Self-organized criticality: An explanation of the 1/f noise

Thermally activated intermittent flow in amorphous solids

Using mean field theory and a mesoscale elastoplastic model, we analyze the steady state shear rheology of thermally activated amorphous solids. At sufficiently high temperature and driving rates, flow is continuous and described by well-established rheological flow laws such as Herschel-Bulkley and logarithmic rate dependence. However, we find that these flow laws change in the regime of intermittent flow, where collective events no longer overlap and serrated flow becomes pronounced. In this regime, we identify a thermal activation stress scale, xa(T,), that wholly captures the effect of driving rate  and temperature T on average flow stress, stress drop (avalanche) size and correlation lengths. Different rheological regimes are summarized in a dynamic phase diagram for the amorphous yielding transition. Theoretical predictions call for a need to re-examine the rheology of very slowly sheared amorphous matter much below the glass transition.

Distribution in the geometrically growing system and its evolution

Recently, we developed a theory of a geometrically growing system. Here, we show that the theory can explain some phenomena of power-law distribution, including classical demographic and economic and novel instances of the COVID-19 pandemic, without introduction of delicate economic or pandemic propagation models but only on a statistical way. A convexity in the low-size part of the distribution diagram is one peculiarity of the theory, which is absent in the power-law distribution. We found that the distribution of the geometrically growing system in the diagram could have a trend to flatten in the evolution of the system so that the relative ratio between the biggest and smallest sizes within the system increases. The system can act as a reverse machine to convert the diffusion in parametric space to a concentration in size.

Quantum Logic Automata Generate Class IV-like patterns and 1/f noise

Owing to recent advancements in brain science and AI, researchers tend to focus on the concept of self-organized criticality or the edge of chaos. On the other hand, quantum cognition, which is rooted in quantum mechanics, is promising for resolving various cognitive illusions. However, until recently, no connection between criticality and quantum mechanics was proposed. Gunji et al. (2024) recently introduced a linkage termed quantum logic automata, which encompasses not only quantum logic but also criticality characterized by power-law distributions. While quantum logic automata can be derived from various structures, only one of them has been proposed and discussed. Here, we define another type of quantum logic automata involving quantum logic and demonstrate that symmetric quantum logic automata lead to complex Class IV-like patterns and power-law distributions. Our findings support the association between criticality and quantum theory.

Nature heals: An informational entropy account of self-organization and change in field psychotherapy

This paper reviews biophysical models of psychotherapeutic change based on synergetics and the free energy principle. These models suggest that introducing sensory surprise into the patient-therapist system can lead to self-organization and the formation of new attractor states, disrupting entrenched patterns of thoughts, emotions, and behaviours. We propose that the therapist can facilitate this process by cultivating epistemic trust and modulating embodied attention to allow surprising affective states to enter shared awareness. Transient increases in free energy enable the update of generative models, expanding the range of experiences available within the patient-therapist phenomenal field. We hypothesize that patterns of disorganization at behavioural and physiological levels, indexed by increased entropy, complexity, and lower determinism, are key markers and predictors of psychotherapeutic gains. Future research should investigate how the therapist's openness to novelty shapes therapeutic outcomes.

Selective consistency of recurrent neural networks induced by plasticity as a mechanism of unsupervised perceptual learning

Understanding the mechanism by which the brain achieves relatively consistent information processing contrary to its inherent inconsistency in activity is one of the major challenges in neuroscience. Recently, it has been reported that the consistency of neural responses to stimuli that are presented repeatedly is enhanced implicitly in an unsupervised way, and results in improved perceptual consistency. Here, we propose the term "selective consistency" to describe this input-dependent consistency and hypothesize that it will be acquired in a self-organizing manner by plasticity within the neural system. To test this, we investigated whether a reservoir-based plastic model could acquire selective consistency to repeated stimuli. We used white noise sequences randomly generated in each trial and referenced white noise sequences presented multiple times. The results showed that the plastic network was capable of acquiring selective consistency rapidly, with as little as five exposures to stimuli, even for white noise. The acquisition of selective consistency could occur independently of performance optimization, as the network's time-series prediction accuracy for referenced stimuli did not improve with repeated exposure and optimization. Furthermore, the network could only achieve selective consistency when in the region between order and chaos. These findings suggest that the neural system can acquire selective consistency in a self-organizing manner and that this may serve as a mechanism for certain types of learning.

Fitness noise in the Bak-Sneppen evolution model in high dimensions

We study the Bak-Sneppen evolution model on a regular hypercubic lattice in high dimensions. Recent work [Phys. Rev. E 108, 044109 (2023)2470-004510.1103/PhysRevE.108.044109] showed the emergence of the 1/f^{α} noise for the fitness observable with α≈1.2 in one-dimension (1D) and α≈2 for the random neighbor (mean-field) version of the model. We examine the temporal correlation of fitness in 2, 3, 4, and 5 dimensions. As obtained by finite-size scaling, the spectral exponent tends to take the mean-field value at the upper critical dimension D_{u}=4, which is consistent with previous studies. Our approach provides an alternative way to understand the upper critical dimension of the model. We also show the local activity power spectra, which offer insight into the return time statistics and the avalanche dimension.

Type of probability distribution reflects how close mixing dynamics in river chemistry are to thermodynamic equilibrium

The distribution of geochemical species are typically either (log)normally distributed or follow power laws. Here we link these types of distributions to the dynamics of the system that generates these distributions, showing that power laws can emerge in dissipative systems far from equilibrium while (log)normal distributions are found for species for which the concentrations are close to equilibrium. We use observations of the chemical composition of river water from the sampling space in central Italy as well as discharge data to test this interpretation. We estimate the dissipation rate that results when groundwater drains into the river and the dissolved chemical species mix with the river water. We show that calcium (Ca2+) and bicarbonate (HCO3-) concentrations are close to saturation along most of the downstream length of the Arno river, with decreasing dissipation rates and a lognormal distribution, while sodium (Na+) and chloride (Cl-) concentrations increase substantially downstream, show increased dissipation rates, and are power-law distributed. This supports our hypothesis that power law distributions appear to be indicative of dissipative systems far from thermodynamic equilibrium, while (log)normal distributions indicate weakly dissipative systems close to equilibrium. What this implies is that probability distributions are likely to be indicative of the thermodynamics of the system and the magnitude of disequilibrium constrains the range over which power-law scaling may be observed. This should help us to better identify the generalities and mechanisms that result in these common types of distributions and to better classify variability in systems according to how dissipative these are.

Hydrodynamic behavior near dynamical criticality of a facilitated conservative lattice gas

We investigate a 2d-conservative lattice gas exhibiting a dynamical active-absorbing phase transition with critical density ρ_{c}. We derive the hydrodynamic equation for this model, showing that all critical exponents governing the large scale behavior near criticality can be obtained from two independent ones. We show that as the supercritical density approaches criticality, distinct length scales naturally appear. Remarkably, this behavior is different from the subcritical one. Numerical simulations support the critical relations and the scale separation.

Role of the Locus Coeruleus Arousal Promoting Neurons in Maintaining Brain Criticality across the Sleep-Wake Cycle

Sleep control depends on a delicate interplay among brain regions. This generates a complex temporal architecture with numerous sleep-stage transitions and intermittent fluctuations to micro-states and brief arousals. These temporal dynamics exhibit hallmarks of criticality, suggesting that tuning to criticality is essential for spontaneous sleep-stage and arousal transitions. However, how the brain maintains criticality remains not understood. Here, we investigate θ- and δ-burst dynamics during the sleep-wake cycle of rats (Sprague-Dawley, adult male) with lesion in the wake-promoting locus coeruleus (LC). We show that, in control rats, θ- and δ-bursts exhibit power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, as well as power-law long-range temporal correlations (LRTCs)-typical of non-equilibrium systems self-organizing at criticality. Furthermore, consecutive θ- and δ-bursts durations are characterized by anti-correlated coupling, indicating a new class of self-organized criticality that emerges from underlying feedback between neuronal populations and brain areas involved in generating arousals and sleep states. In contrast, we uncover that LC lesion leads to alteration of θ- and δ-burst critical features, with change in duration distributions and correlation properties, and increase in θ-δ coupling. Notably, these LC-lesion effects are opposite to those observed for lesions in the sleep-promoting ventrolateral preoptic (VLPO) nucleus. Our findings indicate that critical dynamics of θ- and δ-bursts arise from a balanced interplay of LC and VLPO, which maintains brain tuning to criticality across the sleep-wake cycle-a non-equilibrium behavior in sleep micro-architecture at short timescales that coexists with large-scale sleep-wake homeostasis.

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.

Power-law properties of nocturnal arrhythmia avalanches: A novel marker for incident cardiovascular events

BACKGROUND

Bursting nonsustained cardiac arrhythmia events are a common observation during sleep.

OBJECTIVES

The purpose of this study was to investigate the hypothesis that nocturnal arrhythmia episode durations could follow a power law, whose exponent could predict long-term clinical outcomes.

METHODS

We defined "nocturnal arrhythmia avalanche" (NAA) as any instance of a drop in electrocardiographic (ECG) template-matched R-R intervals ≥30% of R-R baseline, followed by a return to 90% of baseline. We studied NAA in ECG recordings obtained from the Sleep Heart Health Study (SHHS), Osteoporotic Fractures in Men Study (MrOS) Study, and Multi-Ethnic Study of Atherosclerosis (MESA). The association of nocturnal arrhythmia durations with a power-law distribution was evaluated and the association of derived power-law exponents (α) with major adverse cardiovascular (CV) events and mortality assessed with multivariable Cox regression.

RESULTS

A total of 9176 participants were studied. NAA episodes distribution was consistent with power-law vs comparator distributions in all datasets studied (positive log likelihood ratio of power-law vs exponential in MESA: 83%; SHHS: 69%; MrOS: 81%; power-law vs log-normal in MESA: 95%; SHHS: 35%; MrOS: 64%). The NAA power-law exponent (α) showed a significant association of with adverse CV outcomes (association with CV mortality: SHHS hazard ratio 1.39 [1.07-1.79], P = .012; MrOS hazard ratio 1.42 [1.02-1.94], P = .039; association with CV events: MESA HR 3.46 [1.46-8.21], P = .005) in multivariable Cox regression, after adjusting for conventional CV risk factors and nocturnal ectopic rate.

CONCLUSION

The NAA power-law exponent is a reproducible, predictive marker for incident CV events and mortality.

Critical dynamics in spontaneous EEG predict anesthetic-induced loss of consciousness and perturbational complexity

Consciousness has been proposed to be supported by electrophysiological patterns poised at criticality, a dynamical regime which exhibits adaptive computational properties, maximally complex patterns and divergent sensitivity to perturbation. Here, we investigate dynamical properties of the resting-state electroencephalogram (EEG) of healthy subjects undergoing general anesthesia with propofol, xenon or ketamine. Importantly, all participants were unresponsive under anesthesia, while consciousness was retained only during ketamine anesthesia (in the form of vivid dreams), enabling an experimental dissociation between unresponsiveness and unconsciousness. For each condition, we measure (i) avalanche criticality, (ii) chaoticity, and (iii) criticality-related metrics, revealing that states of unconsciousness are characterized by a distancing from both avalanche criticality and the edge of chaos. We then ask whether these same dynamical properties are predictive of the perturbational complexity index (PCI), a TMS-based measure that has shown remarkably high sensitivity in detecting consciousness independently of behavior. We successfully predict individual subjects' PCI values with considerably high accuracy from resting-state EEG dynamical properties alone. Our results establish a firm link between perturbational complexity and criticality, and provide further evidence that criticality is a necessary condition for the emergence of consciousness.

Temporal scaling theory for bursty time series with clusters of arbitrarily many events

Long-term temporal correlations in time series in a form of an event sequence have been characterized using an autocorrelation function that often shows a power-law decaying behavior. Such scaling behavior has been mainly accounted for by the heavy-tailed distribution of interevent times, i.e., the time interval between two consecutive events. Yet, little is known about how correlations between consecutive interevent times systematically affect the decaying behavior of the autocorrelation function. Empirical distributions of the burst size, which is the number of events in a cluster of events occurring in a short time window, often show heavy tails, implying that arbitrarily many consecutive interevent times may be correlated with each other. In the present study, we propose a model for generating a time series with arbitrary functional forms of interevent time and burst size distributions. Then, we analytically derive the autocorrelation function for the model time series. In particular, by assuming that the interevent time and burst size are power-law distributed, we derive scaling relations between power-law exponents of the autocorrelation function decay, interevent time distribution, and burst size distribution. These analytical results are confirmed by numerical simulations. Our approach helps to rigorously and analytically understand the effects of correlations between arbitrarily many consecutive interevent times on the decaying behavior of the autocorrelation function.

Self-organization toward 1/f noise in deep neural networks

In biological neural networks, it has been well recognized that a healthy brain exhibits 1/f noise patterns. However, in artificial neural networks that are increasingly matching or even out-performing human cognition, this phenomenon has yet to be established. In this work, we found that similar to that of their biological counterparts, 1/f noise exists in artificial neural networks when trained on time series classification tasks. Additionally, we found that the activations of the neurons are the closest to 1/f noise when the neurons are highly utilized. Conversely, if the network is too large and many neurons are underutilized, the neuron activations deviate from 1/f noise patterns toward that of white noise.

A General, Noise-Driven Mechanism for the 1/f-Like Behavior of Neural Field Spectra

Consistent observations across recording modalities, experiments, and neural systems find neural field spectra with 1/f-like scaling, eliciting many alternative theories to explain this universal phenomenon. We show that a general dynamical system with stochastic drive and minimal assumptions generates 1/f-like spectra consistent with the range of values observed in vivo without requiring a specific biological mechanism or collective critical behavior.

Emergence of power-law distributions in self-segregation reaction-diffusion processes

Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give rise to power-law distributions, where emergent patterns and structures become visible across vastly different scales. Recent observations reveal power-law distributions in the spatial organization of, e.g., tree clusters and forest patch sizes. Crucially, these patterns do not follow a spatially periodic order but rather a statistical one. Unlike the spatially periodic patterns elucidated by the Turing mechanism, the statistical order of these particular vegetation patterns suggests an incomplete understanding of the underlying mechanisms. Here, we present a self-segregation mechanism, driving the emergence of power-law scalings in pattern-forming systems. The model incorporates an Allee-logistic reaction term, responsible for the local growth, and a nonlinear diffusion process accounting for positive interactions and limited resources. According to a self-organized criticality (SOC) principle, after an initial decrease, the system mass reaches an analytically predictable threshold, beyond which it self-segregates into distinct clusters, due to local positive interactions that promote cooperation. Numerical investigations show that the distribution of cluster sizes obeys a power law with an exponential cutoff.

Observable Atrial and Ventricular Fibrillation Episode Durations Are Conformant With a Power Law Based on System Size and Spatial Synchronization

BACKGROUND

Atrial fibrillation (AF) and ventricular fibrillation (VF) episodes exhibit varying durations, with some spontaneously ending quickly while others persist. A quantitative framework to explain episode durations remains elusive. We hypothesized that observable self-terminating AF and VF episode lengths, whereby durations are known, would conform with a power law based on the ratio of system size and correlation length ([Formula: see text].

METHODS

Using data from computer simulations (2-dimensional sheet and 3-dimensional left-atrial), human ischemic VF recordings (256-electrode sock, n=12 patients), and human AF recordings (64-electrode basket-catheter, n=9 patients; 16-electrode high definition-grid catheter, n=42 patients), conformance with a power law was assessed using the Akaike information criterion, Bayesian information criterion, coefficient of determination (R2, significance=P<0.05) and maximum likelihood estimation. We analyzed fibrillatory episode durations and [Formula: see text], computed by taking the ratio between system size ([Formula: see text], chamber/simulation size) and correlation length (xi, estimated from pairwise correlation coefficients over electrode/node distance).

RESULTS

In all computer models, the relationship between episode durations and [Formula: see text] was conformant with a power law (Aliev-Panfilov R2: 0.90, P<0.001; Courtemanche R2: 0.91, P<0.001; Luo-Rudy R2: 0.61, P<0.001). Observable clinical AF/VF durations were also conformant with a power law relationship (VF R2: 0.86, P<0.001; AF basket R2: 0.91, P<0.001; AF grid R2: 0.92, P<0.001). [Formula: see text] also differentiated between self-terminating and sustained episodes of AF and VF (P<0.001; all systems), as well as paroxysmal versus persistent AF (P<0.001). In comparison, other electrogram metrics showed no statistically significant differences (dominant frequency, Shannon Entropy, mean voltage, peak-peak voltage; P>0.05).

CONCLUSIONS

Observable fibrillation episode durations are conformant with a power law based on system size and correlation length.

Explanation of flicker noise with the Bak-Tang-Wiesenfeld model of self-organized criticality

With the original Bak-Tang-Wisenefeld (BTW) sandpile we uncover the 1/φ noise in the mechanism maintaining self-organized criticality (SOC)-the question raised together with the concept of SOC. The BTW sandpile and the phenomenon of SOC in general are built on the slow time scale at which the system is loaded and the fast time scale at which the stress is transported outward from overloaded locations. Exploring the dynamics of stress in the slow time in the BTW sandpile, we posit that it follows cycles of gradual stress accumulation that end up with an abrupt stress release and the drop of the system to subcritical state. As the system size grows, the intracycle dynamics exhibits the 1/φ-like spectrum that extends boundlessly and corresponds to the stress release within the critical state.

Q factor: A measure of competition between the topper and the average in percolation and in self-organized criticality

We define the Q factor in the percolation problem as the quotient of the size of the largest cluster and the average size of all clusters. As the occupation probability p is increased, the Q factor for the system size L grows systematically to its maximum value Q_{max}(L) at a specific value p_{max}(L) and then gradually decays. Our numerical study of site percolation problems on the square, triangular, and simple cubic lattices exhibits that the asymptotic values of p_{max}, though close, are distinct from the corresponding percolation thresholds of these lattices. We also show, using scaling analysis, that at p_{max} the value of Q_{max}(L) diverges as L^{d} (d denoting the dimension of the lattice) as the system size approaches its asymptotic limit. We further extend this idea to nonequilibrium systems such as the sandpile model of self-organized criticality. Here the Q(ρ,L) factor is the quotient of the size of the largest avalanche and the cumulative average of the sizes of all the avalanches, with ρ the drop density of the driving mechanism. This study was prompted by some observations in sociophysics.

Yielding Is an Absorbing Phase Transition with Vanishing Critical Fluctuations

The yielding transition in athermal complex fluids can be interpreted as an absorbing phase transition between an elastic, absorbing state with high mesoscopic degeneracy and a flowing, active state. We characterize quantitatively this phase transition in an elastoplastic model under fixed applied shear stress, using a finite-size scaling analysis. We find vanishing critical fluctuations of the order parameter (i.e., the shear rate), and relate this property to the convex character of the phase transition (β>1). We locate yielding within a family of models akin to fixed-energy sandpile (FES) models, only with long-range redistribution kernels with zero modes that result from mechanical equilibrium. For redistribution kernels with sufficiently fast decay, this family of models belongs to a short-range universality class distinct from the conserved directed percolation class of usual FES, which is induced by zero modes.

Neuronal avalanches in temporal lobe epilepsy as a noninvasive diagnostic tool investigating large scale brain dynamics

The epilepsy diagnosis still represents a complex process, with misdiagnosis reaching 40%. We aimed at building an automatable workflow, helping the clinicians in the diagnosis of temporal lobe epilepsy (TLE). We hypothesized that neuronal avalanches (NA) represent a feature better encapsulating the rich brain dynamics compared to classically used functional connectivity measures (Imaginary Coherence; ImCoh). We analyzed large-scale activation bursts (NA) from source estimation of resting-state electroencephalography. Using a support vector machine, we reached a classification accuracy of TLE versus controls of 0.86 ± 0.08 (SD) and an area under the curve of 0.93 ± 0.07. The use of NA features increase by around 16% the accuracy of diagnosis prediction compared to ImCoh. Classification accuracy increased with larger signal duration, reaching a plateau at 5 min of recording. To summarize, NA represents an interpretable feature for an automated epilepsy identification, being related with intrinsic neuronal timescales of pathology-relevant regions.

True random number generation using the spin crossover in LaCoO3

While digital computers rely on software-generated pseudo-random number generators, hardware-based true random number generators (TRNGs), which employ the natural physics of the underlying hardware, provide true stochasticity, and power and area efficiency. Research into TRNGs has extensively relied on the unpredictability in phase transitions, but such phase transitions are difficult to control given their often abrupt and narrow parameter ranges (e.g., occurring in a small temperature window). Here we demonstrate a TRNG based on self-oscillations in LaCoO3 that is electrically biased within its spin crossover regime. The LaCoO3 TRNG passes all standard tests of true stochasticity and uses only half the number of components compared to prior TRNGs. Assisted by phase field modeling, we show how spin crossovers are fundamentally better in producing true stochasticity compared to traditional phase transitions. As a validation, by probabilistically solving the NP-hard max-cut problem in a memristor crossbar array using our TRNG as a source of the required stochasticity, we demonstrate solution quality exceeding that using software-generated randomness.

Selectively advantageous instability in biotic and pre-biotic systems and implications for evolution and aging

Rules of biology typically involve conservation of resources. For example, common patterns such as hexagons and logarithmic spirals require minimal materials, and scaling laws involve conservation of energy. Here a relationship with the opposite theme is discussed, which is the selectively advantageous instability (SAI) of one or more components of a replicating system, such as the cell. By increasing the complexity of the system, SAI can have benefits in addition to the generation of energy or the mobilization of building blocks. SAI involves a potential cost to the replicating system for the materials and/or energy required to create the unstable component, and in some cases, the energy required for its active degradation. SAI is well-studied in cells. Short-lived transcription and signaling factors enable a rapid response to a changing environment, and turnover is critical for replacement of damaged macromolecules. The minimal gene set for a viable cell includes proteases and a nuclease, suggesting SAI is essential for life. SAI promotes genetic diversity in several ways. Toxin/antitoxin systems promote maintenance of genes, and SAI of mitochondria facilitates uniparental transmission. By creating two distinct states, subject to different selective pressures, SAI can maintain genetic diversity. SAI of components of synthetic replicators favors replicator cycling, promoting emergence of replicators with increased complexity. Both classical and recent computer modeling of replicators reveals SAI. SAI may be involved at additional levels of biological organization. In summary, SAI promotes replicator genetic diversity and reproductive fitness, and may promote aging through loss of resources and maintenance of deleterious alleles.

Anomalous dynamics of a passive droplet in active turbulence

Motion of a passive deformable object in an active environment serves as a representative of both in-vivo systems such as intracellular particle motion in Acanthamoeba castellanii, or in-vitro systems such as suspension of beads inside dense swarms of Escherichia coli. Theoretical modeling of such systems is challenging due to the requirement of well resolved hydrodynamics which can explore the spatiotemporal correlations around the suspended passive object in the active fluid. We address this critical lack of understanding using coupled hydrodynamic equations for nematic liquid crystals with finite active stress to model the active bath, and a suspended nematic droplet with zero activity. The droplet undergoes deformation fluctuations and its movement shows periods of "runs" and "stays". At relatively low interfacial tension, the droplet begins to break and mix with the outer active bath. We establish that the motion of the droplet is influenced by the interplay of spatial correlations of the flow and the size of the droplet. The mean square displacement shows a transition from ballistic to normal diffusion which depends on the droplet size. We discuss this transition in relation to spatiotemporal scales associated with velocity correlations of the active bath and the droplet.

Optimal input reverberation and homeostatic self-organization toward the edge of synchronization

Transient or partial synchronization can be used to do computations, although a fully synchronized network is sometimes related to the onset of epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal network at the edge of a synchronization transition, thereby avoiding the harmful consequences of a fully synchronized network. We model neurons by maps since they are dynamically richer than integrate-and-fire models and more computationally efficient than conductance-based approaches. We first describe the synchronization phase transition of a dense network of neurons with different tonic spiking frequencies coupled by gap junctions. We show that at the transition critical point, inputs optimally reverberate through the network activity through transient synchronization. Then, we introduce a local homeostatic dynamic in the synaptic coupling and show that it produces a robust self-organization toward the edge of this phase transition. We discuss the potential biological consequences of this self-organization process, such as its relation to the Brain Criticality hypothesis, its input processing capacity, and how its malfunction could lead to pathological synchronization and the onset of seizure-like activity.

Postural control in gymnasts: anisotropic fractal scaling reveals proprioceptive reintegration in vestibular perturbation

Dexterous postural control subtly complements movement variability with sensory correlations at many scales. The expressive poise of gymnasts exemplifies this lyrical punctuation of release with constraint, from coarse grain to fine scales. Dexterous postural control upon a 2D support surface might collapse the variation of center of pressure (CoP) to a relatively 1D orientation-a direction often oriented towards the focal point of a visual task. Sensory corrections in dexterous postural control might manifest in temporal correlations, specifically as fractional Brownian motions whose differences are more and less correlated with fractional Gaussian noises (fGns) with progressively larger and smaller Hurst exponent H. Traditional empirical work examines this arrangement of lower-dimensional compression of CoP along two orthogonal axes, anteroposterior (AP) and mediolateral (ML). Eyes-open and face-forward orientations cultivate greater variability along AP than ML axes, and the orthogonal distribution of spatial variability has so far gone hand in hand with an orthogonal distribution of H, for example, larger in AP and lower in ML. However, perturbing the orientation of task focus might destabilize the postural synergy away from its 1D distribution and homogenize the temporal correlations across the 2D support surface, resulting in narrower angles between the directions of the largest and smallest H. We used oriented fractal scaling component analysis (OFSCA) to investigate whether sensory corrections in postural control might thus become suborthogonal. OFSCA models raw 2D CoP trajectory by decomposing it in all directions along the 2D support surface and fits the directions with the largest and smallest H. We studied a sample of gymnasts in eyes-open and face-forward quiet posture, and results from OFSCA confirm that such posture exhibits the classic orthogonal distribution of temporal correlations. Head-turning resulted in a simultaneous decrease in this angle Δθ, which promptly reversed once gymnasts reoriented their heads forward. However, when vision was absent, there was only a discernible negative trend in Δθ, indicating a shift in the angle's direction but not a statistically significant one. Thus, the narrowing of Δθ may signify an adaptive strategy in postural control. The swift recovery of Δθ upon returning to a forward-facing posture suggests that the temporary reduction is specific to head-turning and does not impose a lasting burden on postural control. Turning the head reduced the angle between these two orientations, facilitating the release of postural degrees of freedom towards a more uniform spread of the CoP across both dimensions of the support surface. The innovative aspect of this work is that it shows how fractality might serve as a control parameter of adaptive mechanisms of dexterous postural control.

Evidence of scale-free clusters of vegetation in tropical rainforests

Tropical rainforests exhibit a rich repertoire of spatial patterns emerging from the intricate relationship between the microscopic interaction between species. In particular, the distribution of vegetation clusters can shed much light on the underlying process that regulates the ecosystem. Analyzing the distribution of vegetation clusters at different resolution scales, we show the first robust evidence of scale-invariant clusters of vegetation, suggesting the coexistence of multiple intertwined scales in the collective dynamics of tropical rainforests. We use field data and computational simulations to confirm our hypothesis, proposing a predictor that could be particularly interesting to monitor the ecological resilience of the world's "green lungs."

Eigen microstates in self-organized criticality

We employ the eigen microstates approach to explore the self-organized criticality (SOC) in two celebrated sandpile models, namely the BTW model and the Manna model. In both models, phase transitions from the absorbing state to the critical state can be understood by the emergence of dominant eigen microstates with significantly increased weights. Spatial eigen microstates of avalanches can be uniformly characterized by a linear system size rescaling. The first temporal eigen microstates reveal scaling relations in both models. Furthermore, by finite-size scaling analysis of the first eigen microstates, we numerically estimate critical exponents, i.e., sqrt[σ_{0}w_{1}]/v[over ̃]_{1}∝L^{D} and v[over ̃]_{1}∝L^{D(1-τ_{s})/2}. Our findings could provide profound insights into eigen microstates of the universality and phase transition in nonequilibrium complex systems governed by self-organized criticality.

Noise-induced excitation wave and its size distribution in coupled FitzHugh-Nagumo equations on a square lattice

There are various research topics such as stochastic resonance, coherent resonance, and neuroavalanche in excitable systems under external noises. We perform numerical simulation of coupled noisy FitzHugh-Nagumo equations on the square lattice. Excitation waves are generated most efficiently at an intermediate noise strength. The cluster size distributions obey a power-law-like distribution at a certain parameter range. However, we consider that this is not a self-organized critical phenomenon, partly because the exponent of the power law is not constant. We have studied the propagation of excitation waves in the coupled noisy FitzHugh-Nagumo equations with a one-dimensional pacemaker region and found that there is a phase-transition-like phenomenon from the short-range propagation to the whole-system propagation by changing the noise strength T. The power-law distribution is observed most clearly near the phase transition of the propagation of excitation waves in the coupled noisy FitzHugh-Nagumo equations without the one-dimensional pacemaker.

Scattering spectra models for physics

Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a pointwise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multiscale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to fourth order. The scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.

Robustness of the emergence of synchronized clusters in branching hierarchical systems under parametric noise

The dynamical robustness of networks in the presence of noise is of utmost fundamental and applied interest. In this work, we explore the effect of parametric noise on the emergence of synchronized clusters in diffusively coupled Chaté-Manneville maps on a branching hierarchical structure. We consider both quenched and dynamically varying parametric noise. We find that the transition to a synchronized fixed point on the maximal cluster is robust in the presence of both types of noise. We see that the small sub-maximal clusters of the system, which coexist with the maximal cluster, exhibit a power-law cluster size distribution. This power-law scaling of synchronized cluster sizes is robust against noise in a broad range of coupling strengths. However, interestingly, we find a window of coupling strength where the system displays markedly different sensitivities to noise for the maximal cluster and the small clusters, with the scaling exponent for the cluster distribution for small clusters exhibiting clear dependence on noise strength, while the cluster size of the maximal cluster of the system displays no significant change in the presence of noise. Our results have implications for the observability of synchronized cluster distributions in real-world hierarchical networks, such as neural networks, power grids, and communication networks, that necessarily have parametric fluctuations.

Turbulence spreading by resonant wave-wave interactions: A fractional kinetics approach

This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and witnessed a renewed attention in the literature recently. Here, we propose a comprehensive theory of turbulence spreading based on fractional kinetics. We argue that the use of fractional-derivative equations permits a general approach focusing on fundamentals of the spreading process regardless of a specific turbulence model and/or specific instability type. The starting point is the Hamiltonian of resonant wave-wave interactions, from which a family of scaling laws for the asymptotic spreading is derived. Both three- and four-wave interactions are considered. The results span from a subdiffusive spreading in the parameter range of weak chaos to avalanche propagation in regimes with population inversion. Attention is paid to how nonergodicity introduces weak mixing, memory and intermittency into spreading dynamics, and how the properties of non-Markovianity and nonlocality emerge from the presence of islands of regular dynamics in phase space. Also we resolve an existing question concerning turbulence spillover into gap regions, where the instability growth is locally suppressed, and show that the spillover occurs through exponential (Anderson-like) localization in case of four-wave interactions and through an algebraic (weak) localization in case of triad interactions. In the latter case an inverse-cubic behavior of the spillover function is found. Wherever relevant, we contrast our findings against the available observational and numerical evidence, and we also commit ourselves to establish connections with the models of turbulence spreading proposed previously.

Criticality in the fracture of silica glass: Insights from molecular mechanics

The universality of avalanches characterizing the inelastic response of disordered materials has the potential to bridge the gap from micro to macroscale. In this study, we explore the statistics and the scaling behavior of avalanches occurring during the fracture process in silica glass using molecular mechanics. We introduce a robust method for capturing and quantifying these avalanches, allowing us to perform rigorous statistical analyses, revealing universal power laws associated with critical phenomena. The influence of an initial crack is explored, observing deviations from mean-field predictions while maintaining the property of criticality. However, the avalanche exponents in the unnotched samples are predicted correctly by the mean-field depinning model. Furthermore, we investigate the strain-dependent probability density function, its cutoff function, and the interrelation between the critical exponents. Finally, we unveil distinct scaling behavior for small and large avalanches of the crack growth, shedding light on the underlying fracture mechanisms in silica glass.

Precision-controlled ultrafast electron microscope platforms. A case study: Multiple-order coherent phonon dynamics in 1T-TaSe2 probed at 50 fs-10 fm scales

We report on the first detailed beam tests attesting the fundamental principle behind the development of high-current-efficiency ultrafast electron microscope systems where a radio frequency (RF) cavity is incorporated as a condenser lens in the beam delivery system. To allow for the experiment to be carried out with a sufficient resolution to probe the performance at the emittance floor, a new cascade loop RF controller system is developed to reduce the RF noise floor. Temporal resolution at 50 fs in full-width-at-half-maximum and detection sensitivity better than 1% are demonstrated on exfoliated 1T-TaSe2 system under a moderate repetition rate. To benchmark the performance, multi-terahertz edge-mode coherent phonon excitation is employed as the standard candle. The high temporal resolution and the significant visibility to very low dynamical contrast in diffraction signals via high-precision phase-space manipulation give strong support to the working principle for the new high-brightness femtosecond electron microscope systems.

Dissecting muscle synergies in the task space

The muscle synergy is a guiding concept in motor control research that relies on the general notion of muscles 'working together' towards task performance. However, although the synergy concept has provided valuable insights into motor coordination, muscle interactions have not been fully characterised with respect to task performance. Here, we address this research gap by proposing a novel perspective to the muscle synergy that assigns specific functional roles to muscle couplings by characterising their task-relevance. Our novel perspective provides nuance to the muscle synergy concept, demonstrating how muscular interactions can 'work together' in different ways: (1) irrespective of the task at hand but also (2) redundantly or (3) complementarily towards common task-goals. To establish this perspective, we leverage information- and network-theory and dimensionality reduction methods to include discrete and continuous task parameters directly during muscle synergy extraction. Specifically, we introduce co-information as a measure of the task-relevance of muscle interactions and use it to categorise such interactions as task-irrelevant (present across tasks), redundant (shared task information), or synergistic (different task information). To demonstrate these types of interactions in real data, we firstly apply the framework in a simple way, revealing its added functional and physiological relevance with respect to current approaches. We then apply the framework to large-scale datasets and extract generalizable and scale-invariant representations consisting of subnetworks of synchronised muscle couplings and distinct temporal patterns. The representations effectively capture the functional interplay between task end-goals and biomechanical affordances and the concurrent processing of functionally similar and complementary task information. The proposed framework unifies the capabilities of current approaches in capturing distinct motor features while providing novel insights and research opportunities through a nuanced perspective to the muscle synergy.

A neurophysiological basis for aperiodic EEG and the background spectral trend

Electroencephalograms (EEGs) display a mixture of rhythmic and broadband fluctuations, the latter manifesting as an apparent 1/f spectral trend. While network oscillations are known to generate rhythmic EEG, the neural basis of broadband EEG remains unexplained. Here, we use biophysical modelling to show that aperiodic neural activity can generate detectable scalp potentials and shape broadband EEG features, but that these aperiodic signals do not significantly perturb brain rhythm quantification. Further model analysis demonstrated that rhythmic EEG signals are profoundly corrupted by shifts in synapse properties. To examine this scenario, we recorded EEGs of human subjects being administered propofol, a general anesthetic and GABA receptor agonist. Drug administration caused broadband EEG changes that quantitatively matched propofol's known effects on GABA receptors. We used our model to correct for these confounding broadband changes, which revealed that delta power, uniquely, increased within seconds of individuals losing consciousness. Altogether, this work details how EEG signals are shaped by neurophysiological factors other than brain rhythms and elucidates how these signals can undermine traditional EEG interpretation.

Probing long-lived radioactive isotopes on the double-logarithmic Segrè chart

Isotopes have been widely applied in a variety of scientific subjects; many aspects of isotopes, however, remain not well understood. In this study, I investigate the relation between the number of neutrons (N) and the number of protons (Z) in stable isotopes of non-radioactive elements and long-lived isotopes of radioactive elements at the double-linear scale (conventional Segrè chart) and the double-logarithmic scale. Statistical analyses show that N is a power-law function of Z for these isotopes: N = 0.73 × Z 1.16. This power-law relation provides better predictions for the numbers of neutrons in stable isotopes of non-radioactive elements and long-lived isotopes of radioactive elements than the linear relation on the conventional Segrè chart. The power-law pattern reveled here offers empirical guidance for probing long-lived isotopes of unknown radioactive elements.

Self-Organized Evolution of the Internal Transport Barrier in Ion-Temperature-Gradient Driven Gyrokinetic Turbulence

Understanding the self-organization of the most promising internal transport barrier in fusion plasmas needs a long-time nonlinear gyrokinetic global simulation. The neighboring equilibrium update method is proposed, which solves the secularity problem in a perturbative simulation and speeds up the numerical computation by more than 10 times. It is found that the internal transport barrier emerges at the magnetic axis due to inward propagated turbulence avalanche, and its outward expansion is the catastrophe of self-organized structure induced by outward propagated avalanche.

Coalescence of limit cycles in the presence of noise

Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional point. Here we ask how dynamics in the vicinity of such a bifurcation are influenced by noise. A pitchfork bifurcation can be used to induce bifurcation behavior. We model a limit cycle with the normal form of the Hopf oscillator, couple it to the pitchfork, and investigate the resulting dynamical system in the presence of noise. We show that the generating functional for the averages of the dynamical variables factorizes between the pitchfork and the oscillator. The statistical properties of the pitchfork in the presence of noise in its various regimes are investigated and a scaling theory is developed for the correlation and response functions, including a possible symmetry-breaking field. The analysis is done by perturbative calculations as well as numerical means. Finally, observables illustrating the coupling of a system with a limit cycle to a pitchfork are discussed and the phase-phase correlations are shown to exhibit nondiffusive behavior with universal scaling.

Resting-state fractal brain connectivity is associated with impaired cognitive performance in healthy aging

Aging affects cognitive functions even in the absence of ongoing pathologies. The neurophysiological basis of age-related cognitive decline (CD), however, is not completely understood. Alterations in both functional brain connectivity and in the fractal scaling of neuronal dynamics have been linked to aging and cognitive performance. Recently, fractal connectivity (FrC) has been proposed - combining the two concepts - for capturing long-term interactions among brain regions. FrC was shown to be influenced by increased mental workload; however, no prior studies investigated how resting-state FrC relates to cognitive performance and plausible CD in healthy aging. We recruited 19 healthy elderly (HE) and 24 young control (YC) participants, who underwent resting-state electroencephalography (EEG) measurements and comprehensive cognitive evaluation using 7 tests of the Cambridge Neurophysiological Test Automated Battery. FrC networks were reconstructed from EEG data using the recently introduced multiple-resampling cross-spectral analysis (MRCSA). Elderly individuals could be characterized with increased response latency and reduced performance in 4-4 tasks, respectively, with both reaction time and accuracy being affected in two tasks. Auto- and cross-spectral exponents - characterizing regional fractal dynamics and FrC, respectively, - were found reduced in HE when compared to YC over most of the cortex. Additionally, fractal scaling of frontoparietal connections expressed an inverse relationship with task performance in visual memory and sustained attention domains in elderly, but not in young individuals. Our results confirm that the fractal nature of brain connectivity - as captured by MRCSA - is affected in healthy aging. Furthermore, FrC appears as a sensitive neurophysiological marker of age-related CD.

Excitation-Inhibition Balance, Neural Criticality, and Activities in Neuronal Circuits

Neural activities in local circuits exhibit complex and multilevel dynamic features. Individual neurons spike irregularly, which is believed to originate from receiving balanced amounts of excitatory and inhibitory inputs, known as the excitation-inhibition balance. The spatial-temporal cascades of clustered neuronal spikes occur in variable sizes and durations, manifested as neural avalanches with scale-free features. These may be explained by the neural criticality hypothesis, which posits that neural systems operate around the transition between distinct dynamic states. Here, we summarize the experimental evidence for and the underlying theory of excitation-inhibition balance and neural criticality. Furthermore, we review recent studies of excitatory-inhibitory networks with synaptic kinetics as a simple solution to reconcile these two apparently distinct theories in a single circuit model. This provides a more unified understanding of multilevel neural activities in local circuits, from spontaneous to stimulus-response dynamics.

Long Timescales, Individual Differences, and Scale Invariance in Animal Behavior

The explosion of data on animal behavior in more natural contexts highlights the fact that these behaviors exhibit correlations across many timescales. However, there are major challenges in analyzing these data: records of behavior in single animals have fewer independent samples than one might expect. In pooling data from multiple animals, individual differences can mimic long-ranged temporal correlations; conversely, long-ranged correlations can lead to an overestimate of individual differences. We suggest an analysis scheme that addresses these problems directly, apply this approach to data on the spontaneous behavior of walking flies, and find evidence for scale-invariant correlations over nearly three decades in time, from seconds to one hour. Three different measures of correlation are consistent with a single underlying scaling field of dimension Δ=0.180±0.005.

Investigating the Emergence of Collective States Within Rugby Sevens Gameplay

Rugby sevens is a small-sided variant of rugby union characterised by fast-moving, high-intensity gameplay and is an example of a team invasion sport, where players work together to achieve a shared goal of attacking and defending as a cohesive unit. The dynamics of such sports can be viewed as self-organizing systems, where individual players form collective patterns without a centralized mechanism of control. Inspired by the analysis of collective movement in animals, this novel study investigates the emergent patterns of order and disorder in sub-elite female rugby sevens using order parameters (typically used to analyse particle systems) to characterize the team's collective state during different phases of play. The findings demonstrate that defensive gameplay is more ordered, with more compact formations, compared to attacking play, and there is a correlation between alignment/order in player motion and group speed. The work further suggests that the collective states formed differ between sequences of play with different levels of ground gained by the attacking team. These observations provide a sound justification for player training with a focus on cohesive defensive movements to resist disruptions from opposing attackers, while employing attacking tactics that disrupt the cohesion and order of opposing teams.

Measuring neuronal avalanches to inform brain-computer interfaces

Large-scale interactions among multiple brain regions manifest as bursts of activations called neuronal avalanches, which reconfigure according to the task at hand and, hence, might constitute natural candidates to design brain-computer interfaces (BCIs). To test this hypothesis, we used source-reconstructed magneto/electroencephalography during resting state and a motor imagery task performed within a BCI protocol. To track the probability that an avalanche would spread across any two regions, we built an avalanche transition matrix (ATM) and demonstrated that the edges whose transition probabilities significantly differed between conditions hinged selectively on premotor regions in all subjects. Furthermore, we showed that the topology of the ATMs allows task-decoding above the current gold standard. Hence, our results suggest that neuronal avalanches might capture interpretable differences between tasks that can be used to inform brain-computer interfaces.

Tenets and Methods of Fractal Analysis (1/f Noise)

This chapter deals with the methodical challenges confronting researchers of the fractal phenomenon known as pink or 1/f noise. This chapter introduces concepts and statistical techniques for identifying fractal patterns in empirical time series. It defines some basic statistical terms, describes two essential characteristics of pink noise (self-similarity and long memory), and outlines four parameters representing the theoretical properties of fractal processes: the Hurst coefficient (H), the scaling exponent (α), the power exponent (β), and the fractional differencing parameter (d) of the ARFIMA (autoregressive fractionally integrated moving average) method. Then, it compares and evaluates different approaches to estimating fractal parameters from observed data and outlines the advantages, disadvantages, and constraints of some popular estimators. The final section of this chapter answers the questions: Which strategy is appropriate for the identification of fractal noise in empirical settings and how can it be applied to the data?

From Cell States to Cell Fates: Control of Cell State Transitions

We examine the coordinated behavior of thousands of genes in cell fate transitions through genome expression as an integrated dynamical system using the concepts of self-organized criticality and coherent stochastic behavior. To quantify the effects of the collective behavior of genes, we adopted the flux balance approach and developed it in a new tool termed expression flux analysis (EFA). Here we describe this tool and demonstrate how its application to specific experimental genome-wide expression data provides new insights into the dynamics of the cell-fate transitions. Particularly, we show that in cell fate change, specific stochastic perturbations can spread over the entire system to guide distinct cell fate transitions through switching cyclic flux flow in the genome engine. Utilization of EFA enables us to elucidate a unified genomic mechanism for when and how cell-fate change occurs through critical transitions.

Altered spread of waves of activities at large scale is influenced by cortical thickness organization in temporal lobe epilepsy: a magnetic resonance imaging-high-density electroencephalography study

Temporal lobe epilepsy is a brain network disorder characterized by alterations at both the structural and the functional levels. It remains unclear how structure and function are related and whether this has any clinical relevance. In the present work, we adopted a novel methodological approach investigating how network structural features influence the large-scale dynamics. The functional network was defined by the spatio-temporal spreading of aperiodic bursts of activations (neuronal avalanches), as observed utilizing high-density electroencephalography in patients with temporal lobe epilepsy. The structural network was modelled as the region-based thickness covariance. Loosely speaking, we quantified the similarity of the cortical thickness of any two brain regions, both across groups and at the individual level, the latter utilizing a novel approach to define the subject-wise structural covariance network. In order to compare the structural and functional networks (at the nodal level), we studied the correlation between the probability that a wave of activity would propagate from a source to a target region and the similarity of the source region thickness as compared with other target brain regions. Building on the recent evidence that large-waves of activities pathologically spread through the epileptogenic network in temporal lobe epilepsy, also during resting state, we hypothesize that the structural cortical organization might influence such altered spatio-temporal dynamics. We observed a stable cluster of structure-function correlation in the bilateral limbic areas across subjects, highlighting group-specific features for left, right and bilateral temporal epilepsy. The involvement of contralateral areas was observed in unilateral temporal lobe epilepsy. We showed that in temporal lobe epilepsy, alterations of structural and functional networks pair in the regions where seizures propagate and are linked to disease severity. In this study, we leveraged on a well-defined model of neurological disease and pushed forward personalization approaches potentially useful in clinical practice. Finally, the methods developed here could be exploited to investigate the relationship between structure-function networks at subject level in other neurological conditions.

The prediction of dynamical quantities in granular avalanches based on graph neural networks

The study of granular avalanches in rotating drums is not only essential to understanding various complex behaviors of interest in granular media from a scientific perspective; it also has valuable applications in regard to industrial processes and geological catastrophes. Despite decades of research studies on avalanches, a proper understanding of their dynamic properties still remains a great challenge to scientists due to a lack of state-of-the-art techniques. In this study, we accurately predict the avalanche dynamic features of three-dimensional granular materials in rotating drums, by using graph neural networks on the basis of their initial static microstructures alone. We find that our method is robust to changes in various model parameters, such as the interaction potential, size polydispersity, and noise in particle coordinates. In addition, with the grain-scale velocities obtained either from our network or from numerical simulations, we find an approximately equal and strong correlation between the global velocity and global velocity fluctuation in our 3D granular avalanche systems, which further demonstrates the predictive power of our trained graph neural networks to uncover the fundamental physics of granular avalanches. We expect our method to provide more insight into the avalanche dynamics of granular materials and other amorphous systems in the future.

Multilevel and multifaceted brain response features in spiking, ERP and ERD: experimental observation and simultaneous generation in a neuronal network model with excitation-inhibition balance

Brain as a dynamic system responds to stimulations with specific patterns affected by its inherent ongoing dynamics. The patterns are manifested across different levels of organization-from spiking activity of neurons to collective oscillations in local field potential (LFP) and electroencephalogram (EEG). The multilevel and multifaceted response activities show patterns seemingly distinct and non-comparable from each other, but they should be coherently related because they are generated from the same underlying neural dynamic system. A coherent understanding of the interrelationships between different levels/aspects of activity features is important for understanding the complex brain functions. Here, based on analysis of data from human EEG, monkey LFP and neuronal spiking, we demonstrated that the brain response activities from different levels of neural system are highly coherent: the external stimulus simultaneously generated event-related potentials, event-related desynchronization, and variation in neuronal spiking activities that precisely match with each other in the temporal unfolding. Based on a biologically plausible but generic network of conductance-based integrate-and-fire excitatory and inhibitory neurons with dense connections, we showed that the multiple key features can be simultaneously produced at critical dynamical regimes supported by excitation-inhibition (E-I) balance. The elucidation of the inherent coherency of various neural response activities and demonstration of a simple dynamical neural circuit system having the ability to simultaneously produce multiple features suggest the plausibility of understanding high-level brain function and cognition from elementary and generic neuronal dynamics.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09889-w.

Correlated noise and critical dimensions

In equilibrium, the Mermin-Wagner theorem prohibits the continuous symmetry breaking for all dimensions d≤2. In this work, we discuss that this limitation can be circumvented in nonequilibrium systems driven by the spatiotemporally long-range anticorrelated noise. We first compute the lower and upper critical dimensions of the O(n) model driven by the spatiotemporally correlated noise by means of the dimensional analysis. Next we consider the spherical model, which corresponds to the large-n limit of the O(n) model and allows us to compute the critical dimensions and critical exponents, analytically. Both results suggest that the critical dimensions increase when the noise is positively correlated in space and time and decrease when anticorrelated. We also report that the spherical model with the correlated noise shows the hyperuniformity and giant number fluctuation even well above the critical point.