Different Avalanche Behaviors in Different Specific Areas of a System Based on Neural Networks

Based on the standard self-organizing map (SOM) neural network model and an integrate-and-fire mecha-nism, we introduce a kind of coupled map lattice system to investigate scale-invariance behavior in the activity of model neural populations. We find power-law distribution behavior of avalanche size in our model. But more importantly, we find there are different avalanche distribution behaviors in different specific areas of our system, which are formed by the topological learning process of the SOM net.     

Different Avalanche Behaviors in Different Specific Areas of a System Based on Neural Networks

Based on the standard self-organizing map (SOM) neural network model and an integrate-and-fire mecha-nism, we introduce a kind of coupled map lattice system to investigate scale-invariance behavior in the activity of modelneural populations. We find power-law distribution behavior of avalanche size in our model. But more importantly, wefind there are different avalanche distribution behaviors in different specific areas of our system, which are formed by thetopological learning process of the SOM net.     

Self-organized Critical Model Based on Complex Brain Networks with Hierarchical Organization

The dynamical behavior in the cortical brain network of macaque is studied by modelling each cortical area with a subnetwork of interacting excitable neurons. We find that the avalanche of our model on different levels exhibits power-law. Furthermore the power-law exponent of the distribution and the average avalanche size are affected by the topology of the network.     

Self-organized Criticality in a Model Based on Neural Network

Based on the LISSOM neural network model, we introduce a model to investigate self-organized criticality in the activity of neural populations. The influence of connection (synapse) between neurons has been adequately considered in this model. It is found to exhibit self-organized criticality (SOC) behavior under appropriate conditions. We also find that the learning process has promotive influence on emergence of SOC behavior. In addition, we analyze the influence of various factors of the model on the SOC behavior, which is characterized by the power-law behavior of the avalanche size distribution.     

Self-organized criticality model for brain plasticity

Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Here we present a model that is based on self-organized criticality and takes into account brain plasticity, which is able to reproduce the spectrum of electroencephalograms (EEG). The model consists of an electrical network with threshold firing and activity-dependent synapse strengths. The system exhibits an avalanche activity in a power-law distribution. The analysis of the power spectra of the electrical signal reproduces very robustly the power-law behavior with the exponent 0.8, experimentally measured in EEG spectra. The same value of the exponent is found on small-world lattices and for leaky neurons, indicating that universality holds for a wide class of brain models.     

Self-organized Criticality in an Integrate-and-Fire Neuron Model Based on Modified Aging Networks

Based on an integrate-and-fire mechanism, we investigate self-organized criticality of a simple neuron model on a modified BA scale-free network with aging nodes. In our model, we find that the distribution of avalanche size follows power-law behavior. The critical exponent τ depends on the aging exponent α. The structures of the network with aging of nodes change with an increase of α. The different topological structures lead to different behaviors in models of integrate-and-fire neurons.     

Avalanche dynamics of idealized neuron function in the brain on an uncorrelated random scale-free network

We study a simple model for a neuron function in a collective brain system. The neural network is composed of an uncorrelated configuration model (UCM) for eliminating the degree correlation of dynamical processes. The interaction of neurons is assumed to be isotropic and idealized. These neuron dynamics are similar to biological evolution in extremal dynamics with locally isotropic interaction but has a different time scale. The functioning of neurons takes place as punctuated patterns based on avalanche dynamics. In our model, the avalanche dynamics of neurons exhibit self-organized criticality which shows power-law behavior of the avalanche sizes. For a given network, the avalanche dynamic behavior is not changed with different degree exponents of networks, γ≥2.4 and various refractory periods referred to the memory effect, T_r. Furthermore, the avalanche size distributions exhibit power-law behavior in a single scaling region in contrast to other networks. However, return time distributions displaying spatiotemporal complexity have three characteristic time scaling regimes Thus, we find that UCM may be inefficient for holding a memory.     

Self-organized Criticality in Hierarchical Brain Network

It is shown that the cortical brain network of the macaque displays a hierarchically clustered organization and the neuron network shows small-world properties. Now the two factors will be considered in our model and the dynamical behavior of the model will be studied. We study the characters of the model and find that the distribution of avalanche size of the model follows power-law behavior.     

Driving rate effects in avalanche-mediated first-order phase transitions

We study the driving-rate and temperature dependence of the power-law exponents that characterize the avalanche distribution in first-order phase transitions. Measurements of acoustic emission in structural transitions in Cu-Zn-Al and Cu-Al-Ni are presented. We show how the observed behavior emerges within a general framework of competing time scales of avalanche relaxation, driving rate, and thermal fluctuations. We confirm our findings by numerical simulations of a prototype model.     

Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally under strongly nonequilibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such a system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.     

A Modified Earthquake Model Based on Generalized Barabási-Albert Scale-Free Networks

A modified Olami-Feder-Christensen model of self-organized criticality on generalized Barabási-Albert (GBA) scale-free networks is investigated. We find that our model displays power-law behavior and the avalanche dynamical behavior is sensitive to the topological structure of networks. Furthermore, the exponent τ of the model depends on b, which weights the distance in comparison with the degree in the GBA network evolution.     

Influence of Selective Edge Removal and Refractory Period in a Self-Organized Critical Neuron Model

A simple model for a set of integrate-and-fire neurons based on the weighted network is introduced. By considering the neurobiological phenomenon in brain development and the difference of the synaptic strength, we construct weighted networks develop with link additions and followed by selective edge removal. Thenetwork exhibits the small-world and scale-free properties with high network efficiency. The model displays an avalanche activity on a power-law distribution. We investigate the effect of selective edge removal and the neuron refractory period on the self-organized criticality of the system.     

Inversion symmetry and exact critical exponents of dissipating waves in the sandpile model

By an inversion symmetry, we show that in the Abelian sandpile model the probability distribution of dissipating waves of topplings that touch the boundary of the system shows a power-law relationship with critical exponent 5/8 and the probability distribution of those dissipating waves that are also last in an avalanche has an exponent of 1. Our extensive numerical simulations not only support these predictions, but also show that inversion symmetry is useful for the analysis of the two-wave probability distributions.     

Scaling behavior of the first arrival time of a random-walking magnetic domain

We report a universal scaling behavior of the first arrival time of a traveling magnetic domain wall into a finite space-time observation window of a magneto-optical microscope enabling direct visualization of a Barkhausen avalanche in real time. The first arrival time of the traveling magnetic domain wall exhibits a nontrivial fluctuation and its statistical distribution is described by universal power-law scaling with scaling exponents of 1.34+/-0.07 for CoCr and CoCrPt films, despite their quite different domain evolution patterns. Numerical simulation of the first arrival time with an assumption that the magnetic domain wall traveled as a random walker well matches our experimentally observed scaling behavior, providing an experimental support for the random-walking model of traveling magnetic domain walls.     

Hysteresis and avalanches in the site-diluted Ising model: comparison with experimental results in Cu–Al–Mn alloys

We study the zero temperature properties of hysteresis in a site-diluted Ising model. The model exhibits a critical line separating a disordered from an incipient ferromagnetic ground state: the shape of the hysteresis loop changes from a smooth cycle (formed as a sequence of tiny avalanches) to a sharp cycle exhibiting a macroscopic reversal of the magnetization for a given value of the field (infinite avalanche). Criticality is characterized by power-law distribution of avalanche sizes. Model predictions are contrasted with experimental results obtained in Cu–Al–Mn alloys.     

Strain Avalanches in Microsized Single Crystals:Avalanche Size Predicted by a Continuum Crystal Plasticity Model

Plastic deformation of small crystals occurs by power-law distributed strain avalanches whose universality is still debated.In this work we introduce a continuum crystal plasticity model for the deformation of microsized single crystals,which is able to reproduce the main experimental observations such as Row intermittency and statistics of strain avalanches.We report exact predictions for scaling exponents and scaling functions associated with random distribution of avalanche sizes.In this way,the developed model provides a routine for a quantitative characterization of the statistical aspects of strain avalanches in microsized single crystals.     

Influence of Different Connectivity Topologies in Small World Networks Modeling Earthquakes

We introduce the Olami-Feder-Christensen (OFC) model on a square lattice with some “rewired“ longrange connections having the properties of small world networks. We find that our model displays the power-law behavior, and connectivity topologies are very important to model‘s avalanche dynamical behaviors. Our model has some behaviors different from the OFC model on a small world network with “added“ long-range connections in our previous work [LIN Min, ZHAO Xiao-Wei, and CHEN Tian-Lun, Commun. Theor. Phys. (Beijing, China) 41 (2004) 557.].     

Self organized criticality in a modified Olami-Feder-Christensen model

A modified version of the Olami-Feder-Christensen model has been introduced to consider avalanche size differences. Our model well demonstrates the power-law behavior and finite size scaling of avalanche size distribution in any range of the adding parameter p _{a d d} of the model. The probability density functions of the avalanche size differences at consecutive time steps (defined as returns) appear to be well approached, in the thermodynamic limit, by q-Gaussian shape with appropriate q values which can be obtained a priori from the avalanche size exponent τ. For small system sizes, however, return distributions are found to be consistent with the crossover formulas proposed recently in Tsallis and Tirnakli [J. Phys. Conf. Ser. 201, 012001 (2010)]. Our results strengthen recent findings of Caruso et al. [Phys. Rev. E 75, 055101(R) (2007)] on the real earthquake data which support the hypothesis that knowing the magnitude of previous earthquakes does not make the magnitude of the next earthquake predictable.     

Direct measurement of microstructural avalanches during the martensitic transition of cobalt using coherent x-ray scattering

Heterogeneous microscale dynamics in the martensitic phase transition of cobalt is investigated with real-time x-ray scattering. During the transformation of the high-temperature face-centered cubic phase to the low-temperature hexagonal close-packed phase, the structure factor evolution suggests that an initial rapid local transformation is followed by a slower period during which strain relaxes. Coherent x-ray scattering measurements performed during the latter part of the transformation show that the kinetics is dominated by discontinuous sudden changes-avalanches. The spatial size of observed avalanches varies widely, from 100 nm to 10 μm, the size of the x-ray beam. An empirical avalanche amplitude quantifies this behavior, exhibiting a power-law distribution. The avalanche rate decreases with inverse time since the onset of the transformation.     

A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks

The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.