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

The power-law distribution in the geometrically growing system: Statistic of the COVID-19 pandemic

The power-law distribution is ubiquitous and seems to have various mechanisms. We find a general mechanism for the distribution. The distribution of a geometrically growing system can be approximated by a log-completely squared chi distribution with one degree of freedom (log-CS χ₁), which reaches asymptotically a power-law distribution, or by a lognormal distribution, which has an infinite asymptotic slope, at the upper limit. For the log-CS χ₁, the asymptotic exponent of the power-law or the slope in a log-log diagram seems to be related only to the variances of the system parameters and their mutual correlation but independent of an initial distribution of the system or any mean value of parameters. We can take the log-CS χ₁ as a unique approximation when the system should have a singular initial distribution. The mechanism shows comprehensiveness to be applicable to wide practice. We derive a simple formula for Zipf's exponent, which will probably demand that the exponent should be near -1 rather than exactly -1. We show that this approach can explain statistics of the COVID-19 pandemic.

Application of the method of parallel trajectories on modeling the dynamics of COVID-19 third wave

In this paper, we present a new method for successfully simulating the dynamics of COVID-19, experimentally focusing on the third wave. This method, namely, the Method of Parallel Trajectories (MPT), is based on the recently introduced self-organized diffusion model. According to this method, accurate simulation of the dynamics of the COVID-19 infected population evolution is accomplished by considering not the total data for the infected population, but successive segments of it. By changing the initial conditions with which each segment of the simulation is produced, we achieve close and detailed monitoring of the evolution of the pandemic, providing a tool for evaluating the overall situation and the fine-tuning of the restrictive measures. Finally, the application of the proposed MPT on simulating the pandemic's third wave dynamics in Greece and Italy is presented, verifying the method's effectiveness.

Model for tectonic tremors: Enduring events, moment rate spectrum, and moment-duration scaling

Numerous attempts have been made to obtain earthquake statistics from a theoretical-physics perspective, but these studies mostly involve regular earthquakes. In recent years, a new category of earthquakes, referred to as slow earthquakes, has been discovered. Slow earthquakes emit only weak or no seismic signals and have different statistics than regular earthquakes. Here we propose a physical model for the tremor, which is a type of slow earthquake, introducing two competing timescales in a cellular automaton model. The proposed model reproduces some observation results for tremors, such as enduring events, moment-duration scaling, size distribution, and the power spectrum of the moment rate function.

Emergence of oscillations in fixed-energy sandpile models on complex networks

Fixed-energy sandpile (FES) models, introduced to understand the self-organized criticality, show a continuous phase transition between absorbing and active phases. In this work, we study the dynamics of the deterministic FES models on random networks. We observe that close to absorbing transition the density of active nodes oscillates and nodes topple in synchrony. The deterministic toppling rule and the small-world property of random networks lead to the emergence of sustained oscillations. The amplitude of oscillations becomes larger with increasing the value of network randomness. The bifurcation diagram for the density of active nodes is obtained. We use the activity-dependent rewiring rule and show that the interplay between the network structure and the FES dynamics leads to the emergence of a bistable region with a first-order transition between the absorbing and active states. Furthermore during the rewiring, the ordered activation pattern of the nodes is broken, which causes the oscillations to disappear.

A Unified Genomic Mechanism of Cell-Fate Change

The purpose of our studies is to elucidate the nature of massive control of the whole genome expression with a particular emphasis on cell-fate change. The whole genome expression is coordinated by the emergence of a critical point (CP: a peculiar set of biphasic genes) with the genome acting as an integrated dynamical system. In response to stimuli, the genome expression self-organizes into local sub-, near-, and super-critical states, each exhibiting distinct collective behaviors with its center of mass acting as a local attractor, coexisting with the whole genome attractor (GA). The CP serves as the organizing center of cell-fate change, and its activation makes local perturbation to spread over the genome affecting GA. The activation of CP is in turn elicited by genes with elevated temporal variance (oscillating-mode genes), normally in charge to keep genome expression at pace with microenvironment fluctuations. When oscillation exceeds a given threshold, the CP synchronizes with the GA driving genome expression state transition. The expression synchronization wave invading the entire genome is fostered by the fusion-splitting dynamics of silencing pericentromere-associated heterochromatin domains and the consequent folding-unfolding transitions of transcribing euchromatin domains. The proposed mechanism is a unified step toward a time-evolutional transition theory of biological regulation.

Comparing the structures of storytelling and magic for science communication with an agent-based model

When scientists engage in Public Understanding of Science to communicate their research to lay audiences, a common suggestion is to structure their talk around storytelling. Thus, it is crucial to know the actual effectiveness of storytelling in science communication compared to other structures. For instance, a structure almost unexplored is the one of magic or illusionism. As storytelling, it has been evolving and improving over humanity's history to become ever more effective, granting magicians a prominent place in the entertainment and art industry. In the present work, we compared various storytelling structures and the structure of magic, through an agent-based computational model. The results open the questioning of story architectures; propose a new way to test ideas in science communication; and show that double-blind control studies are very much needed for further testing the structures of Public Understanding of Science and further developing agent-based models.

Detecting Criticality by Exploring the Acoustic Activity in Terms of the “Natural-Time” Concept

The acoustic activity developed in marble specimens under various loading schemes is explored in terms of the recently introduced F-function. The novelty of the study is that instead of describing the temporal evolution of the F-function in terms of conventional time, the Natural Time concept is employed. Although completely different geometries and loading schemes were considered, the evolution of the F-function in the Natural Time domain exhibits a self-consistent motive: its values increase progressively with fluctuations of varying intensity, however, while the fracture is approaching, a power law appears to systematically govern the response of the specimen/structure loaded. The exponent of this law, somehow corresponding to the intensity of the acoustic activity within the loaded complex, varies within broad limits. The onset of validity of the power law designates that the system has entered into its critical stage, namely that of impending fracture, providing a useful pre-failure signal.

Statistical Analysis of the Membership Management Indicators of the Church of England UK Dioceses during the Recent (XXth Century) “Decade of Evangelism”

The paper focusses on the growth or/and decline in the number of devotees in UK Dioceses of the Church of England during the “Decade of Evangelism” [1990–2000]. In this study, rank-size relationships and subsequent correlations are searched for through various performance indicators of evangelism management. A strong structural regularity is found. Moreover, it is shown that such key indicators appear to fall into two different classes. This unexpected feature seems to indicate some basic universality regimes, in particular to distinguish behaviour measures. Rank correlations between indicators measures further emphasise some difference in evangelism management between Evangelical and Catholic Anglican tradition dioceses (or rather bishops) during that time interval.

Aperiodic measures of neural excitability are associated with anticorrelated hemodynamic networks at rest: A combined EEG-fMRI study

The hallmark of resting EEG spectra are distinct rhythms emerging from a broadband, aperiodic background. This aperiodic neural signature accounts for most of total EEG power, although its significance and relation to functional neuroanatomy remains obscure. We hypothesized that aperiodic EEG reflects a significant metabolic expenditure and therefore might be associated with the default mode network while at rest. During eyes-open, resting-state recordings of simultaneous EEG-fMRI, we find that aperiodic and periodic components of EEG power are only minimally associated with activity in the default mode network. However, a whole-brain analysis identifies increases in aperiodic power correlated with hemodynamic activity in an auditory-salience-cerebellar network, and decreases in aperiodic power are correlated with hemodynamic activity in prefrontal regions. Desynchronization in residual alpha and beta power is associated with visual and sensorimotor hemodynamic activity, respectively. These findings suggest that resting-state EEG signals acquired in an fMRI scanner reflect a balance of top-down and bottom-up stimulus processing, even in the absence of an explicit task.

Eco-epidemiological scaling of Leptospirosis: Vulnerability mapping and early warning forecasts

Infectious disease epidemics are plaguing the world and a lot of research is focused on the development of models to reproduce disease dynamics for eco-environmental and biological investigation, and disease management. Leptospirosis is an example of a neglected zoonosis strongly mediated by ecohydrological dynamics with emerging endemic and epidemic patterns worldwide in both animal and human populations. By accounting for large heterogeneities of affected areas we show how exponential endemics and scale-free epidemics are largely predictable and linked to common socio-environmental features via scaling laws with different exponents that inform about vulnerability factors. This led to the development of a novel pattern-oriented integrated model that can be used as an early-warning signal (EWS) tool for endemic-epidemic regime classification, risk determinant attribution, and near real-time forecast of outbreaks. Forecasts are grounded on expected outbreak recurrence time dependent on exceedance probabilities and statistical EWS that sense outbreak onset. A stochastic spatially-explicit model is shown to comprehensively predict outbreak dynamics (early sensing, timing, magnitude, decay, and eco-environmental determinants) and derive a spreading factor characterizing endemics and epidemics, where average over maximum rainfall is the critical factor characterizing disease transitions. Dynamically, case cross-correlation considering neighboring communities senses 2-weeks in advance outbreaks. Eco-environmental scaling relationships highlight how predicted host suitability and topographic index can be used as epidemiological footprints to effectively distinguish and control Leptospirosis regimes and areas dependent on hydro-climatological dynamics as the main trigger. The spatio-temporal scale-invariance of epidemics - underpinning persistent criticality and neutrality or independence among areas - is emphasized by the high accuracy in reproducing sequence and magnitude of cases via reliable surveillance. Further investigations of robustness and universality of eco-environmental determinants are required; nonetheless a comprehensive and computationally simple EWS method for the full characterization of Leptospirosis is provided. The tool is extendable to other climate-sensitive zoonoses to define vulnerability factors and predict outbreaks useful for optimal disease risk prevention and control.

Linking space-time correlations for a class of self-organized critical systems

The hypothesis of self-organized criticality explains the existence of long-range "space-time" correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in fluctuations at an "external drive" timescale. As an example, we consider a class of sandpile models displaying nontrivial correlations. We apply the scaling method and determine spatial cross-correlation by establishing a relationship between local and global temporal correlations. We find that the spatial cross-correlation decays in a power-law manner with an exponent γ=1-δ, where δ characterizes a scaling of the total power of the global temporal process with the system size.

Towards a Measure for Characterizing the Informational Content of Audio Signals and the Relation between Complexity and Auditory Encoding

The accurate description of a complex process should take into account not only the interacting elements involved but also the scale of the description. Therefore, there can not be a single measure for describing the associated complexity of a process nor a single metric applicable in all scenarios. This article introduces a framework based on multiscale entropy to characterize the complexity associated with the most identifiable characteristic of songs: the melody. We are particularly interested in measuring the complexity of popular songs and identifying levels of complexity that statistically explain the listeners’ preferences. We analyze the relationship between complexity and popularity using a database of popular songs and their relative position in a preferences ranking. There is a tendency toward a positive association between complexity and acceptance (success) of a song that is, however, not significant after adjusting for multiple testing.

Apparent Power Laws Can Occur without Criticality

Power laws often lead to the conclusion that self-organized criticality is at work. This is not the case, and power laws can also occur away from criticality or can occur for other reasons.

Avalanches in cardiology

Sudden cardiac death (SCD) accounts for 15%–60% of mortality in patients with heart disease. Generally, this has been attributed to ventricular tachyarrhythmia. However, ventricular tachyarrhythmia has been documented or strongly suspected on clinical grounds in a relatively small proportion of SCD patients (8%–50%). Attempted prophylaxis of SCD by implantation of cardioverter-defibrillator is associated with variable success in different subsets of high-risk cardiac patients (30%–70%). A significant number of SCD, therefore, appear to be due to catastrophic circulatory failure. Multiple interdependent compensatory mechanisms help to maintain circulation in advanced cardiac disease. Rapid, unexpected, and massive breakdown of the compensated state can be precipitated by small and often imperceptible triggers. The initial critical but stable state followed by rapid circulatory failure and death has been considered to be analogous to snow avalanches. It is typically described in patients with left ventricular (LV) dysfunction (ischemic or nonischemic). It is now recognized that SCD can also happen in conditions where the right ventricle (RV) takes the brunt of the hemodynamic load. Advanced pulmonary arterial hypertension and operated patients of tetralogy of Fallot with pulmonary regurgitation are of particular interest to pediatric cardiologists. A large amount of data is available on LV changes and mechanics, while relatively little information is available on the mechanisms of RV adaptation to increased load and RV failure. Whether the triggers and the decompensatory processes are similar for the two ventricles is a moot point. This article highlights the currently available knowledge on the pathophysiology of SCD in RV overload states, with special reference to RV adaptive and decompensatory mechanisms, and therapeutic measures that can potentially interrupt the vicious downward course (cardiac avalanches).

Computational Power of Asynchronously Tuned Automata Enhancing the Unfolded Edge of Chaos

Asynchronously tuned elementary cellular automata (AT-ECA) are described with respect to the relationship between active and passive updating, and that spells out the relationship between synchronous and asynchronous updating. Mutual tuning between synchronous and asynchronous updating can be interpreted as the model for dissipative structure, and that can reveal the critical property in the phase transition from order to chaos. Since asynchronous tuning easily makes behavior at the edge of chaos, the property of AT-ECA is called the unfolded edge of chaos. The computational power of AT-ECA is evaluated by the quantitative measure of computational universality and efficiency. It shows that the computational efficiency of AT-ECA is much higher than that of synchronous ECA and asynchronous ECA.

Temperature increase drives critical slowing down of fish ecosystems

Fish ecosystems perform ecological functions that are critically important for the sustainability of marine ecosystems, such as global food security and carbon stock. During the 21st century, significant global warming caused by climate change has created pressing challenges for fish ecosystems that threaten species existence and global ecosystem health. Here, we study a coastal fish community in Maizuru Bay, Japan, and investigate the relationships between fluctuations of ST, abundance-based species interactions and salient fish biodiversity. Observations show that a local 20% increase in temperature from 2002 to 2014 underpins a long-term reduction in fish diversity (∼25%) played out by some native and invasive species (e.g. Chinese wrasse) becoming exceedingly abundant; this causes a large decay in commercially valuable species (e.g. Japanese anchovy) coupled to an increase in ecological productivity. The fish community is analyzed considering five temperature ranges to understand its atemporal seasonal sensitivity to ST changes, and long-term trends. An optimal information flow model is used to reconstruct species interaction networks that emerge as topologically different for distinct temperature ranges and species dynamics. Networks for low temperatures are more scale-free compared to ones for intermediate (15-20°C) temperatures in which the fish ecosystem experiences a first-order phase transition in interactions from locally stable to metastable and globally unstable for high temperatures states as suggested by abundance-spectrum transitions. The dynamic dominant eigenvalue of species interactions shows increasing instability for competitive species (spiking in summer due to intermediate-season critical transitions) leading to enhanced community variability and critical slowing down despite higher time-point resilience. Native competitive species whose abundance is distributed more exponentially have the highest total directed interactions and are keystone species (e.g. Wrasse and Horse mackerel) for the most salient links with cooperative decaying species. Competitive species, with higher eco-climatic memory and synchronization, are the most affected by temperature and play an important role in maintaining fish ecosystem stability via multitrophic cascades (via cooperative-competitive species imbalance), and as bioindicators of change. More climate-fitted species follow temperature increase causing larger divergence divergence between competitive and cooperative species. Decreasing dominant eigenvalues and lower relative network optimality for warmer oceans indicate fishery more attracted toward persistent oscillatory states, yet unpredictable, with lower cooperation, diversity and fish stock despite the increase in community abundance due to non-commercial and venomous species. We emphasize how changes in species interaction organization, primarily affected by temperature fluctuations, are the backbone of biodiversity dynamics and yet for functional diversity in contrast to taxonomic richness. Abundance and richness manifest gradual shifts while interactions show sudden shift. The work provides data-driven tools for analyzing and monitoring fish ecosystems under the pressure of global warming or other stressors. Abundance and interaction patterns derived by network-based analyses proved useful to assess ecosystem susceptibility and effective change, and formulate predictive dynamic information for science-based fishery policy aimed to maintain marine ecosystems stable and sustainable.

The mesoscale order of nacreous pearls

A pearl's distinguished beauty and toughness are attributable to the periodic stacking of aragonite tablets known as nacre. Nacre has naturally occurring mesoscale periodicity that remarkably arises in the absence of discrete translational symmetry. Gleaning the inspiring biomineral design of a pearl requires quantifying its structural coherence and understanding the stochastic processes that influence formation. By characterizing the entire structure of pearls (∼3 mm) in a cross-section at high resolution, we show that nacre has medium-range mesoscale periodicity. Self-correcting growth mechanisms actively remedy disorder and topological defects of the tablets and act as a countervailing process to long-range disorder. Nacre has a correlation length of roughly 16 tablets (∼5.5 µm) despite persistent fluctuations and topological defects. For longer distances (>25 tablets , ∼8.5 µm), the frequency spectrum of nacre tablets follows [Formula: see text] behavior, suggesting that growth is coupled to external stochastic processes-a universality found across disparate natural phenomena, which now includes pearls.

Thermodynamics of fluctuations based on time-and-space averages

We develop nonequilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in nonergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration, we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider nonstationary processes, applying time-and-space averages to characterize nonergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales, but not at large length scales. We further characterize fluctuations in capillary-dominated systems, which are nonstationary due to the irreversibility of cooperative events.

Heavy-tailed abundance distributions from stochastic Lotka-Volterra models

Microbial communities found in nature are composed of many rare species and few abundant ones, as reflected by their heavy-tailed abundance distributions. How a large number of species can coexist in those complex communities and why they are dominated by rare species is still not fully understood. We show how heavy-tailed distributions arise as an emergent property from large communities with many interacting species in population-level models. To do so, we rely on generalized Lotka-Volterra models for which we introduce a global maximal capacity. This maximal capacity accounts for the fact that communities are limited by available resources and space. In a parallel ad hoc approach, we obtain heavy-tailed abundance distributions from logistic models, without interactions, through specific distributions of the parameters. We expect both mechanisms, interactions between many species and specific parameter distributions, to be relevant to explain the observed heavy tails.

The Spread of Ideas in a Network-The Garbage-Can Model

The main goal of our work is to show how ideas change in social networks. Our analysis is based on three concepts: (i) temporal networks, (ii) the Axelrod model of culture dissemination, (iii) the garbage can model of organizational choice. The use of the concept of temporal networks allows us to show the dynamics of ideas spreading processes in networks, thanks to the analysis of contacts between agents in networks. The Axelrod culture dissemination model allows us to use the importance of cooperative behavior for the dynamics of ideas disseminated in networks. In the third model decisions on solutions of problems are made as an outcome of sequences of pseudorandom numbers. The origin of this model is the Herbert Simon’s view on bounded rationality. In the Axelrod model, ideas are conveyed by strings of symbols. The outcome of the model should be the diversity of evolving ideas as dependent on the chain length, on the number of possible values of symbols and on the threshold value of Hamming distance which enables the combination.

Slowed canonical progress in large fields of science

The size of scientific fields may impede the rise of new ideas. Examining 1.8 billion citations among 90 million papers across 241 subjects, we find a deluge of papers does not lead to turnover of central ideas in a field, but rather to ossification of canon. Scholars in fields where many papers are published annually face difficulty getting published, read, and cited unless their work references already widely cited articles. New papers containing potentially important contributions cannot garner field-wide attention through gradual processes of diffusion. These findings suggest fundamental progress may be stymied if quantitative growth of scientific endeavors—in number of scientists, institutes, and papers—is not balanced by structures fostering disruptive scholarship and focusing attention on novel ideas.

In many academic fields, the number of papers published each year has increased significantly over time. Policy measures aim to increase the quantity of scientists, research funding, and scientific output, which is measured by the number of papers produced. These quantitative metrics determine the career trajectories of scholars and evaluations of academic departments, institutions, and nations. Whether and how these increases in the numbers of scientists and papers translate into advances in knowledge is unclear, however. Here, we first lay out a theoretical argument for why too many papers published each year in a field can lead to stagnation rather than advance. The deluge of new papers may deprive reviewers and readers the cognitive slack required to fully recognize and understand novel ideas. Competition among many new ideas may prevent the gradual accumulation of focused attention on a promising new idea. Then, we show data supporting the predictions of this theory. When the number of papers published per year in a scientific field grows large, citations flow disproportionately to already well-cited papers; the list of most-cited papers ossifies; new papers are unlikely to ever become highly cited, and when they do, it is not through a gradual, cumulative process of attention gathering; and newly published papers become unlikely to disrupt existing work. These findings suggest that the progress of large scientific fields may be slowed, trapped in existing canon. Policy measures shifting how scientific work is produced, disseminated, consumed, and rewarded may be called for to push fields into new, more fertile areas of study.

Understanding cytoskeletal avalanches using mechanical stability analysis

Eukaryotic cells are mechanically supported by a polymer network called the cytoskeleton, which consumes chemical energy to dynamically remodel its structure. Recent experiments in vivo have revealed that this remodeling occasionally happens through anomalously large displacements, reminiscent of earthquakes or avalanches. These cytoskeletal avalanches might indicate that the cytoskeleton's structural response to a changing cellular environment is highly sensitive, and they are therefore of significant biological interest. However, the physics underlying "cytoquakes" is poorly understood. Here, we use agent-based simulations of cytoskeletal self-organization to study fluctuations in the network's mechanical energy. We robustly observe non-Gaussian statistics and asymmetrically large rates of energy release compared to accumulation in a minimal cytoskeletal model. The large events of energy release are found to correlate with large, collective displacements of the cytoskeletal filaments. We also find that the changes in the localization of tension and the projections of the network motion onto the vibrational normal modes are asymmetrically distributed for energy release and accumulation. These results imply an avalanche-like process of slow energy storage punctuated by fast, large events of energy release involving a collective network rearrangement. We further show that mechanical instability precedes cytoquake occurrence through a machine-learning model that dynamically forecasts cytoquakes using the vibrational spectrum as input. Our results provide a connection between the cytoquake phenomenon and the network's mechanical energy and can help guide future investigations of the cytoskeleton's structural susceptibility.

Breakdown of random matrix universality in Markov models

Biological systems need to react to stimuli over a broad spectrum of timescales. If and how this ability can emerge without external fine-tuning is a puzzle. We consider here this problem in discrete Markovian systems, where we can leverage results from random matrix theory. Indeed, generic large transition matrices are governed by universal results, which predict the absence of long timescales unless fine-tuned. We consider an ensemble of transition matrices and motivate a temperature-like variable that controls the dynamic range of matrix elements, which we show plays a crucial role in the applicability of the large matrix limit: as the dynamic range increases, a phase transition occurs whereby the random matrix theory result is avoided, and long relaxation times ensue, in the entire "ordered" phase. We furthermore show that this phase transition is accompanied by a drop in the entropy rate and a peak in complexity, as measured by predictive information [Bialek, Nemenman, and Tishby Neural Comput. 13, 2409 (2001)NEUCEB0899-766710.1162/089976601753195969]. Extending the Markov model to a Hidden Markov model (HMM), we show that observable sequences inherit properties of the hidden sequences, allowing HMMs to be understood in terms of more accessible Markov models. We then apply our findings to fMRI data from 820 human subjects scanned at wakeful rest. We show that the data can be quantitatively understood in terms of the random model, and that brain activity lies close to the phase transition when engaged in unconstrained, task-free cognition-supporting the brain criticality hypothesis in this context.

Sand-throwing behaviour in pit-building antlion larvae: insights from finite-element modelling

Sandy pitfall traps of antlions are elaborate constructions to capture prey. Antlions exploit the interactions between the particles in their habitat and build a stable trap. This trap is close to the unstable state; prey items will slide towards the centre-where the antlion ambushes-when entering the trap. This is efficient but requires permanent maintenance. According to the present knowledge, antlions throw sand, mainly to cause sandslides towards the centre of the pit. We hypothesized that: (i) sand-throwing causes sandslides towards the centre of the pit and (ii) sand-throwing constantly maintains the pitfall trap and thus keeps its efficiency high. Using laboratory experiments, as well as finite-element analysis, we tested these hypotheses. We show, experimentally and numerically, that sand that accumulates at the centre of the pit will be removed continuously by sand-throwing, this maintenance is leading to slope condition close to an unstable state. This keeps the slope angle steep and the efficiency of the trap constant. Furthermore, the resulting sandslides can relocate the trapped prey towards the centre of the pit. This study adds further insights from specific mechanical properties of a granular medium into the behavioural context of hunting antlion larvae.

1/x power-law in a close proximity of the Bak-Tang-Wiesenfeld sandpile

A cellular automaton constructed by Bak, Tang, and Wiesenfeld (BTW) in 1987 to explain the 1/f noise was recognized by the community for the theoretical foundations of self-organized criticality (SOC). Their conceptual work gave rise to various scientific areas in statistical physics, mathematics, and applied fields. The BTW core principles are based on steady slow loading and an instant huge stress-release. Advanced models, extensively developed far beyond the foundations for 34 years to successfully explain SOC in real-life processes, still failed to generate truncated 1/x probability distributions. This is done here through returning to the original BTW model and establishing its larger potential than the state-of-the-art expects. We establish that clustering of the events in space and time together with the core principles revealed by BTW lead to approximately 1/x power-law in the size-frequency distribution of model events.

Self-organization of whole-gene expression through coordinated chromatin structural transition

The human DNA molecule is a 2-m-long polymer collapsed into the micrometer space of the cell nucleus. This simple consideration rules out any "Maxwell demon"-like explanation of regulation in which a single regulatory molecule (e.g., a transcription factor) finds autonomously its way to the particular target gene whose expression must be repressed or enhanced. A gene-by-gene regulation is still more contrasting with the physical reality when in the presence of cell state transitions involving the contemporary expression change of thousands of genes. This state of affair asks for a statistical mechanics inspired approach where specificity arises from a selective unfolding of chromatin driving the rewiring of gene expression pattern. The arising of "expression waves" marking state transitions related to chromatin structural reorganization through self-organized critical control of whole-genome expression will be described in the present paper. We adopt as a model system the gene expression time course of a cancer cell (MCF-7) population exposed to an efficient stimulus causing a state transition in comparison with an ineffective stimulus. The obtained results will be put into the perspective of biological adaptive systems living on the edge of chaos.

Aperiodic and Periodic Components of Ongoing Oscillatory Brain Dynamics Link Distinct Functional Aspects of Cognition across Adult Lifespan

Signal transmission in the brain propagates via distinct oscillatory frequency bands but the aperiodic component, 1/f activity, almost always co-exists which most of the previous studies have not sufficiently taken into consideration. We used a recently proposed parameterization model that delimits the oscillatory and aperiodic components of neural dynamics on lifespan aging data collected from human participants using magnetoencephalography (MEG). Since healthy aging underlines an enormous change in local tissue properties, any systematic relationship of 1/f activity would highlight their impact on the self-organized critical functional states. Furthermore, we have used patterns of correlation between aperiodic background and metrics of behavior to understand the domain general effects of 1/f activity. We suggest that age-associated global change in 1/f baseline alters the functional critical states of the brain affecting the global information processing impacting critically all aspects of cognition, e.g., metacognitive awareness, speed of retrieval of memory, cognitive load, and accuracy of recall through adult lifespan. This alteration in 1/f crucially impacts the oscillatory features peak frequency (PF) and band power ratio, which relates to more local processing and selective functional aspects of cognitive processing during the visual short-term memory (VSTM) task. In summary, this study leveraging on big lifespan data for the first time tracks the cross-sectional lifespan-associated periodic and aperiodic dynamical changes in the resting state to demonstrate how normative patterns of 1/f activity, PF, and band ratio (BR) measures provide distinct functional insights about the cognitive decline through adult lifespan.

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models-reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

Self-organized multistability in the forest fire model

The forest fire model in statistical physics represents a paradigm for systems close to but not completely at criticality. For large tree growth probabilities p we identify periodic attractors, where the tree density ρ oscillates between discrete values. For lower p this self-organized multistability persists with incrementing numbers of states. Even at low p the system remains quasiperiodic with a frequency ≈p on the way to chaos. In addition, the power-spectrum shows 1/f^{2} scaling (Brownian noise) at the low frequencies f, which turns into white noise for very long simulation times.

Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, [Formula: see text], that determines the strength of the correlation of the noise. To predict [Formula: see text] the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the [Formula: see text] value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same [Formula: see text] parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community.

Large-scale collaboration in ENIGMA-EEG: A perspective on the meta-analytic approach to link neurological and psychiatric liability genes to electrophysiological brain activity

BACKGROUND AND PURPOSE

The ENIGMA-EEG working group was established to enable large-scale international collaborations among cohorts that investigate the genetics of brain function measured with electroencephalography (EEG). In this perspective, we will discuss why analyzing the genetics of functional brain activity may be crucial for understanding how neurological and psychiatric liability genes affect the brain.

METHODS

We summarize how we have performed our currently largest genome-wide association study of oscillatory brain activity in EEG recordings by meta-analyzing the results across five participating cohorts, resulting in the first genome-wide significant hits for oscillatory brain function located in/near genes that were previously associated with psychiatric disorders. We describe how we have tackled methodological issues surrounding genetic meta-analysis of EEG features. We discuss the importance of harmonizing EEG signal processing, cleaning, and feature extraction. Finally, we explain our selection of EEG features currently being investigated, including the temporal dynamics of oscillations and the connectivity network based on synchronization of oscillations.

RESULTS

We present data that show how to perform systematic quality control and evaluate how choices in reference electrode and montage affect individual differences in EEG parameters.

CONCLUSION

The long list of potential challenges to our large-scale meta-analytic approach requires extensive effort and organization between participating cohorts; however, our perspective shows that these challenges are surmountable. Our perspective argues that elucidating the genetic of EEG oscillatory activity is a worthwhile effort in order to elucidate the pathway from gene to disease liability.

Ensemble synchronization in the reassembly of Hydra's nervous system

Although much is known about how the structure of the nervous system develops, it is still unclear how its functional modularity arises. A dream experiment would be to observe the entire development of a nervous system, correlating the emergence of functional units with their associated behaviors. This is possible in the cnidarian Hydra vulgaris, which, after its complete dissociation into individual cells, can reassemble itself back together into a normal animal. We used calcium imaging to monitor the complete neuronal activity of dissociated Hydra as they reaggregated over several days. Initially uncoordinated neuronal activity became synchronized into coactive neuronal ensembles. These local modules then synchronized with others, building larger functional ensembles that eventually extended throughout the entire reaggregate, generating neuronal rhythms similar to those of intact animals. Global synchronization was not due to neurite outgrowth but to strengthening of functional connections between ensembles. We conclude that Hydra's nervous system achieves its functional reassembly through the hierarchical modularity of neuronal ensembles.

Multiscale criticality measures as general-purpose gauges of proper brain function

The brain is universally regarded as a system for processing information. If so, any behavioral or cognitive dysfunction should lend itself to depiction in terms of information processing deficiencies. Information is characterized by recursive, hierarchical complexity. The brain accommodates this complexity by a hierarchy of large/slow and small/fast spatiotemporal loops of activity. Thus, successful information processing hinges upon tightly regulating the spatiotemporal makeup of activity, to optimally match the underlying multiscale delay structure of such hierarchical networks. Reduced capacity for information processing will then be expressed as deviance from this requisite multiscale character of spatiotemporal activity. This deviance is captured by a general family of multiscale criticality measures (MsCr). MsCr measures reflect the behavior of conventional criticality measures (such as the branching parameter) across temporal scale. We applied MsCr to MEG and EEG data in several telling degraded information processing scenarios. Consistently with our previous modeling work, MsCr measures systematically varied with information processing capacity: MsCr fingerprints showed deviance in the four states of compromised information processing examined in this study, disorders of consciousness, mild cognitive impairment, schizophrenia and even during pre-ictal activity. MsCr measures might thus be able to serve as general gauges of information processing capacity and, therefore, as normative measures of brain health.

The structural connectome constrains fast brain dynamics

Brain activity during rest displays complex, rapidly evolving patterns in space and time. Structural connections comprising the human connectome are hypothesized to impose constraints on the dynamics of this activity. Here, we use magnetoencephalography (MEG) to quantify the extent to which fast neural dynamics in the human brain are constrained by structural connections inferred from diffusion MRI tractography. We characterize the spatio-temporal unfolding of whole-brain activity at the millisecond scale from source-reconstructed MEG data, estimating the probability that any two brain regions will significantly deviate from baseline activity in consecutive time epochs. We find that the structural connectome relates to, and likely affects, the rapid spreading of neuronal avalanches, evidenced by a significant association between these transition probabilities and structural connectivity strengths (r = 0.37, p<0.0001). This finding opens new avenues to study the relationship between brain structure and neural dynamics.

Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data

In many applications, one works with neural network models trained by someone else. For such pretrained models, one may not have access to training data or test data. Moreover, one may not know details about the model, e.g., the specifics of the training data, the loss function, the hyperparameter values, etc. Given one or many pretrained models, it is a challenge to say anything about the expected performance or quality of the models. Here, we address this challenge by providing a detailed meta-analysis of hundreds of publicly available pretrained models. We examine norm-based capacity control metrics as well as power law based metrics from the recently-developed Theory of Heavy-Tailed Self Regularization. We find that norm based metrics correlate well with reported test accuracies for well-trained models, but that they often cannot distinguish well-trained versus poorly trained models. We also find that power law based metrics can do much better—quantitatively better at discriminating among series of well-trained models with a given architecture; and qualitatively better at discriminating well-trained versus poorly trained models. These methods can be used to identify when a pretrained neural network has problems that cannot be detected simply by examining training/test accuracies.

In many machine learning applications, one uses pre-trained neural networks, having limited access to training and test data. Martin et al. show how to predict trends in the quality of such neural networks without access to this information, relevant for reproducibility, diagnostics, and validation.

Assessing the ratio between new Covid-19 cases and new tests for Sars-Cov-2 in Italy by fractal investigation

AIM

processing the heterogeneous data on the Italian Covid-19 epidemic by fractal investigation on the trend curve of the ratio between new Covid19 cases/new Sars-Cov-2 tests.

METHODS

New cases of Covid-19 disease and new tests were calculated from raw data freely available on the Italian governing website. The effectiveness of Italian government Decrees aiming to obtain lock-down was assessed by fractal investigation. Self-similarity parameters of presumed fractal shapes obtained 6 days after each Decree were estimated, when possible. Self-organized criticality was also assessed to check for chaos involvement in disturbing the fractal shapes. Shapes were then compared and were used to estimate the number of new tests for Sars-Cov-2 that Italy would be able to perform.

RESULTS

The full lock-down changed the biocomplexity of the Covid-19 epidemic in Italy. If the biocomplexity of Covid-19 did not change after the lock-down, Italy should have been able to perform at least 25490 tests daily (±8940) on average, while real data show that a larger number of tests were done (p<0.001) (thereby obtaining the lowering of contagions). If the same biocomplexity was observed before full lock down, Italy would be able to perform 7088 tests daily (±5163) on average, while real data show that a lower number of tests were done (p=0.029) (thereby observing the worsening of contagions).

CONCLUSION

in case of heterogeneous data, fractal investigation would be prove useful for assessing and estimating trends.

Detection of crossover points in detrended fluctuation analysis: an application to EEG signals of patients with epilepsy

MOTIVATION

The quantification of long-range correlation of electroencephalogram (EEG) signals is an important research direction for its relevance in helping understanding the brain activity. Epileptic seizures have been studied in the past years where different non-linear statistical approaches have been employed to understand the relationship between the EEG signal and the epileptic discharge. One of the most widely used method for to analyse long memory processes is the detrended fluctuation analysis (DFA). However, no objective and pragmatic methods have been developed to detect crossover points and reference channels in DFA.

RESULTS

In this article, we propose: (i) two automatic approaches that successfully detect crossover points in DFA related methods on the log-log plot and (ii) a criteria to choose the reference channel for the log-amplitude function. Moreover, the DFA is applied to EEG signals of 10 epileptic patients collected from the CHB-MIT database, being the log-amplitude function used to compare the different brain hemispheres by making use of the methodology proposed in the article. The existence of long-range power-law correlations is demonstrated and indicates that the EEG signals of epileptic patients present three well-defined regions with the first region showing a 1/f noise (pink noise) for seven subjects and a random walk behaviour for three subjects. The second and third regions show anti-persistence behaviour. Moreover, the results of the log-amplitude function were divided in two groups: the first, including seven subjects, where the increase in the scales results in an increase in the fluctuation in the frontal channels and the second, included three subjects, where the fluctuation for large scales are greater for the parietal channels.

AVAILABILITY AND IMPLEMENTATION

The functions used in this article are available in the R package DFA (Mesquita et al., 2020).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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

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

Barrier-controlled nonequilibrium criticality in reactive particle systems

Nonequilibrium critical phenomena generally exist in many dynamic systems, like chemical reactions and some driven-dissipative reactive particle systems. Here, by using computer simulation and theoretical analysis, we demonstrate the crucial role of the activation barrier on the criticality of dynamic phase transitions in a minimal reactive hard-sphere model. We find that at zero thermal noise, with increasing the activation barrier, the type of transition changes from a continuous conserved directed percolation into a discontinuous dynamic transition by crossing a tricritical point. A mean-field theory combined with field simulation is proposed to explain this phenomenon. The possibility of Ising-type criticality in the nonequilibrium system at finite thermal noise is also discussed.

Thermodynamic Efficiency of Interactions in Self-Organizing Systems

The emergence of global order in complex systems with locally interacting components is most striking at criticality, where small changes in control parameters result in a sudden global reorganization. We study the thermodynamic efficiency of interactions in self-organizing systems, which quantifies the change in the system's order per unit of work carried out on (or extracted from) the system. We analytically derive the thermodynamic efficiency of interactions for the case of quasi-static variations of control parameters in the exactly solvable Curie-Weiss (fully connected) Ising model, and demonstrate that this quantity diverges at the critical point of a second-order phase transition. This divergence is shown for quasi-static perturbations in both control parameters-the external field and the coupling strength. Our analysis formalizes an intuitive understanding of thermodynamic efficiency across diverse self-organizing dynamics in physical, biological, and social domains.

Neural field theory of neural avalanche exponents

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

Leonardo da Vinci and the search for order in neuroscience

Finding order in disorder is a hallmark of science and art. In the time of Leonardo da Vinci, the schism between science and art had yet to arise. In fact, Leonardo freely used scientific methods for his art and vice versa; for example, when he used his observations of turbulent, whirling water to guide his artistic imagination. Half a millennium later, a cornerstone of modern biology is the continuing search for order in dynamic processes. In neuroscience, the search has focussed on understanding complex spacetime brain dynamics. Recently, turbulence has been shown to be a guiding principle underlying the necessary information processing, supporting Leonardo's search for order in disorder. Here, we argue that Leonardo's seminal insights have ongoing relevance for modern neuroscience.

Early warning signals of failures in building management systems

In the context of sensor data generated by Building Management Systems (BMS), early warning signals are still an unexplored topic. The early detection of anomalies can help preventing malfunctions of key parts of a heating, cooling and air conditioning (HVAC) system that may lead to a range of BMS problems, from important energy waste to fatal errors in the worst case. We analyse early warning signals in BMS sensor data for early failure detection. In this paper, the studied failure is a malfunction of one specific Air Handling Unit (AHU) control system that causes temperature spikes of up to 30 degrees Celsius due to overreaction of the heating and cooling valves in response to an anomalous temperature change caused by the pre-heat coil in winter period in a specific area of a manufacturing facility. For such purpose, variance, lag-1 autocorrelation function (ACF1), power spectrum (PS) and variational autoencoder (VAE) techniques are applied to both univariate and multivariate scenarios. The univariate scenario considers the application of these techniques to the control variable only (the one that displays the failure), whereas the multivariate analysis considers the variables affecting the control variable for the same purpose. Results show that anomalies can be detected up to 32 hours prior to failure, which gives sufficient time to BMS engineers to prevent a failure and therefore, an proactive approach to BMS failures is adopted instead of a reactive one.

Criticality in a multisignal system using principal component analysis

In systems with dynamical transitions, criticality is usually defined by the behavior of suitable individual variables of the system. In the case of time series, the usual procedure involves the analysis of the statistical properties of the selected variable as a function of a control parameter in both the time and frequency domains. An interesting question, however, is how to identify criticality when multiple simultaneous signals are required to provide a reliable representation of the system, especially when the signals exhibit different dynamics and do not individually display the characteristic signs of criticality. In that situation, a technique that analyzes the collective behavior of the signals is necessary. In this work we show that the eigenvalues and eigenvectors obtained from principal components analysis (PCA) can be used as a way to identify collective criticality. To do this, we construct a multilayer Ising model comprised of coupled two-dimensional Ising lattices that have distinct critical temperatures when isolated. We apply PCA to the collection of magnetization signals for a range of global temperatures and study the resulting eigenvalues. We find that there exists a single global temperature at which the eigenvalue spectrum follows a power law, and identify this as an indicator of "multicriticality" for the system. We then apply the technique to electroencephalographic recordings of brain activity, as this is a prime example of multiple signals with distinct individual dynamics. The analysis reveals a power-law eigenspectrum, adding further evidence to the brain criticality hypothesis. We also show that the eigenvectors can be used to distinguish the recordings in the resting state from those during a cognitive task, and that there is important information contained in all eigenvectors, not just the first few dominant ones, establishing that PCA has great utility beyond dimensionality reduction.

Robust cortical criticality and diverse dynamics resulting from functional specification

Despite the recognition of the layered structure and evident criticality in the cortex, how the specification of input, output, and computational layers affects the self-organized criticality has not been much explored. By constructing heterogeneous structures with a well-accepted model of leaky neurons, we find that the specification can lead to robust criticality rather insensitive to the strength of external stimuli. This naturally unifies the adaptation to strong inputs without extra synaptic plasticity mechanisms. Low degree of recurrence constitutes an alternative explanation to subcriticality other than the high-frequency inputs. Unlike fully recurrent networks where external stimuli always render subcriticality, the dynamics of networks with sufficient feedforward connections can be driven to criticality and supercriticality. These findings indicate that functional and structural specification and their interplay with external stimuli are of crucial importance for the network dynamics. The robust criticality puts forward networks of the leaky neurons as promising platforms for realizing artificial neural networks that work in the vicinity of critical points.

What causes sudden death in patients with chronic heart failure and a reduced ejection fraction?

Sudden death characterizes the mode of demise in 30–50% of patients with chronic heart failure and a reduced ejection fraction. Occasionally, these events have an identifiable pathophysiological trigger, e.g. myocardial infarction, catecholamine surges, or electrolyte imbalances, but in most circumstances, there is no acute precipitating mechanism. Instead, adverse left ventricular remodelling and fibrosis creates an exceptionally fragile and highly vulnerable substrate, which can be characterized using the model developed in theoretical physics of ‘self-organizing criticality’. This framework has been applied to describe the genesis of avalanches, nodes of traffic congestion unrelated to an accident, the abrupt system-wide failure of electrical grids, and the initiation of cancer and neurodegenerative diseases. Self-organizing criticality within the ventricular myocardium relies on complex adaptations to progressive stress and stretch, which evolve inevitably to an abrupt end (termed ‘cascading failure’), even though the rate of deterioration of the underlying disease process has not changed. The result is acute circulatory collapse (i.e. sudden death) in the absence of an identifiable triggering event. Cascading failure in a severely remodelled or fibrotic heart can become manifest electrically as a first-time ventricular tachyarrhythmia that is responsive to the shock delivered by an implantable cardioverter-defibrillator (ICD). Alternatively, it may present as an acute mechanical failure, which is manifest as (i) asystole, bradyarrhythmia, or electromechanical dissociation; or (ii) incessant ventricular fibrillation that persists despite repetitive ICD discharges; in both instances, the sudden deaths cannot be prevented by an ICD. This conceptual framework explains why anti-remodelling and antifibrotic interventions (i.e. neurohormonal antagonists and cardiac resynchronization) reduce the risk of sudden death in patients with heart failure in the absence of an ICD and provide incremental benefits in those with an ICD. The adoption of anti-remodelling and antifibrotic treatments may explain why the incidence of sudden death in clinical trials of heart failure has declined dramatically over the past 10–15 years, independent of the use of ICDs.