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

Spatiotemporal phase slip patterns for visual evoked potentials, covert object naming tasks, and insight moments extracted from 256 channel EEG recordings

Phase slips arise from state transitions of the coordinated activity of cortical neurons which can be extracted from the EEG data. The phase slip rates (PSRs) were studied from the high-density (256 channel) EEG data, sampled at 16.384 kHz, of five adult subjects during covert visual object naming tasks. Artifact-free data from 29 trials were averaged for each subject. The analysis was performed to look for phase slips in the theta (4-7 Hz), alpha (7-12 Hz), beta (12-30 Hz), and low gamma (30-49 Hz) bands. The phase was calculated with the Hilbert transform, then unwrapped and detrended to look for phase slip rates in a 1.0 ms wide stepping window with a step size of 0.06 ms. The spatiotemporal plots of the PSRs were made by using a montage layout of 256 equidistant electrode positions. The spatiotemporal profiles of EEG and PSRs during the stimulus and the first second of the post-stimulus period were examined in detail to study the visual evoked potentials and different stages of visual object recognition in the visual, language, and memory areas. It was found that the activity areas of PSRs were different as compared with EEG activity areas during the stimulus and post-stimulus periods. Different stages of the insight moments during the covert object naming tasks were examined from PSRs and it was found to be about 512 ± 21 ms for the 'Eureka' moment. Overall, these results indicate that information about the cortical phase transitions can be derived from the measured EEG data and can be used in a complementary fashion to study the cognitive behavior of the brain.

Slope of the power spectral density flattens at low frequencies (<150 Hz) with healthy aging but also steepens at higher frequency (>200 Hz) in human electroencephalogram

The power spectral density (PSD) of the brain signals is characterized by two distinct features: oscillations, which are represented as distinct "bumps," and broadband aperiodic activity, that reduces in power with increasing frequency and is characterized by the slope of the power falloff. Recent studies have shown a change in the slope of the aperiodic activity with healthy aging and mental disorders. However, these studies analyzed slopes over a limited frequency range (<100 Hz). To test whether the PSD slope is affected over a wider frequency range with aging and mental disorder, we analyzed the slope till 800 Hz in electroencephalogram data recorded from elderly subjects (>49 years) who were healthy (n = 217) or had mild cognitive impairment (MCI; n = 11) or Alzheimer's Disease (AD; n = 5). Although the slope reduced up to ~ 150 Hz with healthy aging (as shown previously), surprisingly, at higher frequencies (>200 Hz), it increased with age. These results were observed in all electrodes, for both eyes open and eyes closed conditions, and for different reference schemes. However, slopes were not significantly different in MCI/AD subjects compared with healthy controls. Overall, our results constrain the biophysical mechanisms that are reflected in the PSD slopes in healthy and pathological aging.

Sensory-Processing Sensitivity Is Associated with Increased Neural Entropy

BACKGROUND

This study aimed at answering the following research questions: (1) Does the self-reported level of sensory-processing sensitivity (SPS) correlate with complexity, or criticality features of the electroencephalogram (EEG)? (2) Are there significant EEG differences comparing individuals with high and low levels of SPS?

METHODS

One hundred fifteen participants were measured with 64-channel EEG during a task-free resting state. The data were analyzed using criticality theory tools (detrended fluctuation analysis, neuronal avalanche analysis) and complexity measures (sample entropy, Higuchi's fractal dimension). Correlations with the 'Highly Sensitive Person Scale' (HSPS-G) scores were determined. Then, the cohort's lowest and the highest 30% were contrasted as opposites. EEG features were compared between the two groups by applying a Wilcoxon signed-rank test.

RESULTS

During resting with eyes open, HSPS-G scores correlated significantly positively with the sample entropy and Higuchi's fractal dimension (Spearman's ρ = 0.22, p < 0.05). The highly sensitive group revealed higher sample entropy values (1.83 ± 0.10 vs. 1.77 ± 0.13, p = 0.031). The increased sample entropy in the highly sensitive group was most pronounced in the central, temporal, and parietal regions.

CONCLUSION

For the first time, neurophysiological complexity features associated with SPS during a task-free resting state were demonstrated. Evidence is provided that neural processes differ between low- and highly-sensitive persons, whereby the latter displayed increased neural entropy. The findings support the central theoretical assumption of enhanced information processing and could be important for developing biomarkers for clinical diagnostics.

A systematic approach to brain dynamics: cognitive evolution theory of consciousness

The brain integrates volition, cognition, and consciousness seamlessly over three hierarchical (scale-dependent) levels of neural activity for their emergence: a causal or 'hard' level, a computational (unconscious) or 'soft' level, and a phenomenal (conscious) or 'psyche' level respectively. The cognitive evolution theory (CET) is based on three general prerequisites: physicalism, dynamism, and emergentism, which entail five consequences about the nature of consciousness: discreteness, passivity, uniqueness, integrity, and graduation. CET starts from the assumption that brains should have primarily evolved as volitional subsystems of organisms, not as prediction machines. This emphasizes the dynamical nature of consciousness in terms of critical dynamics to account for metastability, avalanches, and self-organized criticality of brain processes, then coupling it with volition and cognition in a framework unified over the levels. Consciousness emerges near critical points, and unfolds as a discrete stream of momentary states, each volitionally driven from oldest subcortical arousal systems. The stream is the brain's way of making a difference via predictive (Bayesian) processing. Its objective observables could be complexity measures reflecting levels of consciousness and its dynamical coherency to reveal how much knowledge (information gain) the brain acquires over the stream. CET also proposes a quantitative classification of both disorders of consciousness and mental disorders within that unified framework.

Photonic elementary cellular automata for simulation of complex phenomena

Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the level of software. This can be taken one step further by simplifying the underlying physical hardware. Here, we propose and implement a simple photonic hardware platform for simulating complex phenomena based on cellular automata. Using this special-purpose computer, we experimentally demonstrate complex phenomena, including fractals, chaos, and solitons, which are typically associated with much more complex physical systems. The flexibility and programmability of our photonic computer present new opportunities to simulate and harness complexity for efficient, robust, and decentralized information processing using light.

Anomalous Self-Organization in Active Piles

Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity's strength (ζ). This observation helped us to uncover a hidden connection between active SOC systems and α-stable Levy systems. We demonstrate that one can partially sweep α-stable Levy distributions by changing ζ. The system undergoes a crossover towards Bak-Tang-Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point ζ<ζ*≈0.1.

On the Possibility of Reproducing Utsu's Law for Earthquakes with a Spring-Block SOC Model

The Olami, Feder and Christensen (OFC) spring-block model has proven to be a powerful tool for analyzing and comparing synthetic and real earthquakes. This work proposes the possible reproduction of Utsu's law for earthquakes in the OFC model. Based on our previous works, several simulations characterizing real seismic regions were performed. We located the maximum earthquake in these regions and applied Utsu's formulae to identify a possible aftershock area and made comparisons between synthetic and real earthquakes. The research compares several equations to calculate the aftershock area and proposes a new one with the available data. Subsequently, the team performed new simulations and chose a mainshock to analyze the behavior of the surrounding events, so as to identify whether they could be catalogued as aftershocks and relate them to the aftershock area previously determined using the formula proposed. Additionally, the spatial location of those events was considered in order to classify them as aftershocks. Finally, we plot the epicenters of the mainshock, and the possible aftershocks comprised in the calculated area resembling the original work of Utsu. Having analyzed the results, it is likely to say that Utsu's law is reproducible using a spring-block model with a self-organized criticality (SOC) model.

Multifractal Properties of Time Series of Synthetic Earthquakes Obtained from a Spring-Block Model

With the spring-block model proposed by Olami, Feder, and Christensen (OFC), we obtained a time series of synthetic earthquakes with different values of the conservation level (β), which measures the fraction of the energy that a relaxing block passes to its neighbors. The time series have multifractal characteristics, and we analyzed them with the Chhabra and Jensen method. We calculated the width, symmetry, and curvature parameters for each spectrum. As the value of conservation level increases, the spectra widen, the symmetric parameter increases, and the curvature around the maximum of the spectra decreases. In a long series of synthetic seismicity, we located earthquakes of the greatest magnitude and built overlapping windows before and after them. For the time series in each window, we performed multifractal analysis to obtain multifractal spectra. We also calculated the width, symmetry, and curvature around the maximum of the multifractal spectrum. We followed the evolution of these parameters before and after large earthquakes. We found that the multifractal spectra had greater widths, were less skewed to the left, and were very pointed around the maximum before rather than after large earthquakes. We studied and calculated the same parameters and found the same results in the analysis of the Southern California seismicity catalog. This suggests that there seems to be a process of preparation for a great earthquake and that its dynamics are different from the one that occurs after this mainshock based on the behavior of the parameters mentioned before.

Critical Drift in a Neuro-Inspired Adaptive Network

It has been postulated that the brain operates in a self-organized critical state that brings multiple benefits, such as optimal sensitivity to input. Thus far, self-organized criticality has typically been depicted as a one-dimensional process, where one parameter is tuned to a critical value. However, the number of adjustable parameters in the brain is vast, and hence critical states can be expected to occupy a high-dimensional manifold inside a high-dimensional parameter space. Here, we show that adaptation rules inspired by homeostatic plasticity drive a neuro-inspired network to drift on a critical manifold, where the system is poised between inactivity and persistent activity. During the drift, global network parameters continue to change while the system remains at criticality.

Parabolic avalanche scaling in the synchronization of cortical cell assemblies

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

Microscale Neuronal Activity Collectively Drives Chaotic and Inflexible Dynamics at the Macroscale in Seizures

Neuronal activity propagates through the network during seizures, engaging brain dynamics at multiple scales. Such propagating events can be described through the avalanches framework, which can relate spatiotemporal activity at the microscale with global network properties. Interestingly, propagating avalanches in healthy networks are indicative of critical dynamics, where the network is organized to a phase transition, which optimizes certain computational properties. Some have hypothesized that the pathologic brain dynamics of epileptic seizures are an emergent property of microscale neuronal networks collectively driving the brain away from criticality. Demonstrating this would provide a unifying mechanism linking microscale spatiotemporal activity with emergent brain dysfunction during seizures. Here, we investigated the effect of drug-induced seizures on critical avalanche dynamics, using in vivo whole-brain two-photon imaging of GCaMP6s larval zebrafish (males and females) at single neuron resolution. We demonstrate that single neuron activity across the whole brain exhibits a loss of critical statistics during seizures, suggesting that microscale activity collectively drives macroscale dynamics away from criticality. We also construct spiking network models at the scale of the larval zebrafish brain, to demonstrate that only densely connected networks can drive brain-wide seizure dynamics away from criticality. Importantly, such dense networks also disrupt the optimal computational capacities of critical networks, leading to chaotic dynamics, impaired network response properties and sticky states, thus helping to explain functional impairments during seizures. This study bridges the gap between microscale neuronal activity and emergent macroscale dynamics and cognitive dysfunction during seizures.SIGNIFICANCE STATEMENT Epileptic seizures are debilitating and impair normal brain function. It is unclear how the coordinated behavior of neurons collectively impairs brain function during seizures. To investigate this we perform fluorescence microscopy in larval zebrafish, which allows for the recording of whole-brain activity at single-neuron resolution. Using techniques from physics, we show that neuronal activity during seizures drives the brain away from criticality, a regime that enables both high and low activity states, into an inflexible regime that drives high activity states. Importantly, this change is caused by more connections in the network, which we show disrupts the ability of the brain to respond appropriately to its environment. Therefore, we identify key neuronal network mechanisms driving seizures and concurrent cognitive dysfunction.

Sandpile Universality in Social Inequality: Gini and Kolkata Measures

Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini (g) index and the Kolkata (k) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as k, indicates the proportion of the 'wealth' owned by (1-k) fraction of the 'people'. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around g=k≈0.87, starting from the point of perfect equality, where g=0 and k=0.5) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto's 80/20 law (k=0.80), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the g and k indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior.

Response of cross-correlations between high PM2.5 and O3 with increasing time scales to the COVID-19: different trends in BTH and PRD

The air pollution in China currently is characterized by high fine particulate matter (PM2.5) and ozone (O3) concentrations. Compared with single high pollution events, such double high pollution (DHP) events (both PM2.5 and O3 are above the National Ambient Air Quality Standards (NAAQS)) pose a greater threat to public health and environment. In 2020, the outbreak of COVID-19 provided a special time window to further understand the cross-correlation between PM2.5 and O3. Based on this background, a novel detrended cross-correlation analysis (DCCA) based on maximum time series of variable time scales (VM-DCCA) method is established in this paper to compare the cross-correlation between high PM2.5 and O3 in Beijing-Tianjin-Heibei (BTH) and Pearl River Delta (PRD). At first, the results show that PM2.5 decreased while O3 increased in most cities due to the effect of COVID-19, and the increase in O3 is more significant in PRD than in BTH. Secondly, through DCCA, the results show that the PM2.5-O3 DCCA exponents α decrease by an average of 4.40% and 2.35% in BTH and PRD respectively during COVID-19 period compared with non-COVID-19 period. Further, through VM-DCCA, the results show that the PM2.5-O3 VM-DCCA exponents [Formula: see text] in PRD weaken rapidly with the increase of time scales, with decline range of about 23.53% and 22.90% during the non-COVID-19 period and COVID-19 period respectively at 28-h time scale. BTH is completely different. Without significant tendency, its [Formula: see text] is always higher than that in PRD at different time scales. Finally, we explain the above results with the self-organized criticality (SOC) theory. The impact of meteorological conditions and atmospheric oxidation capacity (AOC) variation during the COVID-19 period on SOC state are further discussed. The results show that the characteristics of cross-correlation between high PM2.5 and O3 are the manifestation of the SOC theory of atmospheric system. Relevant conclusions are important for the establishment of regionally targeted PM2.5-O3 DHP coordinated control strategies.

Decision-Making Underlying Support-Searching in Pea Plants

Finding a suitable support is a key process in the life history of climbing plants. Those that find a suitable support have greater performance and fitness than those that remain prostrate. Numerous studies on climbing plant behavior have elucidated the mechanistic details of support-searching and attachment. Far fewer studies have addressed the ecological significance of support-searching behavior and the factors that affect it. Among these, the diameter of supports influences their suitability. When the support diameter increases beyond some point, climbing plants are unable to maintain tensional forces and therefore lose attachment to the trellis. Here, we further investigate this issue by placing pea plants (Pisum sativum L.) in the situation of choosing between supports of different diameters while their movement was recorded by means of a three-dimensional motion analysis system. The results indicate that the way pea plants move can vary depending on whether they are presented with one or two potential supports. Furthermore, when presented with a choice between thin and thick supports, the plants showed a distinct preference for the former than the latter. The present findings shed further light on how climbing plants make decisions regarding support-searching and provide evidence that plants adopt one of several alternative plastic responses in a way that optimally corresponds to environmental scenarios.

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.

Many universality classes in an interface model restricted to non-negative heights

We present a simple one-dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site x and time t, an integer n(x,t) satisfies a linear interface equation with added random noise. Depending on the control parameters, this noise may or may not satisfy the detailed balance condition, so that the growing interfaces are in the Edwards-Wilkinson or in the Kardar-Parisi-Zhang universality class. In addition, there is also a constraint n(x,t)≥0. Points x where n>0 on one side and n=0 on the other are called "fronts." These fronts can be "pushed" or "pulled," depending on the control parameters. For pulled fronts, the lateral spreading is in the directed percolation (DP) universality class, while it is in a different universality class for pushed fronts, and another universality class in between. In the DP case, the activity at each active site can in general be arbitrarily large, in contrast to previous realizations of DP. Finally, we find two different types of transitions when the interface detaches from the line n=0 (with 〈n(x,t)〉→const on one side, and →∞ on the other), again with new universality classes. We also discuss a mapping of this model to the avalanche propagation in a directed Oslo rice pile model in specially prepared backgrounds.

Nonstationary but quasisteady states in self-organized criticality

The notion of self-organized criticality (SOC) was conceived to interpret the spontaneous emergence of long-range correlations in nature. Since then many different models have been introduced to study SOC. All of them have a few common features: externally driven dynamical systems self-organize themselves to nonequilibrium stationary states exhibiting fluctuations of all length scales as the signatures of criticality. In contrast, we have studied here in the framework of the sandpile model a system that has mass inflow but no outflow. There is no boundary, and particles cannot escape from the system by any means. Therefore, there is no current balance, and consequently it is not expected that the system would arrive at a stationary state. In spite of that, it is observed that the bulk of the system self-organizes to a quasisteady state where the grain density is maintained at a nearly constant value. Power law distributed fluctuations of all lengths and time scales have been observed, which are the signatures of criticality. Our detailed computer simulation study gives the set of critical exponents whose values are very close to their counterparts in the original sandpile model. This study indicates that (i) a physical boundary and (ii) the stationary state, though sufficient, may not be the necessary criteria for achieving SOC.

Self-organized criticality of magnetic avalanches in disordered ferrimagnetic material

We observe multiple steplike jumps in a Dy-Fe-Ga-based ferrimagnetic alloy in its magnetic hysteresis curve at 2 K. The observed jumps are found to have a stochastic character with respect to their magnitude and the field position, and the jumps do not correlate with the duration of the field. The distribution of jump size follows a power law variation indicating the scale invariance nature of the jumps. We have invoked a simple two-dimensional random bond Ising-type spin system to model the dynamics. Our computational model can qualitatively reproduce the jumps and their scale-invariant character. It also elucidates that the flipping of antiferromagnetically coupled Dy and Fe clusters is responsible for the observed jumps in the hysteresis loop. These features are described in terms of the self-organized criticality.

1/f noise from the sequence of nonoverlapping rectangular pulses

We analyze the power spectral density of a signal composed of nonoverlapping rectangular pulses. First, we derive a general formula for the power spectral density of a signal constructed from the sequence of nonoverlapping pulses. Then we perform a detailed analysis of the rectangular pulse case. We show that pure 1/f noise can be observed until extremely low frequencies when the characteristic pulse (or gap) duration is long in comparison to the characteristic gap (or pulse) duration, and gap (or pulse) durations are power-law distributed. The obtained results hold for the ergodic and weakly nonergodic processes.

Earthquake magnitude distribution and aftershocks: A statistical geometry explanation

The emergence of a power-law distribution for the energy released during an earthquake is investigated in several models. Generic features are identified which are based on the self-affine behavior of the stress field prior to an event. This field behaves at large scale as a random trajectory in one dimension of space and a random surface in two dimensions. Using concepts of statistical mechanics and results on the properties of these random objects, several predictions are obtained and verified, in particular the value of the power-law exponent of the earthquake energy distribution (the Gutenberg-Richter law) as well as a mechanism for the existence of aftershocks after a large earthquake (the Omori law).

Critical brain wave dynamics of neuronal avalanches

Analytical expressions for scaling of brain wave spectra derived from the general non-linear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent non-linear brain wave dynamics reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different non-linear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order non-linear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Altered spreading of neuronal avalanches in temporal lobe epilepsy relates to cognitive performance: A resting-state hdEEG study

OBJECTIVE

Large aperiodic bursts of activations named neuronal avalanches have been used to characterize whole-brain activity, as their presence typically relates to optimal dynamics. Epilepsy is characterized by alterations in large-scale brain network dynamics. Here we exploited neuronal avalanches to characterize differences in electroencephalography (EEG) basal activity, free from seizures and/or interictal spikes, between patients with temporal lobe epilepsy (TLE) and matched controls.

METHOD

We defined neuronal avalanches as starting when the z-scored source-reconstructed EEG signals crossed a specific threshold in any region and ending when all regions returned to baseline. This technique avoids data manipulation or assumptions of signal stationarity, focusing on the aperiodic, scale-free components of the signals. We computed individual avalanche transition matrices to track the probability of avalanche spreading across any two regions, compared them between patients and controls, and related them to memory performance in patients.

RESULTS

We observed a robust topography of significant edges clustering in regions functionally and structurally relevant for the TLE, such as the entorhinal cortex, the inferior parietal and fusiform area, the inferior temporal gyrus, and the anterior cingulate cortex. We detected a significant correlation between the centrality of the entorhinal cortex in the transition matrix and the long-term memory performance (delay recall Rey-Osterrieth Complex Figure Test).

SIGNIFICANCE

Our results show that the propagation patterns of large-scale neuronal avalanches are altered in TLE during the resting state, suggesting a potential diagnostic application in epilepsy. Furthermore, the relationship between specific patterns of propagation and memory performance support the neurophysiological relevance of neuronal avalanches.

Criticality in probabilistic models of spreading dynamics in brain networks: Epileptic seizures

The spread of seizures across brain networks is the main impairing factor, often leading to loss-of-consciousness, in people with epilepsy. Despite advances in recording and modeling brain activity, uncovering the nature of seizure spreading dynamics remains an important challenge to understanding and treating pharmacologically resistant epilepsy. To address this challenge, we introduce a new probabilistic model that captures the spreading dynamics in patient-specific complex networks. Network connectivity and interaction time delays between brain areas were estimated from white-matter tractography. The model's computational tractability allows it to play an important complementary role to more detailed models of seizure dynamics. We illustrate model fitting and predictive performance in the context of patient-specific Epileptor networks. We derive the phase diagram of spread size (order parameter) as a function of brain excitability and global connectivity strength, for different patient-specific networks. Phase diagrams allow the prediction of whether a seizure will spread depending on excitability and connectivity strength. In addition, model simulations predict the temporal order of seizure spread across network nodes. Furthermore, we show that the order parameter can exhibit both discontinuous and continuous (critical) phase transitions as neural excitability and connectivity strength are varied. Existence of a critical point, where response functions and fluctuations in spread size show power-law divergence with respect to control parameters, is supported by mean-field approximations and finite-size scaling analyses. Notably, the critical point separates two distinct regimes of spreading dynamics characterized by unimodal and bimodal spread-size distributions. Our study sheds new light on the nature of phase transitions and fluctuations in seizure spreading dynamics. We expect it to play an important role in the development of closed-loop stimulation approaches for preventing seizure spread in pharmacologically resistant epilepsy. Our findings may also be of interest to related models of spreading dynamics in epidemiology, biology, finance, and statistical physics.

A complex systems perspective on psychedelic brain action

Recent findings suggesting the potential transdiagnostic efficacy of psychedelic-assisted therapy have fostered the need to deepen our understanding of psychedelic brain action. Functional neuroimaging investigations have found that psychedelics reduce the functional segregation of large-scale brain networks. However, beyond this general trend, findings have been largely inconsistent. We argue here that a perspective based on complexity science that foregrounds the distributed, interactional, and dynamic nature of brain function may render these inconsistencies intelligible. We propose that psychedelics induce a mode of brain function that is more dynamically flexible, diverse, integrated, and tuned for information sharing, consistent with greater criticality. This 'meta' perspective has the potential to unify past findings and guide intuitions toward compelling mechanistic models.

LSD-induced increase of Ising temperature and algorithmic complexity of brain dynamics

A topic of growing interest in computational neuroscience is the discovery of fundamental principles underlying global dynamics and the self-organization of the brain. In particular, the notion that the brain operates near criticality has gained considerable support, and recent work has shown that the dynamics of different brain states may be modeled by pairwise maximum entropy Ising models at various distances from a phase transition, i.e., from criticality. Here we aim to characterize two brain states (psychedelics-induced and placebo) as captured by functional magnetic resonance imaging (fMRI), with features derived from the Ising spin model formalism (system temperature, critical point, susceptibility) and from algorithmic complexity. We hypothesized, along the lines of the entropic brain hypothesis, that psychedelics drive brain dynamics into a more disordered state at a higher Ising temperature and increased complexity. We analyze resting state blood-oxygen-level-dependent (BOLD) fMRI data collected in an earlier study from fifteen subjects in a control condition (placebo) and during ingestion of lysergic acid diethylamide (LSD). Working with the automated anatomical labeling (AAL) brain parcellation, we first create "archetype" Ising models representative of the entire dataset (global) and of the data in each condition. Remarkably, we find that such archetypes exhibit a strong correlation with an average structural connectome template obtained from dMRI (r = 0.6). We compare the archetypes from the two conditions and find that the Ising connectivity in the LSD condition is lower than in the placebo one, especially in homotopic links (interhemispheric connectivity), reflecting a significant decrease of homotopic functional connectivity in the LSD condition. The global archetype is then personalized for each individual and condition by adjusting the system temperature. The resulting temperatures are all near but above the critical point of the model in the paramagnetic (disordered) phase. The individualized Ising temperatures are higher in the LSD condition than in the placebo condition (p = 9 × 10-5). Next, we estimate the Lempel-Ziv-Welch (LZW) complexity of the binarized BOLD data and the synthetic data generated with the individualized model using the Metropolis algorithm for each participant and condition. The LZW complexity computed from experimental data reveals a weak statistical relationship with condition (p = 0.04 one-tailed Wilcoxon test) and none with Ising temperature (r(13) = 0.13, p = 0.65), presumably because of the limited length of the BOLD time series. Similarly, we explore complexity using the block decomposition method (BDM), a more advanced method for estimating algorithmic complexity. The BDM complexity of the experimental data displays a significant correlation with Ising temperature (r(13) = 0.56, p = 0.03) and a weak but significant correlation with condition (p = 0.04, one-tailed Wilcoxon test). This study suggests that the effects of LSD increase the complexity of brain dynamics by loosening interhemispheric connectivity-especially homotopic links. In agreement with earlier work using the Ising formalism with BOLD data, we find the brain state in the placebo condition is already above the critical point, with LSD resulting in a shift further away from criticality into a more disordered state.

Dynamic correlations in the conserved Manna sandpile

We study dynamic correlations for current and mass, as well as the associated power spectra, in the one-dimensional conserved Manna sandpile. We show that, in the thermodynamic limit, the variance of cumulative bond current up to time T grows subdiffusively as T^{1/2-μ} with the exponent μ≥0 depending on the density regimes considered and, likewise, the power spectra of current and mass at low frequency f varies as f^{1/2+μ} and f^{-3/2+μ}, respectively. Our theory predicts that, far from criticality, μ=0 and, near criticality, μ=(β+1)/2ν_{⊥}z>0 with β, ν_{⊥}, and z being the order parameter, correlation length, and dynamic exponents, respectively. The anomalous suppression of fluctuations near criticality signifies a "dynamic hyperuniformity," characterized by a set of fluctuation relations, in which current, mass, and tagged-particle displacement fluctuations are shown to have a precise quantitative relationship with the density-dependent activity (or its derivative). In particular, the relation, D_{s}(ρ[over ¯])=a(ρ[over ¯])/ρ[over ¯], between the self-diffusion coefficient D_{s}(ρ[over ¯]), activity a(ρ[over ¯]) and density ρ[over ¯] explains a previous simulation observation [Eur. Phys. J. B 72, 441 (2009)10.1140/epjb/e2009-00367-0] that, near criticality, the self-diffusion coefficient in the Manna sandpile has the same scaling behavior as the activity.

Spatial-Temporal Genome Regulation in Stress-Response and Cell-Fate Change

Complex functioning of the genome in the cell nucleus is controlled at different levels: (a) the DNA base sequence containing all relevant inherited information; (b) epigenetic pathways consisting of protein interactions and feedback loops; (c) the genome architecture and organization activating or suppressing genetic interactions between different parts of the genome. Most research so far has shed light on the puzzle pieces at these levels. This article, however, attempts an integrative approach to genome expression regulation incorporating these different layers. Under environmental stress or during cell development, differentiation towards specialized cell types, or to dysfunctional tumor, the cell nucleus seems to react as a whole through coordinated changes at all levels of control. This implies the need for a framework in which biological, chemical, and physical manifestations can serve as a basis for a coherent theory of gene self-organization. An international symposium held at the Biomedical Research and Study Center in Riga, Latvia, on 25 July 2022 addressed novel aspects of the abovementioned topic. The present article reviews the most recent results and conclusions of the state-of-the-art research in this multidisciplinary field of science, which were delivered and discussed by scholars at the Riga symposium.

Differential associations between scale-free neural dynamics and different levels of cognitive ability

As indicators of cognitive function, scale-free neural dynamics are gaining increasing attention in cognitive neuroscience. Although the functional relevance of scale-free dynamics has been extensively reported, one fundamental question about its association with cognitive ability remains unanswered: is the association universal across a wide spectrum of cognitive abilities or confined to specific domains? Based on dual-process theory, we designed two categories of tasks to analyze two types of cognitive processes-automatic and controlled-and examined their associations with scale-free neural dynamics characterized from resting-state electroencephalography (EEG) recordings obtained from a large sample of human adults (N = 102). Our results showed that resting-state scale-free neural dynamics did not predict individuals' behavioral performance in tasks that primarily engaged the automatic process but did so in tasks that primarily engaged the controlled process. In addition, by fitting the scale-free parameters separately in different frequency bands, we found that the cognitive association of scale-free dynamics was more strongly manifested in higher-band EEG spectrum. Our findings indicate that resting-state scale-free dynamics are not universal neural indicators for all cognitive abilities but are mainly associated with high-level cognition that entails controlled processes. This finding is compatible with the widely claimed role of scale-free dynamics in reflecting properties of complex dynamic systems.

Stable and Unstable Perturbations in Universal Scaling Phenomena Far from Equilibrium

We study the dynamics of perturbations around nonthermal fixed points associated with universal scaling phenomena in quantum many-body systems far from equilibrium. For an N-component scalar quantum field theory in 3+1 space-time dimensions, we determine the stability scaling exponents using a self-consistent large-N expansion to next-to-leading order. Our analysis reveals the presence of both stable and unstable perturbations, the latter leading to quasiexponential deviations from the fixed point in the infrared. We identify a tower of far-from-equilibrium quasiparticle states and their dispersion relations by computing the spectral function. With the help of linear response theory, we demonstrate that unstable dynamics arises from a competition between elastic scattering processes among the quasiparticle states. What ultimately renders the fixed point dynamically attractive is the phenomenon of a "scaling instability," which is the universal scaling of the unstable regime toward the infrared due to a self-similar quasiparticle cascade. Our results provide ab initio understanding of emergent stability properties in self-organized scaling phenomena.

Temporal Structure in Sensorimotor Variability: A Stable Trait, But What For?

Human performance shows substantial endogenous variability over time, and this variability is a robust marker of individual differences. Of growing interest to psychologists is the realisation that variability is not fully random, but often exhibits temporal dependencies. However, their measurement and interpretation come with several controversies. Furthermore, their potential benefit for studying individual differences in healthy and clinical populations remains unclear. Here, we gather new and archival datasets featuring 11 sensorimotor and cognitive tasks across 526 participants, to examine individual differences in temporal structures. We first investigate intra-individual repeatability of the most common measures of temporal structures - to test their potential for capturing stable individual differences. Secondly, we examine inter-individual differences in these measures using: (1) task performance assessed from the same data, (2) meta-cognitive ratings of on-taskness from thought probes occasionally presented throughout the task, and (3) self-assessed attention-deficit related traits. Across all datasets, autocorrelation at lag 1 and Power Spectra Density slope showed high intra-individual repeatability across sessions and correlated with task performance. The Detrended Fluctuation Analysis slope showed the same pattern, but less reliably. The long-term component (d) of the ARFIMA(1,d,1) model showed poor repeatability and no correlation to performance. Overall, these measures failed to show external validity when correlated with either mean subjective attentional state or self-assessed traits between participants. Thus, some measures of serial dependencies may be stable individual traits, but their usefulness in capturing individual differences in other constructs typically associated with variability in performance seems limited. We conclude with comprehensive recommendations for researchers.

Supplementary Information

The online version contains supplementary material available at 10.1007/s42113-022-00162-1.

The ensemble of gene regulatory networks at mutation-selection balance

The evolution of diverse phenotypes both involves and is constrained by molecular interaction networks. When these networks influence patterns of expression, we refer to them as gene regulatory networks (GRNs). Here, we develop a model of GRN evolution analogous to work from quasi-species theory, which is itself essentially the mutation-selection balance model from classical population genetics extended to multiple loci. With this GRN model, we prove that-across a broad spectrum of selection pressures-the dynamics converge to a stationary distribution over GRNs. Next, we show from first principles how the frequency of GRNs at equilibrium is related to the topology of the genotype network, in particular, via a specific network centrality measure termed the eigenvector centrality. Finally, we determine the structural characteristics of GRNs that are favoured in response to a range of selective environments and mutational constraints. Our work connects GRN evolution to quasi-species theory-and thus to classical populations genetics-providing a mechanistic explanation for the observed distribution of GRNs evolving in response to various evolutionary forces, and shows how complex fitness landscapes can emerge from simple evolutionary rules.

Chaotic dynamics in spatially distributed neuronal networks generate population-wide shared variability

Neural activity in the cortex is highly variable in response to repeated stimuli. Population recordings across the cortex demonstrate that the variability of neuronal responses is shared among large groups of neurons and concentrates in a low dimensional space. However, the source of the population-wide shared variability is unknown. In this work, we analyzed the dynamical regimes of spatially distributed networks of excitatory and inhibitory neurons. We found chaotic spatiotemporal dynamics in networks with similar excitatory and inhibitory projection widths, an anatomical feature of the cortex. The chaotic solutions contain broadband frequency power in rate variability and have distance-dependent and low-dimensional correlations, in agreement with experimental findings. In addition, rate chaos can be induced by globally correlated noisy inputs. These results suggest that spatiotemporal chaos in cortical networks can explain the shared variability observed in neuronal population responses.

Emergent, Non-Aging, Extendable, and Rechargeable Exchange Bias in 2D Fe3 GeTe2 Homostructures Induced by Moderate Pressuring

As a crucial concept in magnetism and spintronics, exchange bias (ExB) measures the asymmetry in the hysteresis loop of a pinned ferromagnet (FM)/antiferromagnet (AFM) interface. Previous studies are mainly focused on FM/AFM heterostructures composed of conventional bulk materials, whose complex interfaces prohibit precise control and full understanding of the phenomenon. Here, the enabling power of 2D magnets is exploited to demonstrate the emergence, non-aging, extendability, and rechargeability of ExB in van der Waals Fe₃ GeTe₂ homostructures, upon moderate pressuring. The emergence of the ExB is attributed to a local stress-induced FM-to-AFM transition, as validated using first-principles calculations, and confirmed in magneto-optical Kerr effect and second harmonic generation measurements. It is also observed that, negligible ExB aging before the training effect suddenly takes place through avalanching, pronounced delay of the avalanche via timed pressure repetition (extendability), ExB recovery in the post-training sample upon refreshed pressuring (rechargeability), and demonstrate its versatile tunability. These striking findings offer unprecedented insights into the underlying principles of ExB and its training, with immense technological applications in sight.

Scale-free dynamics of core-periphery topography

The human brain's cerebral cortex exhibits a topographic division into higher-order transmodal core and lower-order unimodal periphery regions. While timescales between the core and periphery region diverge, features of their power spectra, especially scale-free dynamics during resting-state and their mdulation in task states, remain unclear. To answer this question, we investigated the ~1/f-like pink noise manifestation of scale-free dynamics in the core-periphery topography during rest and task states applying infra-slow inter-trial intervals up to 1 min falling inside the BOLD's infra-slow frequency band. The results demonstrate (1) higher resting-state power-law exponent (PLE) in the core compared to the periphery region; (2) significant PLE increases in task across the core and periphery regions; and (3) task-related PLE increases likely followed the task's atypically low event rates, namely the task's periodicity (inter-trial interval = 52-60 s; 0.016-0.019 Hz). A computational model and a replication dataset that used similar infra-slow inter-trial intervals provide further support for our main findings. Altogether, the results show that scale-free dynamics differentiate core and periphery regions in the resting-state and mediate task-related effects.

Evidence of Critical Dynamics in Movements of Bees inside a Hive

Social insects such as honey bees exhibit complex behavioral patterns, and their distributed behavioral coordination enables decision-making at the colony level. It has, therefore, been proposed that a high-level description of their collective behavior might share commonalities with the dynamics of neural processes in brains. Here, we investigated this proposal by focusing on the possibility that brains are poised at the edge of a critical phase transition and that such a state is enabling increased computational power and adaptability. We applied mathematical tools developed in computational neuroscience to a dataset of bee movement trajectories that were recorded within the hive during the course of many days. We found that certain characteristics of the activity of the bee hive system are consistent with the Ising model when it operates at a critical temperature, and that the system's behavioral dynamics share features with the human brain in the resting state.

The Role of Alpha Oscillations among the Main Neuropsychiatric Disorders in the Adult and Developing Human Brain: Evidence from the Last 10 Years of Research

Alpha oscillations (7-13 Hz) are the dominant rhythm in both the resting and active brain. Accordingly, translational research has provided evidence for the involvement of aberrant alpha activity in the onset of symptomatological features underlying syndromes such as autism, schizophrenia, major depression, and Attention Deficit and Hyperactivity Disorder (ADHD). However, findings on the matter are difficult to reconcile due to the variety of paradigms, analyses, and clinical phenotypes at play, not to mention recent technical and methodological advances in this domain. Herein, we seek to address this issue by reviewing the literature gathered on this topic over the last ten years. For each neuropsychiatric disorder, a dedicated section will be provided, containing a concise account of the current models proposing characteristic alterations of alpha rhythms as a core mechanism to trigger the associated symptomatology, as well as a summary of the most relevant studies and scientific contributions issued throughout the last decade. We conclude with some advice and recommendations that might improve future inquiries within this field.

'Phase transitions' in bacteria - From structural transitions in free living bacteria to phenotypic transitions in bacteria within biofilms

Phase transitions are common in inanimate systems and have been studied extensively in natural sciences. Less explored are the rich transitions that take place at the micro- and nano-scales in biological systems. In conventional phase transitions, large-scale properties of the media change discontinuously in response to continuous changes in external conditions. Such changes play a significant role in the dynamic behaviours of organisms. In this review, we focus on some transitions in both free-living and biofilms of bacteria. Particular attention is paid to the transitions in the flagellar motors and filaments of free-living bacteria, in cellular gene expression during the biofilm growth, in the biofilm morphology transitions during biofilm expansion, and in the cell motion pattern transitions during the biofilm formation. We analyse the dynamic characteristics and biophysical mechanisms of these phase transition phenomena and point out the parallels between these transitions and conventional phase transitions. We also discuss the applications of some theoretical and numerical methods, established for conventional phase transitions in inanimate systems, in bacterial biofilms.

A master equation for power laws

We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power laws that describes how the number of cascades changes over time (cascades are consecutive transitions that end when the initial state is reached). The partial differential equation has a closed form solution which gives an explicit dependence of the number of cascades on their size and on time. Furthermore, the power law solution has a natural cut-off, a feature often seen in empirical data. This is due to the finite size a cascade can have in a finite time horizon. The derivation of the equation provides a justification for an exponent equal to 2, which agrees well with several empirical distributions, including Richardson's Law on the size and frequency of deadly conflicts. Nevertheless, the equation can be solved for any exponent value. In addition, we propose an urn model where the number of consecutive ball extractions follows a power law. In all cases, the power law is manifest over the entire range of cascade sizes, as shown through log-log plots in the frequency and rank distributions.

A Digital Template for the Generic Multi-Risk (GenMR) Framework: A Virtual Natural Environment

Extreme disasters, defined as low-probability-high-consequences events, are often due to cascading effects combined to amplifying environmental factors. While such a risk complexity is commonly addressed by the modeling of site-specific multi-risk scenarios, there exists no harmonized approach that considers the full space of possibilities, based on the general relationships between the environment and the perils that populate it. In this article, I define the concept of a digital template for multi-risk R&D and prototyping in the Generic Multi-Risk (GenMR) framework. This digital template consists of a virtual natural environment where different perils may occur. They are geological (earthquakes, landslides, volcanic eruptions), hydrological (river floods, storm surges), meteorological (windstorms, heavy rains), and extraterrestrial (asteroid impacts). Both geological and hydrological perils depend on the characteristics of the natural environment, here defined by two environmental layers: topography and soil. Environmental objects, which alter the layers, are also defined. They are here geomorphic structures linked to some peril source characteristics. Hazard intensity footprints are then generated for primary, secondary, and tertiary perils. The role of the natural environment on intensity footprints and event cascading is emphasized, one example being the generation of a "quake lake". Future developments, à la SimCity, are finally discussed.

Phase transitions in evolutionary dynamics

Sharp changes in state, such as transitions from survival to extinction, are hallmarks of evolutionary dynamics in biological systems. These transitions can be explored using the techniques of statistical physics and the physics of nonlinear and complex systems. For example, a survival-to-extinction transition can be characterized as a non-equilibrium phase transition to an absorbing state. Here, we review the literature on phase transitions in evolutionary dynamics. We discuss directed percolation transitions in cellular automata and evolutionary models, and models that diverge from the directed percolation universality class. We explore in detail an example of an absorbing phase transition in an agent-based model of evolutionary dynamics, including previously unpublished data demonstrating similarity to, but also divergence from, directed percolation, as well as evidence for phase transition behavior at multiple levels of the model system's evolutionary structure. We discuss phase transition models of the error catastrophe in RNA virus dynamics and phase transition models for transition from chemistry to biochemistry, i.e., the origin of life. We conclude with a review of phase transition dynamics in models of natural selection, discuss the possible role of phase transitions in unraveling fundamental unresolved questions regarding multilevel selection and the major evolutionary transitions, and assess the future outlook for phase transitions in the investigation of evolutionary dynamics.

Sampling effects and measurement overlap can bias the inference of neuronal avalanches

To date, it is still impossible to sample the entire mammalian brain with single-neuron precision. This forces one to either use spikes (focusing on few neurons) or to use coarse-sampled activity (averaging over many neurons, e.g. LFP). Naturally, the sampling technique impacts inference about collective properties. Here, we emulate both sampling techniques on a simple spiking model to quantify how they alter observed correlations and signatures of criticality. We describe a general effect: when the inter-electrode distance is small, electrodes sample overlapping regions in space, which increases the correlation between the signals. For coarse-sampled activity, this can produce power-law distributions even for non-critical systems. In contrast, spike recordings do not suffer this particular bias and underlying dynamics can be identified. This may resolve why coarse measures and spikes have produced contradicting results in the past.

From mechanisms to markers: novel noninvasive EEG proxy markers of the neural excitation and inhibition system in humans

Brain function is a product of the balance between excitatory and inhibitory (E/I) brain activity. Variation in the regulation of this activity is thought to give rise to normal variation in human traits, and disruptions are thought to potentially underlie a spectrum of neuropsychiatric conditions (e.g., Autism, Schizophrenia, Downs' Syndrome, intellectual disability). Hypotheses related to E/I dysfunction have the potential to provide cross-diagnostic explanations and to combine genetic and neurological evidence that exists within and between psychiatric conditions. However, the hypothesis has been difficult to test because: (1) it lacks specificity-an E/I dysfunction could pertain to any level in the neural system- neurotransmitters, single neurons/receptors, local networks of neurons, or global brain balance - most researchers do not define the level at which they are examining E/I function; (2) We lack validated methods for assessing E/I function at any of these neural levels in humans. As a result, it has not been possible to reliably or robustly test the E/I hypothesis of psychiatric disorders in a large cohort or longitudinal patient studies. Currently available, in vivo markers of E/I in humans either carry significant risks (e.g., deep brain electrode recordings or using Positron Emission Tomography (PET) with radioactive tracers) and/or are highly restrictive (e.g., limited spatial extent for Transcranial Magnetic Stimulation (TMS) and Magnetic Resonance Spectroscopy (MRS). More recently, a range of novel Electroencephalography (EEG) features has been described, which could serve as proxy markers for E/I at a given level of inference. Thus, in this perspective review, we survey the theories and experimental evidence underlying 6 novel EEG markers and their biological underpinnings at a specific neural level. These cheap-to-record and scalable proxy markers may offer clinical utility for identifying subgroups within and between diagnostic categories, thus directing more tailored sub-grouping and, therefore, treatment strategies. However, we argue that studies in clinical populations are premature. To maximize the potential of prospective EEG markers, we first need to understand the link between underlying E/I mechanisms and measurement techniques.

Onset and dynamics of avalanches in a rotating cylinder: From experimental data to a geometric model

Particle image velocimetry has been applied to measure particle velocities on the free surface of a bed of particles within a rotating cylinder during avalanching. The particle velocities were used to examine the validity of existing avalanche models and to propose an alternative model. The movement of particles depends on their location on the surface of the bed: Particles located near the center of the bed travel the farthest, while the distance traveled decreases at an increasing rate for particles located farther from the center. The start of an avalanche can be determined to a single initiation point that can be located on the bottom half of the bed; the avalanche quickly propagates through the entire free surface with 90% of the surface in motion within 257 ms (approximately 20% of the total duration of an avalanche). The experimental insight is used to formulate a geometric model, in which three equal-sized sections flow down the bed surface during an avalanch. The predictions of the model are validated by experimental mixing measurements.

Spontaneous neuronal avalanches as a correlate of access consciousness

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

Evidence of self-organized criticality in time series by the horizontal visibility graph approach

Determination of self-organized criticality (SOC) is crucial in evaluating the dynamical behavior of a time series. Here, we apply the complex network approach to assess the SOC characteristics in synthesis and real-world data sets. For this purpose, we employ the horizontal visibility graph (HVG) method and construct the relevant networks for two numerical avalanche-based samples (i.e., sand-pile models), several financial markets, and a solar nano-flare emission model. These series are shown to have long-temporal correlations via the detrended fluctuation analysis. We compute the degree distribution, maximum eigenvalue, and average clustering coefficient of the constructed HVGs and compare them with the values obtained for random and chaotic processes. The results manifest a perceptible deviation between these parameters in random and SOC time series. We conclude that the mentioned HVG's features can distinguish between SOC and random systems.

Categorizing and Harmonizing Natural, Technological, and Socio-Economic Perils Following the Catastrophe Modeling Paradigm

The literature on probabilistic hazard and risk assessment shows a rich and wide variety of modeling strategies tailored to specific perils. On one hand, catastrophe (CAT) modeling, a recent professional and scientific discipline, provides a general structure for the quantification of natural (e.g., geological, hydrological, meteorological) and man-made (e.g., terrorist, cyber) catastrophes. On the other hand, peril characteristics and related processes have yet to be categorized and harmonized to enable adequate comparison, limit silo effects, and simplify the implementation of emerging risks. We reviewed the literature for more than 20 perils from the natural, technological, and socio-economic systems to categorize them by following the CAT modeling hazard pipeline: (1) event source → (2) size distribution → (3) intensity footprint. We defined the following categorizations, which are applicable to any type of peril, specifically: (1) point/line/area/track/diffuse source, (2) discrete event/continuous flow, and (3) spatial diffusion (static)/threshold (passive)/sustained propagation (dynamic). We then harmonized the various hazard processes using energy as the common metric, noting that the hazard pipeline's underlying physical process consists of some energy being transferred from an energy stock (the source), via an event, to the environment (the footprint).

Temporal and spatial evolution of the distribution related to the number of COVID-19 pandemic

This work systematically conducts a data analysis based on the numbers of both cumulative and daily confirmed COVID-19 cases and deaths in a time span through April 2020 to June 2022 for over 200 countries around the world. Such research feature aims to reveal the temporal and spatial evolution of the country-level distribution observed in COVID-19 pandemic, and obtains some interesting results as follows. (1) The distributions of the numbers for cumulative confirmed cases and deaths obey power-law in early stages of COVID-19 and stretched exponential function in subsequent course. (2) The distributions of the numbers for daily confirmed cases and deaths obey power-law in early and late stages of COVID-19 and stretched exponential function in middle stages. The crossover region between power-law and stretched exponential behavior seems to depend on the evolution of "infection" event and "death" event. Such observation implies a kind of important symmetry related to the dynamics process of COVID-19 spreading. (3) The distributions of the normalized numbers for each metric show a temporal scaling behavior in 2-year period, and are well described by stretched exponential function. The observation of power-law and stretched exponential behavior in such country-level distributions suggests underlying intrinsic dynamics of a virus spreading process in human interconnected society. And thus it is important for understanding and mathematically modeling the COVID-19 pandemic.

Neural Mechanisms and Psychology of Psychedelic Ego Dissolution

Neuroimaging studies of psychedelics have advanced our understanding of hierarchical brain organization and the mechanisms underlying their subjective and therapeutic effects. The primary mechanism of action of classic psychedelics is binding to serotonergic 5-HT2A receptors. Agonist activity at these receptors leads to neuromodulatory changes in synaptic efficacy that can have a profound effect on hierarchical message-passing in the brain. Here, we review the cognitive and neuroimaging evidence for the effects of psychedelics: in particular, their influence on selfhood and subject-object boundaries-known as ego dissolution-surmised to underwrite their subjective and therapeutic effects. Agonism of 5-HT2A receptors, located at the apex of the cortical hierarchy, may have a particularly powerful effect on sentience and consciousness. These effects can endure well after the pharmacological half-life, suggesting that psychedelics may have effects on neural plasticity that may play a role in their therapeutic efficacy. Psychologically, this may be accompanied by a disarming of ego resistance that increases the repertoire of perceptual hypotheses and affords alternate pathways for thought and behavior, including those that undergird selfhood. We consider the interaction between serotonergic neuromodulation and sentience through the lens of hierarchical predictive coding, which speaks to the value of psychedelics in understanding how we make sense of the world and specific predictions about effective connectivity in cortical hierarchies that can be tested using functional neuroimaging. SIGNIFICANCE STATEMENT: Classic psychedelics bind to serotonergic 5-HT2A receptors. Their agonist activity at these receptors leads to neuromodulatory changes in synaptic efficacy, resulting in a profound effect on information processing in the brain. Here, we synthesize an abundance of brain imaging research with pharmacological and psychological interpretations informed by the framework of predictive coding. Moreover, predictive coding is suggested to offer more sophisticated interpretations of neuroimaging findings by bridging the role between the 5-HT2A receptors and large-scale brain networks.

Theoretical foundations of studying criticality in the brain

Criticality is hypothesized as a physical mechanism underlying efficient transitions between cortical states and remarkable information-processing capacities in the brain. While considerable evidence generally supports this hypothesis, nonnegligible controversies persist regarding the ubiquity of criticality in neural dynamics and its role in information processing. Validity issues frequently arise during identifying potential brain criticality from empirical data. Moreover, the functional benefits implied by brain criticality are frequently misconceived or unduly generalized. These problems stem from the nontriviality and immaturity of the physical theories that analytically derive brain criticality and the statistic techniques that estimate brain criticality from empirical data. To help solve these problems, we present a systematic review and reformulate the foundations of studying brain criticality, that is, ordinary criticality (OC), quasi-criticality (qC), self-organized criticality (SOC), and self-organized quasi-criticality (SOqC), using the terminology of neuroscience. We offer accessible explanations of the physical theories and statistical techniques of brain criticality, providing step-by-step derivations to characterize neural dynamics as a physical system with avalanches. We summarize error-prone details and existing limitations in brain criticality analysis and suggest possible solutions. Moreover, we present a forward-looking perspective on how optimizing the foundations of studying brain criticality can deepen our understanding of various neuroscience questions.