models. Here, using computational modeling, we found bistable synchronization dynamics to emerge through elevated positive feedback and occur exclusively in a regimen of critical-like dynamics. We then assessed bistability in vivo with resting-state MEG in healthy adults (7 females, 11 males) and stereo-electroencephalography in epilepsy patients (28 females, 36 males). This analysis revealed that a large fraction of the neocortices exhibited varying degrees of bistability in neuronal oscillations from 3 to 200 Hz. In line with our modeling results, the neuronal bistability was positively correlated with classic assessment of brain criticality across narrow-band frequencies. Excessive bistability was predictive of epileptic pathophysiology in the patients, whereas moderate bistability was positively correlated with task performance in the healthy subjects. These empirical findings thus reveal the human brain as a one-of-a-kind complex system that exhibits critical-like dynamics in a continuum between continuous and discontinuous phase transitions.SIGNIFICANCE STATEMENT In the model, while synchrony per se was controlled by connectivity, increasing positive local feedback led to gradually emerging bistable synchrony with scale-free dynamics, suggesting a continuum between second- and first-order phase transitions in synchrony dynamics inside a critical-like regimen. In resting-state MEG and SEEG, bistability of ongoing neuronal oscillations was pervasive across brain areas and frequency bands and was observed only with concurring critical-like dynamics as the modeling predicted. As evidence for functional relevance, moderate bistability was positively correlated with executive functioning in the healthy subjects, and excessive bistability was associated with epileptic pathophysiology. These findings show that critical-like neuronal dynamics in vivo involves both continuous and discontinuous phase transitions in a frequency-, neuroanatomy-, and state-dependent manner.

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.

The fractal brain: scale-invariance in structure and dynamics

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

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.

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.

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.

Disentangling the critical signatures of neural activity

The critical brain hypothesis has emerged as an attractive framework to understand neuronal activity, but it is still widely debated. In this work, we analyze data from a multi-electrodes array in the rat's cortex and we find that power-law neuronal avalanches satisfying the crackling-noise relation coexist with spatial correlations that display typical features of critical systems. In order to shed a light on the underlying mechanisms at the origin of these signatures of criticality, we introduce a paradigmatic framework with a common stochastic modulation and pairwise linear interactions inferred from our data. We show that in such models power-law avalanches that satisfy the crackling-noise relation emerge as a consequence of the extrinsic modulation, whereas scale-free correlations are solely determined by internal interactions. Moreover, this disentangling is fully captured by the mutual information in the system. Finally, we show that analogous power-law avalanches are found in more realistic models of neural activity as well, suggesting that extrinsic modulation might be a broad mechanism for their generation.

Avalanche criticality in individuals, fluid intelligence, and working memory

The critical brain hypothesis suggests that efficient neural computation can be achieved through critical brain dynamics. However, the relationship between human cognitive performance and scale‐free brain dynamics remains unclear. In this study, we investigated the whole‐brain avalanche activity and its individual variability in the human resting‐state functional magnetic resonance imaging (fMRI) data. We showed that though the group‐level analysis was inaccurate because of individual variability, the subject wise scale‐free avalanche activity was significantly associated with maximal synchronization entropy of their brain activity. Meanwhile, the complexity of functional connectivity, as well as structure–function coupling, is maximized in subjects with maximal synchronization entropy. We also observed order–disorder phase transitions in resting‐state brain dynamics and found that there were longer times spent in the subcritical regime. These results imply that large‐scale brain dynamics favor the slightly subcritical regime of phase transition. Finally, we showed evidence that the neural dynamics of human participants with higher fluid intelligence and working memory scores are closer to criticality. We identified brain regions whose critical dynamics showed significant positive correlations with fluid intelligence performance and found that these regions were located in the prefrontal cortex and inferior parietal cortex, which were believed to be important nodes of brain networks underlying human intelligence. Our results reveal the possible role that avalanche criticality plays in cognitive performance and provide a simple method to identify the critical point and map cortical states on a spectrum of neural dynamics, ranging from subcriticality to supercriticality.

Avalanches and edge-of-chaos learning in neuromorphic nanowire networks

The brain's efficient information processing is enabled by the interplay between its neuro-synaptic elements and complex network structure. This work reports on the neuromorphic dynamics of nanowire networks (NWNs), a unique brain-inspired system with synapse-like memristive junctions embedded within a recurrent neural network-like structure. Simulation and experiment elucidate how collective memristive switching gives rise to long-range transport pathways, drastically altering the network's global state via a discontinuous phase transition. The spatio-temporal properties of switching dynamics are found to be consistent with avalanches displaying power-law size and life-time distributions, with exponents obeying the crackling noise relationship, thus satisfying criteria for criticality, as observed in cortical neuronal cultures. Furthermore, NWNs adaptively respond to time varying stimuli, exhibiting diverse dynamics tunable from order to chaos. Dynamical states at the edge-of-chaos are found to optimise information processing for increasingly complex learning tasks. Overall, these results reveal a rich repertoire of emergent, collective neural-like dynamics in NWNs, thus demonstrating the potential for a neuromorphic advantage in 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.

Statistical complexity is maximized close to criticality in cortical dynamics

Complex systems are typically characterized as an intermediate situation between a complete regular structure and a random system. Brain signals can be studied as a striking example of such systems: cortical states can range from highly synchronous and ordered neuronal activity (with higher spiking variability) to desynchronized and disordered regimes (with lower spiking variability). It has been recently shown, by testing independent signatures of criticality, that a phase transition occurs in a cortical state of intermediate spiking variability. Here we use a symbolic information approach to show that, despite the monotonical increase of the Shannon entropy between ordered and disordered regimes, we can determine an intermediate state of maximum complexity based on the Jensen disequilibrium measure. More specifically, we show that statistical complexity is maximized close to criticality for cortical spiking data of urethane-anesthetized rats, as well as for a network model of excitable elements that presents a critical point of a nonequilibrium phase transition.

Spike-phase coupling as an order parameter in a leaky integrate-and-fire model

It is known that the leaky integrate-and-fire neural model shows a transition from irregular to synchronous firing by increasing the coupling between the neurons. However, a quantitative characterization of this order-disorder transition, that is, the determination of the order of transition and also the critical exponents in the case of continuous transition, is not entirely known. In this work, we consider a network of N excitatory neurons with local connections, residing on a square lattice with periodic boundary conditions. The cooperation between neurons K plays the role of the control parameter that generates criticality when the critical cooperation strength K_{c} is adopted. We introduce the population-averaged voltage (PAV) as a representative value of the network's cooperative activity. Then, we show that the coupling between the timing of spikes and the phase of temporal fluctuations of PAV defined as m resorts to identify a Kuramoto order parameter. By increasing K, we find a continuous transition from irregular spiking to a phase-locked state at the critical point K_{c}. We deploy the finite-size scaling analysis to calculate the critical exponents of this transition. To explore the formal indicator of criticality, we study the neuronal avalanches profile at this critical point and find a scaling behavior with the exponents in a fair agreement with the experimental values both in vivo and in vitro.

Stability of motor cortex network states during learning-associated neural reorganizations

A substantial reorganization of neural activity and neuron-to-movement relationship in motor cortical circuits accompanies the emergence of reproducible movement patterns during motor learning. Little is known about how this tempest of neural activity restructuring impacts the stability of network states in recurrent cortical circuits. To investigate this issue, we reanalyzed data in which we recorded for 14 days via population calcium imaging the activity of the same neural populations of pyramidal neurons in layer 2/3 and layer 5 of forelimb motor and premotor cortex in mice during the daily learning of a lever-press task. We found that motor cortex network states remained stable with respect to the critical network state during the extensive reorganization of both neural population activity and its relation to lever movement throughout learning. Specifically, layer 2/3 cortical circuits unceasingly displayed robust evidence for operating at the critical network state, a regime that maximizes information capacity and transmission and provides a balance between network robustness and flexibility. In contrast, layer 5 circuits operated away from the critical network state for all 14 days of recording and learning. In conclusion, this result indicates that the wide-ranging malleability of synapses, neurons, and neural connectivity during learning operates within the constraint of a stable and layer-specific network state regarding dynamic criticality, and suggests that different cortical layers operate under distinct constraints because of their specialized goals.NEW & NOTEWORTHY The neural activity reorganizes throughout motor learning, but how this reorganization impacts the stability of network states is unclear. We used two-photon calcium imaging to investigate how the network states in layer 2/3 and layer 5 of forelimb motor and premotor cortex are modulated by motor learning. We show that motor cortex network states are layer-specific and constant regarding criticality during neural activity reorganization, and suggests that layer-specific constraints could be motivated by different functions.

A Review of the Serrated-Flow Phenomenon and Its Role in the Deformation Behavior of High-Entropy Alloys

High-entropy alloys (HEAs) are a novel class of alloys that have many desirable properties. The serrated flow that occurs in high-entropy alloys during mechanical deformation is an important phenomenon since it can lead to significant changes in the microstructure of the alloy. In this article, we review the recent findings on the serration behavior in a variety of high-entropy alloys. Relationships among the serrated flow behavior, composition, microstructure, and testing condition are explored. Importantly, the mechanical-testing type (compression/tension), testing temperature, applied strain rate, and serration type for certain high-entropy alloys are summarized. The literature reveals that the serrated flow can be affected by experimental conditions such as the strain rate and test temperature. Furthermore, this type of phenomenon has been successfully modeled and analyzed, using several different types of analytical methods, including the mean-field theory formalism and the complexity-analysis technique. Importantly, the results of the analyses show that the serrated flow in HEAs consists of complex dynamical behavior. It is anticipated that this review will provide some useful and clarifying information regarding the serrated-flow mechanisms in this material system. Finally, suggestions for future research directions in this field are proposed, such as the effects of irradiation, additives (such as C and Al), the presence of nanoparticles, and twinning on the serrated flow behavior in HEAs.

Edge of Chaos and Avalanches in Neural Networks with Heavy-Tailed Synaptic Weight Distribution

We propose an analytically tractable neural connectivity model with power-law distributed synaptic strengths. When threshold neurons with biologically plausible number of incoming connections are considered, our model features a continuous transition to chaos and can reproduce biologically relevant low activity levels and scale-free avalanches, i.e., bursts of activity with power-law distributions of sizes and lifetimes. In contrast, the Gaussian counterpart exhibits a discontinuous transition to chaos and thus cannot be poised near the edge of chaos. We validate our predictions in simulations of networks of binary as well as leaky integrate-and-fire neurons. Our results suggest that heavy-tailed synaptic distribution may form a weakly informative sparse-connectivity prior that can be useful in biological and artificial adaptive systems.

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d < 4, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law–tailed synchronization durations, with τ_t ≃ 1.2(1), away from experimental values for the brain. For comparison, on a large two-dimensional lattice, having additional random, long-range links, we obtain a mean-field value: τ_t ≃ 1.6(1). However, below the transition of the connectome we found global coupling control-parameter dependent exponents 1 < τ_t ≤ 2, overlapping with the range of human brain experiments. We also studied the effects of random flipping of a small portion of link weights, mimicking a network with inhibitory interactions, and found similar results. The control-parameter dependent exponent suggests extended dynamical criticality below the transition point.

Spike-Timing-Dependent Plasticity With Axonal Delay Tunes Networks of Izhikevich Neurons to the Edge of Synchronization Transition With Scale-Free Avalanches

Critical brain hypothesis has been intensively studied both in experimental and theoretical neuroscience over the past two decades. However, some important questions still remain: (i) What is the critical point the brain operates at? (ii) What is the regulatory mechanism that brings about and maintains such a critical state? (iii) The critical state is characterized by scale-invariant behavior which is seemingly at odds with definitive brain oscillations? In this work we consider a biologically motivated model of Izhikevich neuronal network with chemical synapses interacting via spike-timing-dependent plasticity (STDP) as well as axonal time delay. Under generic and physiologically relevant conditions we show that the system is organized and maintained around a synchronization transition point as opposed to an activity transition point associated with an absorbing state phase transition. However, such a state exhibits experimentally relevant signs of critical dynamics including scale-free avalanches with finite-size scaling as well as critical branching ratios. While the system displays stochastic oscillations with highly correlated fluctuations, it also displays dominant frequency modes seen as sharp peaks in the power spectrum. The role of STDP as well as time delay is crucial in achieving and maintaining such critical dynamics, while the role of inhibition is not as crucial. In this way we provide possible answers to all three questions posed above. We also show that one can achieve supercritical or subcritical dynamics if one changes the average time delay associated with axonal conduction.

Dynamic Computation in Visual Thalamocortical Networks

Contemporary neurodynamical frameworks, such as coordination dynamics and winnerless competition, posit that the brain approximates symbolic computation by transitioning between metastable attractive states. This article integrates these accounts with electrophysiological data suggesting that coherent, nested oscillations facilitate information representation and transmission in thalamocortical networks. We review the relationship between criticality, metastability, and representational capacity, outline existing methods for detecting metastable oscillatory patterns in neural time series data, and evaluate plausible spatiotemporal coding schemes based on phase alignment. We then survey the circuitry and the mechanisms underlying the generation of coordinated alpha and gamma rhythms in the primate visual system, with particular emphasis on the pulvinar and its role in biasing visual attention and awareness. To conclude the review, we begin to integrate this perspective with longstanding theories of consciousness and cognition.

Synaptic modifications driven by spike-timing-dependent plasticity in weakly coupled bursting neurons

In the course of development, sleep, or mental disorders, certain neurons in the brain display spontaneous spike-burst activity. The synaptic plasticity evoked by such activity is here studied in the presence of spike-timing-dependent plasticity (STDP). In two chemically coupled bursting model neurons, the spike-burst activity can translate the STDP related to pre- and postsynaptic spike activity into burst-timing-dependent plasticity (BTDP), based on the timing of bursts of pre- and postsynaptic neurons. The resulting BTDP exhibits exponential decays with the same time scales as those of STDP. In weakly coupled bursting neuron networks, the synaptic modification driven by the spike-burst activity obeys a power-law distribution. The model can also produce a power-law distribution of synaptic weights. Here, the considered bursting behavior is made of stereotypical groups of spikes, and bursting is evenly spaced by long intervals.

Single-Cell Membrane Potential Fluctuations Evince Network Scale-Freeness and Quasicriticality

What information single neurons receive about general neural circuit activity is a fundamental question for neuroscience. Somatic membrane potential (V _m) fluctuations are driven by the convergence of synaptic inputs from a diverse cross-section of upstream neurons. Furthermore, neural activity is often scale-free, implying that some measurements should be the same, whether taken at large or small scales. Together, convergence and scale-freeness support the hypothesis that single V _m recordings carry useful information about high-dimensional cortical activity. Conveniently, the theory of "critical branching networks" (one purported explanation for scale-freeness) provides testable predictions about scale-free measurements that are readily applied to V _m fluctuations. To investigate, we obtained whole-cell current-clamp recordings of pyramidal neurons in visual cortex of turtles with unknown genders. We isolated fluctuations in V _m below the firing threshold and analyzed them by adapting the definition of "neuronal avalanches" (i.e., spurts of population spiking). The V _m fluctuations which we analyzed were scale-free and consistent with critical branching. These findings recapitulated results from large-scale cortical population data obtained separately in complementary experiments using microelectrode arrays described previously (Shew et al., 2015). Simultaneously recorded single-unit local field potential did not provide a good match, demonstrating the specific utility of V _m Modeling shows that estimation of dynamical network properties from neuronal inputs is most accurate when networks are structured as critical branching networks. In conclusion, these findings extend evidence of critical phenomena while also establishing subthreshold pyramidal neuron V _m fluctuations as an informative gauge of high-dimensional cortical population activity.SIGNIFICANCE STATEMENT The relationship between membrane potential (V _m) dynamics of single neurons and population dynamics is indispensable to understanding cortical circuits. Just as important to the biophysics of computation are emergent properties such as scale-freeness, where critical branching networks offer insight. This report makes progress on both fronts by comparing statistics from single-neuron whole-cell recordings with population statistics obtained with microelectrode arrays. Not only are fluctuations of somatic V _m scale-free, they match fluctuations of population activity. Thus, our results demonstrate appropriation of the brain's own subsampling method (convergence of synaptic inputs) while extending the range of fundamental evidence for critical phenomena in neural systems from the previously observed mesoscale (fMRI, LFP, population spiking) to the microscale, namely, V _m fluctuations.

Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: Continuously varying exponents mimic M/EEG results

We revisit the CROS ("CRitical OScillations") model which was recently proposed as an attempt to reproduce both scale-invariant neuronal avalanches and long-range temporal correlations. With excitatory and inhibitory stochastic neurons locally connected in a two-dimensional disordered network, the model exhibits a transition where alpha-band oscillations emerge. Precisely at the transition, the fluctuations of the network activity have nontrivial detrended fluctuation analysis (DFA) exponents, and avalanches (defined as supra-threshold activity) have power law distributions of size and duration. We show that, differently from previous results, the exponents governing the distributions of avalanche size and duration are not necessarily those of the mean-field directed percolation universality class (3/2 and 2, respectively). Instead, in a narrow region of parameter space, avalanche exponents obtained via a maximum-likelihood estimator vary continuously and follow a linear relation, in good agreement with results obtained from M/EEG data. In that region, moreover, the values of avalanche and DFA exponents display a spread with positive correlations, reproducing human MEG results.

Robustness of Griffiths effects in homeostatic connectome models

I provide numerical evidence for the robustness of the Griffiths phase (GP) reported previously in dynamical threshold model simulations on a large human brain network with N=836733 connected nodes. The model, with equalized network sensitivity, is extended in two ways: introduction of refractory states or by randomized time-dependent thresholds. The nonuniversal power-law dynamics in an extended control parameter region survives these modifications for a short refractory state and weak disorder. In case of temporal disorder the GP shrinks and for stronger heterogeneity disappears, leaving behind a mean-field type of critical transition. Activity avalanche size distributions below the critical point decay faster than in the original model, but the addition of inhibitory interactions sets it back to the range of experimental values.