Concept Of Self-organized Criticality Research Articles

Quantum logic automata generate class IV-like patterns and [formula omitted] 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.

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.

Integrative biology for integrative medicine: A complete approach

BackgroundIndia's AYUSH systems of medicine, Ayurveda, Yoga and Naturopathy, Unani, Siddha and Sowa-Rigpa, and Homeopathy, use natural self-healing abilities of body and mind. Their ways to treat non-communicable diseases reduce use of modern drugs with their side-effects. Scientific acceptance requires them to be explained from a modern biological perspective. This paper indicates how to achieve such an integrative approach, using aspects of biology not yet taught in medical schools. MethodsA new, ‘Sandwich Model’ of biology is introduced that includes holistic epigenetic regulation; also, complexity biology's concept of self-organized criticality; a systems treatment of organism function from Ayurveda; and Ayurveda's six stages of etiology, Shadkriyakala. ResultsMolecular biology is upgraded by the sandwich model's layer of epigenetics, leading to a new, scientific definition of health as optimized regulation. Fractal Physiology then expands this to explain self-healing, used in all AYUSH systems. Ayurveda contributes in two ways: its systems approach yields a holistic understanding of organism functioning, while Shadkriyakala improves our understanding of pathophysiology. DiscussionThese additions create an integrative biology; modern biology expands to include AYUSH systems' concepts. It provides a scientific basis for India's plan for integrative medical education, with AYUSH systems treated as equal to modern medicine.

Fractal analysis in the quantification of medical imaging associated with multiple sclerosis pathology.

Multiple sclerosis (MS) is an inveterate phlogistic situation characterized by focal and vaguely diffusive de-myelination and neurodegeneration, in the sphere of central nervous system (CNS). The brain's chronic inflammatory reaction includes astrocyte stimulation and microglial motivation, as well as macrophages marginal conscription. This lasting serious soreness of the brain is connected with neurodegeneration period and disability advance. The present study is considering two main purposes as follows. Primarily, to apply the fractal analysis in the idea of documenting the fractals dominance at all stages of the nervous system hierarchy, giving faith to the precept of their funciar relevancy. Secondly, to take into account the problems unresolved of the thorough connections between self-organized criticality concept and self-similarity notion. More precisely, in reality we will obtain information about the fractal size and lacunarity of magnetic resonance imaging (MRI), on the areas of interest of the brain, rich in microglial cells with fringes from peripheral macrophages cells. This approach will play a decisive role in the action of detecting neural disabilities, such as in particular multiple sclerosis cortical onset, the final goal of our investigation. The diagnosis is based on interpretation of both histological sample pictures and images obtained by nuclear magnetic resonance. Using fractal analysis, we have calculated, for each image separately, both the fractal dimension and the lacunarity, as an objective quantitative measure of the demyelinating action. For three histopathological samples on glial cells, with visible erosions, the fractal dimension has value over 1.89 and the lacunarity value is between 0.050 and 0.079. In the gray level stages of the studied MRI pictures, the fractal dimension is above the value of 1.7 and the lacunarity is between the values of 0.0286 and 0.0393.

Self-organized criticality: a new approach to multihadron production

We apply the concept of self-organized criticality in statistical physics to the study of multihadron production in high energy collisions.

Criticality or Supersymmetry Breaking?

In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In contrast with the phenomenological concept of self-organized criticality, the recently found approximation-free supersymmetric theory of stochastics (STS) identifies this phase as the noise-induced chaos (N-phase), i.e., the phase where the topological supersymmetry pertaining to all stochastic dynamical systems is broken spontaneously by the condensation of the noise-induced (anti)instantons. Here, we support this picture in the context of neurodynamics. We study a 1D chain of neuron-like elements and find that the dynamics in the N-phase is indeed featured by positive stochastic Lyapunov exponents and dominated by (anti)instantonic processes of (creation) annihilation of kinks and antikinks, which can be viewed as predecessors of boundaries of neuroavalanches. We also construct the phase diagram of emulated stochastic neurodynamics on Spikey neuromorphic hardware and demonstrate that the width of the N-phase vanishes in the deterministic limit in accordance with STS. As a first result of the application of STS to neurodynamics comes the conclusion that a conscious brain can reside only in the N-phase.

Nonstationary Fast-driven, Self-organized Criticality in Solar Flares

Abstract The original concept of self-organized criticality, applied to solar flare statistics, assumed a slow-driven and stationary flaring rate, which implies timescale separation (between flare durations and interflare waiting times). The concept reproduces power-law distributions for flare peak fluxes and durations, but predicts an exponential waiting time distribution. In contrast to these classical assumptions, we observe (i) multiple energy dissipation episodes during most flares, (ii) violation of the principle of timescale separation, (iii) a fast-driven and nonstationary flaring rate, (iv) a power-law distribution for waiting times Δt, with a slope of α Δt ≈ 2.0, as predicted from the universal reciprocality between mean flaring rates and mean waiting times, and (v) pulses with rise times and decay times of the dissipated magnetic free energy on timescales of 12 ± 6 minutes, and up to 13 times in long-duration (≲4 hr) flares. These results are inconsistent with coronal long-term energy storage, but require photospheric–chromospheric current injections into the corona.

Quantifying fire trends in boreal forests with Landsat time series and self-organized criticality

Boreal forests are globally extensive and store large amounts of carbon, but recent climate change has led to drier conditions and increasing fire activity. The objective of this study is to quantify trends in fire size and frequency using data spanning multiple scales in space and time. We use multi-temporal Landsat image compositing on Google Earth Engine and validate results with reference fire maps from the Canadian Park Service. We also interpret general fire trends through the concept of Self-Organized Criticality (SOC). Our study site is Wood Buffalo National Park, which is a fire hot spot in Canada due to frequent lightning ignitions. The relativize differenced normalized burn ratio (RdNBR) was the most accurate Landsat-based burn severity metric we evaluated (52.2% producer's accuracy, 87.6% user's accuracy). The Landsat-based burn severity maps provided a better fit for a linear relationship on the log-log scale of fire size and frequency than a manually drawn fire map. Landsat-based fire trends since 1990 conformed to a power-law distribution with a slope of 1.9, which is related to fractal dimensions of the satellite-based fire perimeter shapes. The unburned and low-severity patches within the burn severity mosaic influenced the power-law slope and associated fractal dimensionality. This study demonstrates a multi-scale and multi-dataset technique to quantify general fire trends and changing fire cycles in remote locations and establishes a baseline database for assessing future fire activity. Testing criticality by power laws helps to quantify emergent trends of contemporary fire regimes, which could inform the strategic application of prescribed fire and other management activities. Natural resource managers can utilize information from this study to understand local ecosystem adaptability to large fire events and ecosystem stability in the context of recent increasing fire activity.

Hierarchical block model for earthquakes.

The presented model for earthquakes is based on two fundamental principles: the hierarchical structure of seismic areas and the concept of self-organized criticality. The model reproduces the basic empirical properties of seismic processes: the frequency-energy scaling relation (the Gutenberg-Richter law), the generalized Omori law for temporal decay of aftershocks, the aftershock productivity law, the fractal distributions of hypocenters (epicenters) with power-law dependencies of the number of events on distances between hypocenters (epicenters), and, finally, the γ distribution for waiting times. In the model, the threshold energies depend on the block sizes and are distributed according to the Gauss law. After strong earthquakes they are redistributed at the decreasing average values. The change of threshold energies leads to the triggering of aftershock series.

Defect Structure of Deformed Heterogeneous Materials: Acoustic Emission and X-Ray Microtomography

Laboratory investigations of deformation of heterogeneous brittle materials (rocks) by acoustic emission (AE) and X-ray computer microtomography (CT) are presented. The experiments involved loading of cylindrical samples of Westerly granite under the condition of uniaxial compression and recording of AE signals emitted during deformation of samples at different loading-unloading stages. After each unloading of the sample a tomographic survey was performed. Totally, 11 loading-unloading stages and tomographic surveys were carried out. The defect structure evolution is considered in the framework of the concept of self-organized criticality. It has been found that the type of the energy distribution function of AE signals can be used as an indicator of the deformed material state and transition to a critical fracture stage. An exponential function points to a noncritical state of a deformed material, and a power-law function indicates that the defect accumulation has passed to a critical stage. This result is confirmed by X-ray microtomographic data.

Application of the Theory of Self-Organized Criticality to the Investigation of Historical Processes

The article demonstrates heuristic possibilities of the theory of self-organized criticality (SOC) in the investigation of historical processes. Key SOC concepts and ideas are explained. Specifically, tools that can be used for identifying pink noise, an attribute of a critical state, are described. The results of spectral analyses of historical demographic data (i.e., birth and death rates in Russian settlements in the 19th and 20th centuries) and historical market data (i.e., grain prices in regions of Russia in the 18th, 19th, and early 20th centuries) are presented. It was found that noise color in the data series differed substantially across different periods. Based on these observations, the assumption that a change in noise color can serve as an indicator of changes in historical processes was made. In some cases, this indicator can enable one to establish the time, speed, and direction of state changes in historical processes. Pink noise was discovered in the examined birth and death rate dynamics, as well as in the dynamics of prices across periods. The described methods have the potential to be used beyond the limits of the presently considered historical subjects, including in investigations of different types of social transformation.

Hydrologic Modification and Vanishing Self-Organized Criticality of River Flows Caused by Dam Operations

AbstractWidespread dam construction has significantly altered natural hydrologic processes and consequently affected river ecosystems. The concept of self-organized criticality (SOC) implies the ability of a system to create and maintain its own function and has important implications for the entire ecosystem, thus can be used to assess anthropogenic disturbances. This study focuses on how reservoir operations affect the SOC behavior of river flows. Taking five large-sized reservoirs in China as examples, the maximum likelihood methods, Kolmogorov Smirnov testing and Detrended Fluctuation Analysis, are used to examine the typical SOC fingerprints for daily river flow series, including their power law frequency-magnitude distributions and long-range correlations. The results show that with increasing reservoir-modified pressure, the frequency-magnitude relationships of natural flows gradually deviate from heavy-tailed power laws and tend to behave as normal or lognormal distributions, characterized by vani...

25 Years of Self-organized Criticality: Space and Laboratory Plasmas

Studies of complexity in extended dissipative dynamical systems, in nature and in laboratory, require multiple approaches and the framework of self-organized criticality (SOC) has been used extensively in the studies of such nonequilibrium systems. Plasmas are inherently nonlinear and many ubiquitous features such as multiscale behavior, intermittency and turbulence have been analyzed using SOC concepts. The role of SOC in advancing our understanding of space and laboratory plasmas as nonequilibrium systems is reviewed in this article. The main emphasis is on how SOC and related approaches have provided new insights and models of nonequilibrium plasma phenomena. Among the natural plasmas the magnetosphere, driven by the solar wind, is a prominent example and extensive data from ground-based and space-borne instruments have been used to study phenomena of direct relevance to space weather, viz. geomagnetic storms and substorms. During geomagnetically active periods the magnetosphere is far from equilibrium, due to its internal dynamics and being driven by the turbulent solar wind, and substorms are prominent features of the complex driven system. Studies using solar wind and magnetospheric data have shown both global and multiscale features of substorms. While the global behavior exhibits system-wide changes, the multiscale behavior shows scaling features. Along with the studies based on observational data, analogue models of the magnetosphere have advanced the understanding of space plasmas as well as the role of SOC in natural systems. In laboratory systems, SOC has been used in modeling the plasma behavior in fusion experiments, mainly in tokamaks and stellarators. Tokamaks are the dominant plasma confinement system and modeling based on SOC have provided a complementary approach to the understanding of plasma behavior under fusion conditions. These studies have provided insights into key features of toroidally confined plasmas, e.g., the existence of critical temperature gradients above which the transport rates increase drastically. The SOC models address the transport properties from a more general approach, compared to those based on turbulence arising from specific plasma instabilities, and provide a better framework for modeling features such as superdiffusion. The studies of space and laboratory plasmas as nonequilibrium systems have been motivated by features such as scaling and critical behavior, and have provided new insights by highlighting the properties that are common with other systems.

Complex networks and activity spreading

We give a brief survey of the basic notions of the theory of complex networks and various models of activity spreading in networks. We consider the role of random graph theory for the study of complex networks, describe small world and scale-free networks, activity spreading models in social networks, percolation processes, the concept of self-organized criticality, and two versions of its formalization: cellular automata and the chip firing game. We note the common elements of all considered models.

Approaching Criticality via the Zero Dissipation Limit in the Abelian Avalanche Model

The discrete height abelian sandpile model was introduced by Bak, Tang & Wiesenfeld and Dhar as an example for the concept of self-organized criticality. When the model is modified to allow grains to disappear on each toppling, it is called bulk-dissipative. We provide a detailed study of a continuous height version of the abelian sandpile model, called the abelian avalanche model, which allows an arbitrarily small amount of dissipation to take place on every toppling. We prove that for non-zero dissipation, the infinite volume limit of the stationary measure of the abelian avalanche model exists and can be obtained via a weighted spanning tree measure. We show that in the whole non-zero dissipation regime, the model is not critical, i.e., spatial covariances of local observables decay exponentially. We then study the zero dissipation limit and prove that the self-organized critical model is recovered, both for the stationary measure and for the dynamics. We obtain rigorous bounds on toppling probabilities and introduce an exponent describing their scaling at criticality. We rigorously establish the mean-field value of this exponent for $d > 4$.

Seismic waves in 3-D: from mantle asymmetries to reliable seismic hazard assessment

A global cross-section of the Earth parallel to the tectonic equator (TE) path, the great circle representing the equator of net lithosphere rotation, shows a difference in shear wave velocities between the western and eastern flanks of the three major oceanic rift basins. The low-velocity layer in the upper asthenosphere, at a depth range of 120 to 200 km, is assumed to represent the decoupling between the lithosphere and the underlying mantle. Along the TE-perturbed (TE-pert) path, a ubiquitous LVZ, about 1,000-km-wide and 100-km-thick, occurs in the asthenosphere. The existence of the TE-pert is a necessary prerequisite for the existence of a continuous global flow within the Earth. Ground-shaking scenarios were constructed using a scenario-based method for seismic hazard analysis (NDSHA), using realistic and duly validated synthetic time series, and generating a data bank of several thousands of seismograms that account for source, propagation, and site effects. Accordingly, with basic self-organized criticality concepts, NDSHA permits the integration of available information provided by the most updated seismological, geological, geophysical, and geotechnical databases for the site of interest, as well as advanced physical modeling techniques, to provide a reliable and robust background for the development of a design basis for cultural heritage and civil infrastructures. Estimates of seismic hazard obtained using the NDSHA and standard probabilistic approaches are compared for the Italian territory, and a case-study is discussed. In order to enable a reliable estimation of the ground motion response to an earthquake, three-dimensional velocity models have to be considered, resulting in a new, very efficient, analytical procedure for computing the broadband seismic wave-field in a 3-D anelastic Earth model.

Pragmatic Choice in Conversation

How do people decide what to say in context? Many theories of pragmatics assume that people have specialized knowledge that drives them to utter certain words in different situations. But these theories are mostly unable to explain both the regularity and variability in people's speech behaviors. Our purpose in this article is to advance a view of pragmatics based on complexity theory, which specifically explains the pragmatic choices speakers make in conversations. The concept of self-organized criticality sheds light on how a history of utterances and subtle details of a situation surrounding a conversation may directly specify language behavior. Under this view, pragmatic choice in discourse does not reflect the output of any dedicated pragmatic module but arises from a complex coordination or coupling between speakers and their varying communicative tasks.

Frequency distributions: from the sun to the earth

Abstract. The space environment is forever changing on all spatial and temporal scales. Energy releases are observed in numerous dynamic phenomena (e.g. solar flares, coronal mass ejections, solar energetic particle events) where measurements provide signatures of the dynamics. Parameters (e.g. peak count rate, total energy released, etc.) describing these phenomena are found to have frequency size distributions that follow power-law behavior. Natural phenomena on Earth, such as earthquakes and landslides, display similar power-law behavior. This suggests an underlying universality in nature and poses the question of whether the distribution of energy is the same for all these phenomena. Frequency distributions provide constraints for models that aim to simulate the physics and statistics observed in the individual phenomenon. The concept of self-organized criticality (SOC), also known as the "avalanche concept", was introduced by Bak et al. (1987, 1988), to characterize the behavior of dissipative systems that contain a large number of elements interacting over a short range. The systems evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. It is found that frequency distributions of the output parameters from the chain reaction taken over a period of time can be represented by power-laws. During the last decades SOC has been debated from all angles. New SOC models, as well as non-SOC models have been proposed to explain the power-law behavior that is observed. Furthermore, since Bak's pioneering work in 1987, people have searched for signatures of SOC everywhere. This paper will review how SOC behavior has become one way of interpreting the power-law behavior observed in natural occurring phenomenon in the Sun down to the Earth.

Biophysical Models of Human Behavior: Is There A Place for Logic?

Renato Ramos (2011) uses Bak, Tang, and Wiesenfeld's (1987) concept of self-organized criticality (SOC) to recontextualize free will in social terms by demonstrating that “behavior of human social ...

Biophysical Models of Human Behavior: Is There a Place for Free Will?

This article proposes a recontextualization of the conception of free will in terms of social events rather than in mental experiences. My objective is to demonstrate that the behavior of human social groups composed of individuals freely interacting among each other exhibits well-defined patterns that can precisely be described by a physics formalism. Although not directly approaching the nature of the mental states involved in each individual behavior, I argue that the emergence of organized social behavior occurs under the influence of free will. First, I briefly introduce the concept of self-organized criticality (SOC) that is central to the understanding of my argument. Second, I review experimental data showing that normal individuals and patients with different mental disorders exhibit a social behavior pattern compatible with the presence of SOC. Third, a brief discussion about the functioning of free will in psychiatric disorders is presented. Finally, the implications for psychological and social theories of including free will in this kind of physical model are discussed.