scholarly journals Neuronal avalanches recorded in the awake and sleeping monkey do not show a power law but can be reproduced by a self-organized critical model

2009 ◽  
Vol 10 (S1) ◽  
Author(s):  
Viola Priesemann ◽  
Michael Wibral ◽  
Matthias HJ Munk
Keyword(s):  
Power Law ◽  
Self Organized ◽  
Critical Model ◽  
Neuronal Avalanches

Subtle nonlinearity in popular album charts

1999 ◽  
Vol 02 (03) ◽  
pp. 197-208 ◽  
Author(s):  
R. Alexander Bentley ◽  
Herbert D. G. Maschner
Keyword(s):  
Time Series ◽  
Popular Music ◽  
Power Law ◽  
Large Scale ◽  
Selective Sampling ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Critical Model ◽  
Power Law Distributions ◽  
Multiplicative Processes

Large-scale patterns of culture change may be explained by models of self organized criticality, or alternatively, by multiplicative processes. We speculate that popular album activity may be similar to critical models of extinction in that interconnected agents compete to survive within a limited space. Here we investigate whether popular music albums as listed on popular album charts display evidence of self-organized criticality, including a self-affine time series of activity and power-law distributions of lifetimes and exit activity in the chart. We find it difficult to distinguish between multiplicative growth and critical model hypotheses for these data. However, aspects of criticality may be masked by the selective sampling that a "Top 200" listing necessarily implies.

scholarly journals Observational evidence in favor of scale-free evolution of sunspot groups

2018 ◽  
Vol 618 ◽  
pp. A183
Author(s):  
A. Shapoval ◽  
J.-L. Le Mouël ◽  
M. Shnirman ◽  
V. Courtillot
Keyword(s):  
Weibull Distribution ◽  
Power Law ◽  
Large Range ◽  
Scale Free ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Spatio Temporal ◽  
Computational Procedures ◽  
Definition Of ◽  
Sunspot Groups

Context. The hypothesis stating that the distribution of sunspot groups versus their size (φ) follows a power law in the domain of small groups was recently highlighted but rejected in favor of a Weibull distribution. Aims. In this paper we reconsider this question, and are led to the opposite conclusion. Methods. We have suggested a new definition of group size, namely the spatio-temporal “volume” (V) obtained as the sum of the observed daily areas instead of a single area associated with each group. Results. With this new definition of “size”, the width of the power-law part of the distribution φ ∼ 1/Vβ increases from 1.5 to 2.5 orders of magnitude. The exponent β is close to 1. The width of the power-law part and its exponent are stable with respect to the different catalogs and computational procedures used to reduce errors in the data. The observed distribution is not fit adequately by a Weibull distribution. Conclusions. The existence of a wide 1/V part of the distribution φ suggests that self-organized criticality underlies the generation and evolution of sunspot groups and that the mechanism responsible for it is scale-free over a large range of sizes.

scholarly journals STABILITY ANALYSIS OF CELLULAR AUTOMATA GENERATED CLUSTERS

2005 ◽  
Vol 12 (1) ◽  
pp. 83-90
Author(s):  
R. Šiugždaite
Keyword(s):  
Cellular Automata ◽  
Power Law ◽  
State Parameter ◽  
Urban System ◽  
Complex Behaviour ◽  
Cellular Automata Model ◽  
Self Organized ◽  
Tai Ji ◽  
Long Time ◽  
Ca Model

The development of regional urban system still remains one of the main problems during the human race history. There are a lot of problems inside this system like overcrowded cities and decaying countryside. All these situations can be reproduced by modelling them using Cellular Automata (CA) [1, 2, 5]. CA models implement algorithms with simple rules and parameter controls, but the result can be a complex behaviour. A stability of naturally formed self‐organized urban system depends on its critical state parameter τ in the power law log(f(x)) = ‐τlog(x). If the system reaches self‐organized critical (SOC) state then it remains in it for a long time. The CA model URBACAM (URBAnistic Cellular Automata Model) describes the long‐lasting term behaviour and shows that the change in behaviour is sensitive to the urban parameter τ of the power law. Regionines urbanistines sistemos vystymasis išlieka viena iš opiausiu problemu žmonijos istorijoje. Keletas tokiu uždaviniu kaip miestu perpildymas, nykstančios kaimo vietoves ir t.t. gali būti nesunkiai modeliuojami naudojant lasteliu automatus (LA). LA metodas ypatingas tuo, kad realizuoja algoritma paprastu taisykliu bei parametru valdymo pagalba, tačiau rezultate galima gauti sudetinga elgsena. Natūraliai susiformavusiu urbanistiniu sistemu stabilumas priklauso nuo sistemos krizines savirangos būsenos (KSB) parametro τ. Jei sistema pasiekia KSB, tai ji ilga laika išlieka joje. LA modelis URBACAM charakterizuoja ilgalaike elgsena ir parodo, jog modelyje jos kitimus itakoja eksponentinio desnio urbanistinis parametras τ.

scholarly journals Extra investigation of the self-organized critical Manna model at higher critical dimension

2021 ◽  
pp. 1-12
Author(s):  
Andrey Viktorovich Podlazov
Keyword(s):  
Power Law ◽  
Critical Dimension ◽  
The Self ◽  
Two Dimensional ◽  
Upper Critical Dimension ◽  
Self Organized ◽  
Logarithmic Corrections ◽  
Universal Indicator ◽  
Sandpile Models ◽  
Power Law Distributions

I investigate the nature of the upper critical dimension for isotropic conservative sandpile models and calculate the emerging logarithmic corrections to power-law distributions. I check the results experimentally using the case of Manna model with the theoretical solution known for all statement starting from the two-dimensional one. In addition, based on this solution, I construct a non-trivial super-universal indicator for this model. It characterizes the distribution of avalanches by time the border of their region needs to pass its width.

"SPIRAL WAVE–TRAVELING CLUSTERING" INTERMITTENCY AND 1/f-NOISE IN A 2D COUPLED MAP LATTICE

1999 ◽  
Vol 09 (05) ◽  
pp. 929-937 ◽  
Author(s):  
MARK A. PUSTOVOIT ◽  
VALERY I. SBITNEV
Keyword(s):  
Probability Density ◽  
Exponential Decay ◽  
Power Law ◽  
Strange Attractor ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
The Self ◽  
Saddle Node Bifurcation ◽  
Self Organized

Intermittency of checkerboard spiral waves and traveling clusterings originating from sudden shrinking of the strange attractor of the 2D CML in the neighborhood of the saddle-node bifurcation boundary is found. A power-law probability density for lifetimes in the spiral wave (laminar) phase is observed, while in the checkerboard clusterings (bursting) phase the above quantity exhibits an exponential decay. This difference can be interpreted through the self-organized behavior of the spiral waves, and the passive relaxation of the disordered checkerboard clusterings.

Self-Organized Criticality and Dynamic Instability of Microtubule Growth

1995 ◽  
Vol 50 (9-10) ◽  
pp. 739-740 ◽  
Author(s):  
Peter Babinec ◽  
Melánia Babincová
Keyword(s):  
Power Law ◽  
Dynamic Instability ◽  
Relative Number ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Microtubule Growth

Abstract We have shown that the distribution of lengths of site nucleated microtubules obey an algebraic power law relationship D(s) = As-τ, where D(s) is relative number of microtubules with length 5, A and τ are constants. This relationship indicates the possibility of a self-organized criticality in the dynamic instability of microtubule growth

scholarly journals Avalanches and criticality in self-organized nanoscale networks

2019 ◽  
Vol 5 (11) ◽  
pp. eaaw8438 ◽  
Author(s):  
J. B. Mallinson ◽  
S. Shirai ◽  
S. K. Acharya ◽  
S. K. Bose ◽  
E. Galli ◽  
...  
Keyword(s):  
Integrated Circuits ◽  
Power Law ◽  
Low Cost ◽  
Reservoir Computing ◽  
Critical Dynamics ◽  
Computational Approaches ◽  
Self Organized ◽  
Computational Performance ◽  
The Brain ◽  
Regular Arrays

Current efforts to achieve neuromorphic computation are focused on highly organized architectures, such as integrated circuits and regular arrays of memristors, which lack the complex interconnectivity of the brain and so are unable to exhibit brain-like dynamics. New architectures are required, both to emulate the complexity of the brain and to achieve critical dynamics and consequent maximal computational performance. We show here that electrical signals from self-organized networks of nanoparticles exhibit brain-like spatiotemporal correlations and criticality when fabricated at a percolating phase transition. Specifically, the sizes and durations of avalanches of switching events are power law distributed, and the power law exponents satisfy rigorous criteria for criticality. These signals are therefore qualitatively and quantitatively similar to those measured in the cortex. Our self-organized networks provide a low-cost platform for computational approaches that rely on spatiotemporal correlations, such as reservoir computing, and are an important step toward creating neuromorphic device architectures.

Power-Law Phenomena in Adhesive De-Bonding

1996 ◽  
Vol 458 ◽  
Author(s):  
G. Kendall ◽  
P. J. Cote ◽  
D. Crayon ◽  
F. J. Bonetto
Keyword(s):  
Power Law ◽  
Characteristic Length ◽  
Power Laws ◽  
Structural Features ◽  
Fractal Nature ◽  
Pressure Sensitive Adhesive ◽  
Self Organized ◽  
Pressure Sensitive ◽  
Self Organized Criticality ◽  
Glass Interface

ABSTRACTAcoustic emission (AE) events were recorded during the peeling of pressure-sensitive adhesive (PSA) tape from a silicate glass surface. The distributions of AE event durations and energies are found to have the form of power laws. Power-law dependencies (hyperbolic distributions) are recognized as a consequence of self-organized criticality (SOC), resulting from the absence of any characteristic length or time scales. In these studies, standard optical microscopy was used to characterize the fractal nature of the PSA-glass interface. The present results suggest that it is the inherent static structural features found at the fractal PSA-glass interface which produce the observed hyperbolic distributions in AE events, rather than a true SOC process.

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