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

Origin of yield stress and mechanical plasticity in model biological tissues

During development and under normal physiological conditions, biological tissues are continuously subjected to substantial mechanical stresses. In response to large deformations, cells in a tissue must undergo multicellular rearrangements to maintain integrity and robustness. However, how these events are connected in time and space remains unknown. Here, using theoretical modeling, we study the mechanical plasticity of cell monolayers under large deformations. Our results suggest that the jamming-unjamming (solid-fluid) transition can vary significantly depending on the degree of deformation, implying that tissues are highly unconventional materials. We elucidate the origins of this behavior. We also demonstrate how large deformations are accommodated through a series of cellular rearrangements, similar to avalanches in non-living materials. We find that these 'tissue avalanches' are governed by stress redistribution and the spatial distribution of "soft" or vulnerable spots, which are more prone to undergo rearrangements. Finally, we propose a simple and experimentally accessible framework to infer tissue-level stress and predict avalanches based on static images.

Critical fragility in sociotechnical systems

Sociotechnical systems, where technological and human elements interact in a goal-oriented manner, provide important functional support to our societies. Here, we draw attention to the underappreciated concept of timeliness-i.e., system elements being available at the right place at the right time-that has been ubiquitously and integrally adopted as a quality standard in the modus operandi of sociotechnical systems. We point out that a variety of incentives, often reinforced by competitive pressures, prompt system operators to myopically optimize for efficiencies, running the risk of inadvertently taking timeliness to the limit of its operational performance, correspondingly making the system critically fragile to perturbations by pushing the entire system toward the proverbial "edge of a cliff." Invoking a stylized model for operational delays, we identify the limiting operational performance of timeliness, as a true critical point, where the smallest of perturbations can lead to a systemic collapse. Specifically for firm-to-firm production networks, we suggest that the proximity to critical fragility is an important ingredient for understanding the fundamental "excess volatility puzzle" in economics. Further, in generality for optimizing sociotechnical systems, we propose that critical fragility is a crucial aspect in managing the trade-off between efficiency and robustness.

Gaussian fluctuations of nonreciprocal systems

Nonreciprocal systems can be thought of as disobeying Newton's third law-an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest toward such systems. On a fundamental level, they can be a basis of describing nonequilibrium and active states of matter, with applications ranging from physics to social sciences. However, often the first step to understanding complex nonlinear models is to linearize about the steady states. It is thus useful to develop a careful understanding of linear nonreciprocal systems, similar to our understanding of Gaussian systems in equilibrium statistical mechanics. In this work we explore simplest linear nonreciprocal models with noise and spatial extent. We describe their regions of stability and show how nonreciprocity can enhance the stability of a system. We demonstrate the appearance of exceptional and critical exceptional points with the respective enhancement of fluctuations for the latter. We show how strong nonreciprocity can lead to a finite-momentum instability. Finally, we comment how nonreciprocity can be a source of colored, 1/f type noise.

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.

Scale-free Spatio-temporal Correlations in Conformational Fluctuations of Intrinsically Disordered Proteins

The self-assembly of intrinsically disordered proteins (IDPs) into condensed phases and the formation of membrane-less organelles (MLOs) can be considered as the phenomenon of collective behavior. The conformational dynamics of IDPs are essential for their interactions and the formation of a condensed phase. From a physical perspective, collective behavior and the emergence of phase are associated with long-range correlations. Here the conformational dynamics of IDPs and the correlations therein are analyzed, using µs-scale atomistic molecular dynamics (MD) simulations and single-molecule Förster resonance energy transfer (smFRET) experiments. The existence of typical scale-free spatio-temporal correlations in IDP conformational fluctuations is demonstrated. Their conformational evolutions exhibit "1/f noise" power spectra and are accompanied by the appearance of residue domains following a power-law size distribution. Additionally, the motions of residues present scale-free behavioral correlation. These scale-free correlations resemble those in physical systems near critical points, suggesting that IDPs are poised at a critical state. Therefore, IDPs can effectively respond to finite differences in sequence compositions and engender considerable structural heterogeneity which is beneficial for IDP interactions and phase formation.

Structure, motion, and multiscale search of traveling networks

Network models are widely applied to describe connectivity and flow in diverse systems. In contrast, the fact that many connected systems move through space as the result of dynamic restructuring has received little attention. Therefore, we introduce the concept of 'traveling networks', and we analyze a tree-based model where the leaves are stochastically manipulated to grow, branch, and retract. We derive how these restructuring rates determine key attributes of network structure and motion, enabling a compact understanding of higher-level network behaviors such as multiscale search. These networks self-organize to the critical point between exponential growth and decay, allowing them to detect and respond to environmental signals with high sensitivity. Finally, we demonstrate how the traveling network concept applies to real-world systems, such as slime molds, the actin cytoskeleton, and human organizations, exemplifying how restructuring rules and rates in general can select for versatile search strategies in real or abstract spaces.

Principles Entailed by Complexity, Crucial Events, and Multifractal Dimensionality

Complexity is one of those descriptive terms adopted in science that we think we understand until it comes time to form a coherent definition upon which everyone can agree. Suddenly, we are awash in conditions that qualify this or that situation, much like we were in the middle of the last century when it came time to determine the solutions to differential equations that were not linear. Consequently, this tutorial is not an essay on the mathematics of complexity nor is it a rigorous review of the recent growth spurt of complexity science, but is rather an exploration of how physiologic time series (PTS) in the life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions are discarded and so-called ordinary statistical events in PTS are replaced with crucial events (CEs) using mutifractal dimensionality as the working measure of complexity. The empirical datasets considered include respiration, electrocardiograms (ECGs), and electroencephalograms (EEGs), and as different as these time series appear from one another when recorded, they are in fact shown to be in synchrony when properly processed using the technique of modified diffusion entropy analysis (MDEA). This processing reveals a new synchronization mechanism among the time series which simultaneously measures their complexity by means of the multifractal dimension of each time series and are shown to track one another across time. These results reveal a set of priciples that capture the manner in which information is exchanged among physiologic organ networks.

Proton Pump Inhibitor Omeprazole Alters the Spiking Characteristics of Proteinoids

This study reveals the significant effect of the proton pump inhibitor omeprazole on the spiking behavior of proteinoids, leading to a transformative shift in the field of unconventional computing. Through the application of different concentrations of omeprazole, we see a notable modification in the spiking characteristics of proteinoids, including significant alterations in amplitude, frequency, and temporal patterns. By using Boolean logic techniques, we analyze the complex dynamics of the proteinoid-omeprazole system, revealing underlying patterns and connections that question our understanding of biological computing. Our research reveals the unexplored potential of proteinoids as a foundation for unconventional computing. Moreover, our research indicates that the electrical spiking observed in proteinoids may be linked to the movement of protons. This discovery offers new insights into the fundamental mechanisms governing the spiking activity of proteinoids, presenting promising opportunities for future research in this area. Additionally, it opens up possibilities of developing new computational models that exploit the inherent nonlinearity and complexity of biological systems. By combining the effects of omeprazole-induced spikes with Boolean logic, a wide range of opportunities arise for information processing, pattern identification, and problem-solving. This pushes the limits of what can be achieved with bioelectronics.

Segregation-dislocation self-organized structures ductilize a work-hardened medium entropy alloy

Dislocations are the intrinsic origin of crystal plasticity. However, initial high-density dislocations in work-hardened materials are commonly asserted to be detrimental to ductility according to textbook strengthening theory. Inspired by the self-organized critical states of non-equilibrium complex systems in nature, we explored the mechanical response of an additively manufactured medium entropy alloy with segregation-dislocation self-organized structures (SD-SOS). We show here that when initial dislocations are in the form of SD-SOS, the textbook theory that dislocation hardening inevitably sacrifices ductility can be overturned. Our results reveal that the SD-SOS, in addition to providing dislocation sources by emitting dislocations and stacking faults, also dynamically interacts with gliding dislocations to generate sustainable Lomer-Cottrell locks and jogs for dislocation storage. The effective dislocation multiplication and storage capabilities lead to the continuous refinement of planar slip bands, resulting in high ductility in the work-hardened alloy produced by additive manufacturing. These findings set a precedent for optimizing the mechanical behavior of alloys via tuning dislocation configurations.

Analysis of Aftershocks from California and Synthetic Series by Using Visibility Graph Algorithm

The use of the Visibility Graph Algorithm (VGA) has proven to be a valuable tool for analyzing both real and synthetic seismicity series. Specifically, VGA transforms time series into a network representation in which structural properties such as node connectivity, clustering, and community structure can be quantitatively measured, thereby revealing underlying correlations and dynamics that may remain hidden in traditional linear or spectral analyses. The time series transformation into complex networks with VGA provides a new approach to analyze seismic dynamics, allowing scientists to extract trends and behaviors that may not be possible by classical time-series analysis. On the other hand, many studies attempt to find viable trends in order to identify preparation mechanisms prior to a strong earthquake or to analyze the aftershocks. In this work, the seismic activity of Southern California Earthquake was analyzed focusing only on the significant earthquakes. For this purpose, seismic series preceding and following each earthquake were constructed using a windowing method with different overlaps and the slope of the connectivity (k) versus magnitude (M) graph (k-M slope) and the average degree were computed from the mapped complex networks. The results revealed a significant decrease in these parameters after the earthquake, due to the contribution of the aftershocks from the main event. Interestingly, the study was extended to synthetic seismicity series and the same behavior was observed for both k-M slope and average degree. This finding suggests that the spring-block model reproduces a relaxation mechanism following a large-magnitude event like those of real seismic aftershocks. However, this conclusion contrasts with conclusions drawn by other researchers. These results highlight the utility of VGA in studying events that precede and follow major earthquakes. This technique may be used to extract some useful trends in seismicity, which could eventually be employed for a deeper understanding and possible forecasting of seismic behavior.

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.

Scaling behavior in the number theoretic division model of self-organized criticality

We revisit the number theoretic division model of self-organized criticality [B. Luque et al.Phys. Rev. Lett. 101, 158702 (2008)10.1103/PhysRevLett.101.158702]. The model consists of a pool of M-1 ordered integers {2,3,⋯,M}, and the aim is to dynamically form a primitive set of integers, where no number can be divided or divisible by others. Using extensive simulation studies and finite-size scaling method, we find the primitive set size fluctuations in the division model to show power spectral density of the form 1/f^{α} in the frequency regime 1/M≪f≪1/2 with α≈2 (different from α≈1.80(1) as reported previously) along with an additional scaling in terms of the system size ∼M^{b}. We also show similar power spectra properties for a class of random walks with a power-law distributed jump size (Lévy flights).

Describing self-organized criticality as a continuous phase transition

Can the concept of self-organized criticality, exemplified by models such as the sandpile model, be described within the framework of continuous phase transitions? In this paper, we provide extensive numerical evidence supporting an affirmative answer. Specifically, we explore the Bak, Tang, and Wiesenfeld (BTW) and Manna sandpile models as instances of percolation transitions from disordered to ordered phases. To facilitate this analysis, we introduce the concept of drop density-a continuously adjustable control variable that quantifies the average number of particles added to a site. By tuning this variable, we observe a transition in the sandpile from a subcritical to a critical phase. Additionally, we define the scaled size of the largest avalanche occurring from the beginning of the sandpile as the order parameter for the self-organized critical transition and analyze its scaling behavior. Furthermore, we calculate the correlation length exponent and note its divergence as the critical point is approached. The finite-size scaling analysis of the avalanche size distribution works quite well at the critical point of the BTW sandpile.

Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg-Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial Distribution

We discuss a model of seismic activity that is based on the concept of energy in a cluster of sources of seismic activity. We show that specific cases of the studied model lead to the Gutenberg-Richter relationship and the Omori law. These laws are valid for earthquakes that happen in a single cluster of sources of seismic activity. Further, we discuss the distribution of earthquakes for several clusters containing sources of seismic activity. This distribution contains, as a specific case, a version of the negative binomial distribution. We show that at least a part of the roll-off effect connected to the parameter b of the Gutenberg- Richter law occurs because one records earthquakes that happen in more than one cluster of sources of seismic activity.

On Oscillations in the External Electrical Potential of Sea Urchins

Sea urchins display complex bioelectric activity patterns, even with their decentralized nervous system. Electrophysiological recordings showed distinct spiking patterns. The baseline potential was about 8.80 mV. It had transient spikes with amplitudes up to 21.05 mV. We observed many types of depolarization events. They included burst-like activity and prolonged state fluctuations lasting several seconds. Frequency domain analysis showed a power-law behavior. It had a scaling exponent of 6.21 ± 0.06, indicating critical dynamics. The analysis showed potential variations between 3.69 and 21.05 mV. The oscillation periods ranged from 4 to 3102 s. The varied timing of bioelectric signals suggests that these organisms can process information. This challenges traditional views of neural computation in simpler animals. These findings provide quantitative insights into the complex signaling mechanisms of the sea urchin's distributed nervous system.

Self-organized and self-sustained ensemble activity patterns in simulation of mouse primary motor cortex

The idea of self-organized signal processing in the cerebral cortex has become a focus of research since Beggs and Plentz1 reported avalanches in local field potential recordings from organotypic cultures and acute slices of rat somatosensory cortex. How the cortex intrinsically organizes signals remains unknown. A current hypothesis was proposed by the condensed matter physicists Bak, Tang, and Wiesenfeld2 when they conjectured that if neuronal avalanche activity followed inverse power law distributions, then brain activity may be set around phase transitions within self-organized signals. We asked if we would observe self-organized signals in an isolated slice of our data driven detailed simulation of the mouse primary motor cortex? If we did, would we observe avalanches with power-law distributions in size and duration and what would they look like? Our results demonstrate that a brief unstructured stimulus (100ms, 57μA current) to a small subset of neurons (about 181 of more than 10,000) in a simulated mouse primary motor cortex slice results in self-organized and self-sustained avalanches with power-law size and duration distributions and values similar to those reported from in vivo and in vitro experiments. We observed 4 cross-layer and cross-neuron population patterns, 3 of which displayed a dominant rhythmic component. Avalanches were each composed of one or more of the 4 population patterns.

A Study on the Fracture of Brittle Heterogeneous Materials Using Non-Extensive Statistical Mechanics and the Energy Distribution Function

The fracture process of heterogeneous materials is studied here in the framework of the discipline of Non-Extensive Statistical Mechanics. Acoustic emission data provided by an experimental protocol with concrete specimens, plain or fiber-reinforced, under bending are taken advantage of. This innovation of the study lies in the fact that the analysis of the acoustic activity is implemented in terms of the energy content of the acoustic signals rather than of their interevent time or their interevent distance. The Energy Distribution Functions were properly fitted using the expression proposed by Shcherbakov, Kuksenko and Chmelet. This study reveals that the loading and fracture processes of the specific materials are definitely non-additive and non-extensive. It is concluded that the presence of notches is crucial since it assigns non-additivity and non-extensivity from relatively low loading levels due to the early formation of the fracture process zone around the crown of the notch. The values of the Tsallis entropic index, q, that were determined are in very good agreement with the respective ones obtained in previous studies by means of different analysis tools. Finally, a clear correlation between the index q and the average energy content of the acoustic signals is highlighted for the whole range of values of the energy content of the acoustic signals.

Burst-tree structure and higher-order temporal correlations

Understanding the characteristics of temporal correlations in a time series is crucial for developing accurate models in natural and social sciences. The burst-tree decomposition method was recently introduced to reveal temporal correlations in a time series in the form of an event sequence, in particular, the hierarchical structure of bursty trains of events for the entire range of timescales [Jo et al., Sci. Rep. 10, 12202 (2020)10.1038/s41598-020-68157-1]. Such structure cannot be solely captured by the interevent time distribution but can show higher-order correlations beyond interevent times. It has been found to be simply characterized by the burst-merging kernel governing which bursts are merged together as the timescale for defining bursts increases. In this work, we study the effects of kernels on the higher-order temporal correlations in terms of burst-size distributions, memory coefficients for bursts, and the autocorrelation function. We employ several kernels, including the constant, sum, product, and diagonal kernels as well as those inspired by empirical results. We generically find that kernels with preferential merging lead to heavy-tailed burst-size distributions, while kernels with assortative merging lead to positive correlations between burst sizes. The decaying exponent of the autocorrelation function depends not only on the kernel but also on the power-law exponent of the interevent time distribution. In addition, thanks to the analogy to the coagulation process, analytical solutions of burst-size distributions for some kernels could be obtained. Our findings may shed light on the role of burst-merging kernels as underlying mechanisms of higher-order temporal correlations in a time series.

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.

Studying power-grid synchronization with incremental refinement of model heterogeneity

The dynamics of electric power systems are widely studied through the phase synchronization of oscillators, typically with the use of the Kuramoto equation. While there are numerous well-known order parameters to characterize these dynamics, shortcoming of these metrics are also recognized. To capture all transitions from phase disordered states over phase locking to fully synchronized systems, new metrics were proposed and demonstrated on homogeneous models. In this paper, we aim to address a gap in the literature, namely, to examine how the gradual improvement of power grid models affects the goodness of certain metrics. To study how the details of models are perceived by the different metrics, 12 variations of a power grid model were created, introducing varying levels of heterogeneity through the coupling strength, the nodal powers, and the moment of inertia. The grid models were compared using a second-order Kuramoto equation and adaptive Runge-Kutta solver, measuring the values of the phase, the frequency, and the universal order parameters. Finally, frequency results of the models were compared to grid measurements. We found that the universal order parameter was able to capture more details of the grid models, especially in cases of decreasing moment of inertia. Even the most heterogeneous models showed notable synchronization, encouraging the use of such models. Finally, we show local frequency results related to the multi-peaks of static models, which implies that spatial heterogeneity can also induce such multi-peak behavior.

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.

Comparing prediction efficiency in the BTW and Manna sandpiles

The state-of-the-art in the theory of self-organized criticality reveals that a certain inactivity precedes extreme events, which are located on the tail of the event probability distribution with respect to their sizes. The existence of the inactivity allows for the prediction of these events in advance. In this work, we explore the predictability of the Bak-Tang-Wiesenfeld (BTW) and Manna models on the square lattice as a function of the lattice length. For both models, we use an algorithm that forecasts the occurrence of large events after a fall in activity. The efficiency of the prediction can be universally described in terms of the event size divided by an appropriate power-law function of the lattice length. The power-law exponents are projected to be 2.75 and 3 for the Manna and BTW models respectively. The scaling with the exponent 2.75 is known for collapsing of the entire size-frequency relationship in the Manna model. However, the correspondence between events on different lattices in the BTW model requires a variety of exponents where 3 is the largest. This indicates that in thermodynamic limit, prediction does exist in the Manna but not in the BTW model, at least based on inactivity. The difference in the universality classes may underline the difference in the prediction.

Emergence and Criticality in Spatiotemporal Synchronization: The Complementarity Model

This work concerns the long-term collective excitability properties and the statistical analysis of the critical events displayed by a recently introduced spatiotemporal many-body model, proposed as a new paradigm for Artificial Life. Numerical simulations show that excitable collective structures emerge in the form of dynamic networks, created by bursts of spatiotemporal activity (avalanches) at the edge of a synchronization phase transition. The spatiotemporal dynamics is portraited by a movie and quantified by time varying collective parameters, showing that the dynamic networks undergo a "life cycle," made of self-creation, homeostasis, and self-destruction. The power spectra of the collective parameters show 1/f power law tails. The statistical properties of the avalanches, evaluated in terms of size and duration, show power laws with characteristic exponents in agreement with those values experimentally found in the neural networks literature. The mechanism underlying avalanches is argued in terms of local-to-collective excitability. The connections that link the present work to self-organized criticality, neural networks, and Artificial Life are discussed.

Emergence of self-organized criticality and phase transition in the Olami-Feder-Christensen model with a single defect

We examine the conditions for the emergence of self-organized criticality in the Olami-Feder-Christensen model by introducing a single defect under periodic boundary conditions. Our findings reveal that strong localized energy dissipation is crucial for self-organized criticality emergence, while weak localized or global energy dissipation leads to its disappearance in this model. Furthermore, slight dissipation perturbations to a system in a self-organized criticality reveal a novel state characterized by a limit cycle of distinct configurations. This newly discovered state offers significant insights into the fundamental mechanisms governing the emergence of self-organized criticality.

Signatures of self-organized dynamics in rapidly driven critical sandpiles

We study two prototypical models of self-organized criticality, namely sandpile automata with deterministic (Bak-Tang-Wiesenfeld) and probabilistic (Manna model) dynamical rules, focusing on the nature of stress fluctuations induced by driving-adding grains during avalanche propagation, and dissipation through avalanches that hit the system boundary. Our analysis of stress evolution time series reveals robust cyclical trends modulated by collective fluctuations with dissipative avalanches. These modulated cycles attain higher harmonics, characterized by multifractal measures within a broad range of timescales. The features of the associated singularity spectra capture the differences in the dynamic rules behind the self-organized critical states at adiabatic driving and their pertinent response to the increased driving rate, which alters the process of stochasticity and causes a loss of avalanche scaling. In sequences of outflow current carried by dissipative avalanches, the first return distributions follow the q-Gaussian law in the adiabatic limit. They appear to follow different laws at an intermediate scale with an increased driving rate, describing different pathways to the gradual loss of cooperative behavior in these two models. The robust appearance of cyclical trends and their multifractal modulation thus represents another remarkable feature of self-organized dynamics beyond the scaling of avalanches. It can also help identify the prominence of self-organizational phenomenology in an empirical time series when underlying interactions and driving modes remain hidden.

Adaptive rewiring: a general principle for neural network development

The nervous system, especially the human brain, is characterized by its highly complex network topology. The neurodevelopment of some of its features has been described in terms of dynamic optimization rules. We discuss the principle of adaptive rewiring, i.e., the dynamic reorganization of a network according to the intensity of internal signal communication as measured by synchronization or diffusion, and its recent generalization for applications in directed networks. These have extended the principle of adaptive rewiring from highly oversimplified networks to more neurally plausible ones. Adaptive rewiring captures all the key features of the complex brain topology: it transforms initially random or regular networks into networks with a modular small-world structure and a rich-club core. This effect is specific in the sense that it can be tailored to computational needs, robust in the sense that it does not depend on a critical regime, and flexible in the sense that parametric variation generates a range of variant network configurations. Extreme variant networks can be associated at macroscopic level with disorders such as schizophrenia, autism, and dyslexia, and suggest a relationship between dyslexia and creativity. Adaptive rewiring cooperates with network growth and interacts constructively with spatial organization principles in the formation of topographically distinct modules and structures such as ganglia and chains. At the mesoscopic level, adaptive rewiring enables the development of functional architectures, such as convergent-divergent units, and sheds light on the early development of divergence and convergence in, for example, the visual system. Finally, we discuss future prospects for the principle of adaptive rewiring.

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.

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.

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.